6.1 Credit Policy
Firms routinely extend credit to their customers. This increases the sales of the firms and enables the customers to buy the goods even when they do not have any cash available. For instance a lumberyard may sell building material to a contractor on 60-day credit. When the contractor finishes his job and gets paid, he will also pay the bill from the lumberyard. The cost to the lumberyard for extending credit consists of two items: the cost of capital made available to the contractor, and second, the possibility of default. In some cases the seller is unable the recover the proceeds of a sale from a customer. The seller is prepared to take this risk.
Suppose the cost of capital to a firm is r. The firm has decided to make a credit sale to customer for an amount S. The cost of goods sold is C. The default risk of the firm is expressed in terms of a discrete probability distribution, Pi that the payment Si will be received after time i. The firm does not impose any penalties for late payments. Then we can write the NPV of this credit policy as
n PiSi
NPV = − C + (1 + r)i(6.1)
i=1
We can also compare the NPV of two different credit policies with the help of this expression.
6.2 Analysis of Credit Decisions
The corporations have to make the decision whether to grant credit to a customer, or to reject his application. This credit decision is usually based on the previous experience with this customer. If it is a new customer, the firm must make appropriate inquiries about the credit history of the new customer. There are well established credit reporting agencies that will rank the customers according to their creditworthiness. Based on their recommendations, the company must make its own credit-granting decision.
One way to analyze credit problems is to compute the NPV of a credit decision. Let us develop such a model. Suppose a company sells goods to a customer with value S, while the cost of goods sold is C. The probability that the customer will default is p, thus the probability that he will pay on time is 1 − p. If the customer pays on time, he will do so after time n. Since the billing cycles are generally in months, we assume that the time is n months. If the customer defaults, the firm may still be able to recover a fraction R of the
(
105
)
original sales after time m months. The risk-adjusted cost of capital to the firm is r, per month. The NPV of this decision is
(
T
re
a
s
u
r
y
M
a
n
a
g
e
m
e
n
t
) (
6.
A
cco
u
n
ts
Rec
ei
v
a
bl
e
M
a
n
a
g
e
m
e
n
t
)
(1−p)S
pRS
NPV(one-time) = − C + (1 + r)n + (1 + r)m = N1
This is a single period decision model. It ignores the possibility that the customer may come back for additional purchases. The NPV of the first encounter of the customer is N1.
To make a somewhat better model, we assume that the customer will buy an amount S every month. The firm will continue to give the customer credit until he actually defaults. The NPV of a two-period .
The document discusses various actuarial statistics concepts in 10 sections:
1. It defines the difference between simple and compound interest, and provides a table comparing key aspects.
2. It presents the formula for calculating the present value of an annuity.
3. It provides an example problem calculating the value of a college fund after making monthly deposits over 10 years.
4. It defines a sinking fund as periodic payments designed to produce a given sum in the future, such as to pay off a loan.
5. It continues with additional concepts including cash flow, simple vs compound interest calculations, and repayment of loans.
6. It discusses the relationship between effective and nominal interest rates.
time value of money
,
concept of time value of money
,
significance of time value of money
,
present value vs future value
,
solve for the present value
,
simple vs compound interest rate
,
nominal vs effective annual interest rates
,
future value of a lump sum
,
solve for the future value
,
present value of a lump sum
,
types of annuity
,
future value of an annuity
The document describes several types of loans:
- Pure discount loans where the borrower receives funds upfront and repays the full amount later.
- Interest-only loans where the borrower makes periodic interest payments and repays the principal at maturity.
- Constant payment loans where the borrower makes equal monthly payments of principal and interest over the loan term to fully repay the loan.
It also discusses alternative mortgage instruments such as graduated payment mortgages, price level adjusted mortgages, adjustable rate mortgages, and reverse annuity mortgages.
This document provides an overview of key concepts related to cash flows and valuation. It discusses the accountant's approach to the statement of cash flows, which explains changes in cash balance rather than measuring firm value. The financial analyst's approach is more concerned with cash flows to equity and the firm. Present and future value concepts are introduced, along with discount rates and how they relate to risk. Annuities, including growing annuities, are defined and the formulas for present and future value are provided. Applications to valuing bonds and saving for college are discussed. The document aims to explain fundamental valuation concepts.
The document discusses the concept of time value of money and how interest rates affect the present and future value of money. It covers simple and compound interest calculations and formulas. The key points are:
- Time value of money results from interest - money is worth more in the present than in the future due to its earning potential.
- Compound interest provides a higher return than simple interest since interest is earned on prior interest amounts as well.
- Present value calculations discount future cash flows back to the present using interest rates, while future value calculations compound an amount forward over time.
- Effective interest rates calculate the actual annual return when interest compounds more frequently than annually.
Quiz #2This Quiz counts for 15 of the course grade. Make s.docxcatheryncouper
Quiz #2
This Quiz counts for 15% of the course grade. Make sure you SHOW ALL WORK and LABEL IT CLEARLY. You MUST provide financial calculator inputs AND the answer. Answer-Only responses, even if correct, WILL NOT receive full credit.
Part 1 (12 points) __________
1. If we know the amount for which a coin was purchased thirty (30) years ago, and the annual rate at which its value has grown, finding the VALUE TODAY is a:
a. Future Value (FV) calculation
b. Present Value (PV) calculation
c. Annuity Calculation (because the growth rate remains constant for each of the fifty years)
d. A Perpetuity (because the present value of any sum fifty years out has VERY LITTLE PV)
2. Monthly principal and interest payments under a loan contract with a fixed interest rate and under which the loan will be paid down to $0 after the last payment; with payments beginning ONE MONTH AFTER the borrower gets the Loan Proceeds are in the form of:
a. A Perpetuity
b. A Consol
c. An Annuity DUE
d. An ORDINARY Annuity
3. The button on the TVM row on a financial calculator which is NOT USED in a simple lump sum FUTURE VALUE problem is:
a. the Present Value (PV) key
b. the Future Value (FV) key
c. the Interest Rate (I/Y) key
d. the Payment (PMT) key
e. the Number of Periods (N) key
4. Which one of the following will increase the PRESENT VALUE of a lump sum future amount? Assume the interest rate is a positive value and all interest is reinvested.
a. increase in the time period
b. increase in the rate of return
c. decrease in the future value
d. decrease in the rate of return
5. Which of the following statements is TRUE?
a. In an annuity due there is one less “interest” period than in an ordinary annuity
b. For the same stream of Cash Flows (CFs), the future value of an annuity due is GREATER THAN the future value of an ordinary annuity.
c. The “default assumption” with annuity CFs is that they take the form of an annuity due.
6. Which one of the following statements is correct?
a. The present value of an annuity increases when the interest rate increases.
b. The present value of an annuity is unaffected by the number of the annuity payments.
c. The future value of an annuity is unaffected by the amount of each annuity payment.
d.The present value of an annuity increases when the interest rate decreases.
7. The future value of a series of Cash Flows over time can be computed by:
a. computing the future value of the average cash flow and multiplying that amount by the number of cash flows.
b. summing the amount of each of the individual cash flows and multiplying the summation by (1 + r)t, where t equals the total number of cash flows.
c.summing the future values of each of the individual cash flows.
d. discounting each of the individual cash flows and summing the results.
8. ( TRUE or FALSE ) In a “pure discount” Loan, the borrower receives the full amount of the Loan Note at ori ...
The document discusses life-cycle costing techniques used in engineering economics and construction project design. Life-cycle costing considers all costs over the full life of a project, not just initial construction costs, to identify the design with the highest net benefits. It allows comparison of alternatives with different costs and benefits over time by using the time value of money. Examples are provided to illustrate compound interest calculations and the use of interest tables to evaluate alternatives based on their present worth.
This document discusses the time value of money and provides examples of calculating present value and future value for single and multiple cash flows. It introduces the concepts of compounding, discounting, and annuities. Key formulas are presented for calculating future value (FV=PV(1+r)^n) and present value (PV=FV/(1+r)^n) of a single sum, as well as the present value of an annuity (S=C[1-(1+r)^-n]/r) and perpetuity (S=C/r). Several examples demonstrate applying the formulas to problems involving single payments, interest rates, and multiple payments over time.
The document discusses various actuarial statistics concepts in 10 sections:
1. It defines the difference between simple and compound interest, and provides a table comparing key aspects.
2. It presents the formula for calculating the present value of an annuity.
3. It provides an example problem calculating the value of a college fund after making monthly deposits over 10 years.
4. It defines a sinking fund as periodic payments designed to produce a given sum in the future, such as to pay off a loan.
5. It continues with additional concepts including cash flow, simple vs compound interest calculations, and repayment of loans.
6. It discusses the relationship between effective and nominal interest rates.
time value of money
,
concept of time value of money
,
significance of time value of money
,
present value vs future value
,
solve for the present value
,
simple vs compound interest rate
,
nominal vs effective annual interest rates
,
future value of a lump sum
,
solve for the future value
,
present value of a lump sum
,
types of annuity
,
future value of an annuity
The document describes several types of loans:
- Pure discount loans where the borrower receives funds upfront and repays the full amount later.
- Interest-only loans where the borrower makes periodic interest payments and repays the principal at maturity.
- Constant payment loans where the borrower makes equal monthly payments of principal and interest over the loan term to fully repay the loan.
It also discusses alternative mortgage instruments such as graduated payment mortgages, price level adjusted mortgages, adjustable rate mortgages, and reverse annuity mortgages.
This document provides an overview of key concepts related to cash flows and valuation. It discusses the accountant's approach to the statement of cash flows, which explains changes in cash balance rather than measuring firm value. The financial analyst's approach is more concerned with cash flows to equity and the firm. Present and future value concepts are introduced, along with discount rates and how they relate to risk. Annuities, including growing annuities, are defined and the formulas for present and future value are provided. Applications to valuing bonds and saving for college are discussed. The document aims to explain fundamental valuation concepts.
The document discusses the concept of time value of money and how interest rates affect the present and future value of money. It covers simple and compound interest calculations and formulas. The key points are:
- Time value of money results from interest - money is worth more in the present than in the future due to its earning potential.
- Compound interest provides a higher return than simple interest since interest is earned on prior interest amounts as well.
- Present value calculations discount future cash flows back to the present using interest rates, while future value calculations compound an amount forward over time.
- Effective interest rates calculate the actual annual return when interest compounds more frequently than annually.
Quiz #2This Quiz counts for 15 of the course grade. Make s.docxcatheryncouper
Quiz #2
This Quiz counts for 15% of the course grade. Make sure you SHOW ALL WORK and LABEL IT CLEARLY. You MUST provide financial calculator inputs AND the answer. Answer-Only responses, even if correct, WILL NOT receive full credit.
Part 1 (12 points) __________
1. If we know the amount for which a coin was purchased thirty (30) years ago, and the annual rate at which its value has grown, finding the VALUE TODAY is a:
a. Future Value (FV) calculation
b. Present Value (PV) calculation
c. Annuity Calculation (because the growth rate remains constant for each of the fifty years)
d. A Perpetuity (because the present value of any sum fifty years out has VERY LITTLE PV)
2. Monthly principal and interest payments under a loan contract with a fixed interest rate and under which the loan will be paid down to $0 after the last payment; with payments beginning ONE MONTH AFTER the borrower gets the Loan Proceeds are in the form of:
a. A Perpetuity
b. A Consol
c. An Annuity DUE
d. An ORDINARY Annuity
3. The button on the TVM row on a financial calculator which is NOT USED in a simple lump sum FUTURE VALUE problem is:
a. the Present Value (PV) key
b. the Future Value (FV) key
c. the Interest Rate (I/Y) key
d. the Payment (PMT) key
e. the Number of Periods (N) key
4. Which one of the following will increase the PRESENT VALUE of a lump sum future amount? Assume the interest rate is a positive value and all interest is reinvested.
a. increase in the time period
b. increase in the rate of return
c. decrease in the future value
d. decrease in the rate of return
5. Which of the following statements is TRUE?
a. In an annuity due there is one less “interest” period than in an ordinary annuity
b. For the same stream of Cash Flows (CFs), the future value of an annuity due is GREATER THAN the future value of an ordinary annuity.
c. The “default assumption” with annuity CFs is that they take the form of an annuity due.
6. Which one of the following statements is correct?
a. The present value of an annuity increases when the interest rate increases.
b. The present value of an annuity is unaffected by the number of the annuity payments.
c. The future value of an annuity is unaffected by the amount of each annuity payment.
d.The present value of an annuity increases when the interest rate decreases.
7. The future value of a series of Cash Flows over time can be computed by:
a. computing the future value of the average cash flow and multiplying that amount by the number of cash flows.
b. summing the amount of each of the individual cash flows and multiplying the summation by (1 + r)t, where t equals the total number of cash flows.
c.summing the future values of each of the individual cash flows.
d. discounting each of the individual cash flows and summing the results.
8. ( TRUE or FALSE ) In a “pure discount” Loan, the borrower receives the full amount of the Loan Note at ori ...
The document discusses life-cycle costing techniques used in engineering economics and construction project design. Life-cycle costing considers all costs over the full life of a project, not just initial construction costs, to identify the design with the highest net benefits. It allows comparison of alternatives with different costs and benefits over time by using the time value of money. Examples are provided to illustrate compound interest calculations and the use of interest tables to evaluate alternatives based on their present worth.
This document discusses the time value of money and provides examples of calculating present value and future value for single and multiple cash flows. It introduces the concepts of compounding, discounting, and annuities. Key formulas are presented for calculating future value (FV=PV(1+r)^n) and present value (PV=FV/(1+r)^n) of a single sum, as well as the present value of an annuity (S=C[1-(1+r)^-n]/r) and perpetuity (S=C/r). Several examples demonstrate applying the formulas to problems involving single payments, interest rates, and multiple payments over time.
This document provides an overview of key concepts related to the time value of money, including calculating the future and present value of annuities. It defines annuities as equal annual cash flows and provides formulas and examples for determining the future value and present value of annuities using interest tables. It also introduces the concepts of sinking fund factor and capital recovery factor for calculating present and future values.
This document provides an overview of key concepts for calculating present and future values, including:
1) How to calculate present and future values of single cash flows using discount factors and compound interest formulas.
2) How to calculate present value for a stream of multiple cash flows by summing the discounted cash flows.
3) Examples are provided to illustrate calculating present value for investments, loans, perpetuities, annuities, and growing cash flows.
4) Shortcuts for calculating perpetuities and annuities are explained.
5) The differences between nominal interest rates, effective interest rates, and how interest is quoted are defined.
6) Useful spreadsheet functions for present value calculations are listed.
The document discusses the time value of money and how to value cash flows that occur at different points in time. It introduces key concepts like compound interest, discounting, perpetuities, annuities, and net present value. It provides formulas for calculating the present and future value of lump sums, perpetuities, annuities, growing perpetuities, and growing annuities. Tools like spreadsheets and calculators can simplify time value of money calculations. The internal rate of return is the interest rate that makes the net present value of a project's cash flows equal to zero.
The document discusses the cash credit system for working capital loans in India and proposes a solution to optimize interest costs. It presents a mathematical model to determine the fixed and variable components of a working capital loan that would minimize a borrower's total annual interest burden, given their projected monthly borrowing needs. The model solution is to set the fixed component at a level where the monthly borrowing exceeds it for n/12 of the year, where n/12 is equal to the interest rate of the fixed component over the total rate.
The document discusses the time value of money, which refers to the concept that money has greater value when received now rather than in the future due to opportunity costs, inflation, and uncertainty. It provides formulas for calculating future value, present value, and interest rates. It also discusses compound interest and how money can double over time depending on the interest rate and compounding periods. Examples are provided to demonstrate calculations for simple vs compound interest and different compounding periods.
The document discusses financial functions in Excel used to analyze investment projects, including NPV, IRR, XNPV, and XIRR. NPV compares the present value of cash inflows to outflows to determine if a project is profitable. IRR is the discount rate that makes NPV equal to zero. XNPV and XIRR are used for uneven cash flows. Other functions discussed are PMT, PV, FV, NPER, and RATE.
This document provides a summary of key concepts related to liabilities from Chapter 9 of an accounting textbook. It defines current and noncurrent liabilities, and discusses specific current liability accounts like accounts payable, accrued liabilities, and notes payable. It also covers liability ratios like the current ratio and accounts payable turnover ratio. Additionally, it discusses long-term liabilities such as notes payable, bonds, and capital versus operating leases. The chapter explores the time value of money concept of present value as it applies to liabilities.
The document discusses net present value calculations for various cash flow scenarios over multiple time periods, including:
- One-period and multi-period future value, present value, and net present value calculations
- Growing perpetuities, annuities, and growing annuities
- Effective annual interest rates and calculations for different compounding periods
- Examples of valuing cash flows using time value of money formulas and financial calculators
This document discusses the concept of time value of money, which means that a unit of money received today is worth more than the same amount received in the future. It explains the techniques of compounding and discounting, which allow converting cash flows received or paid at different points in time to a common point for comparison. Compounding calculates the future value of an amount invested now, growing at a specified interest rate over time. Discounting calculates the present value of a future cash flow. The document provides examples of using compounding and discounting formulas to solve time value of money problems involving single and multiple cash flows over time.
This document summarizes key concepts related to interest rates, including:
- Annual percentage rates (APRs) understate actual interest earned due to compounding, while effective annual rates (EARs) account for compounding.
- Amortizing loans make monthly payments that include both interest and principal, with the interest portion declining over time as the balance falls.
- Nominal interest rates do not account for inflation, while real rates represent purchasing power growth after adjusting for inflation.
- Riskier loans have higher interest rates than risk-free government bonds to compensate investors for default risk.
This document discusses nominal and effective interest rates, including continuous compounding. It defines nominal and effective interest rates, and how to calculate effective rates for different compounding periods. It provides examples of calculating effective rates for annual, semi-annual, quarterly, and continuous compounding. It also discusses how to handle calculations when the payment period is equal to, longer than, or shorter than the compounding period. This includes using the appropriate effective rate and number of periods in calculations.
This document discusses key concepts related to engineering economics, including capital, interest, cash flow diagrams, present worth, future value, nominal interest rates, effective interest rates, and simple vs compound interest. It provides examples and formulas for calculating future value, present worth, nominal interest rates, and effective interest rates. The key points are:
- Interest rates are used to determine the time value of money and allow economic comparisons of cash flows over different time periods.
- Compound interest accounts for interest earned on both the principal amount and previously accumulated interest.
- More frequent compounding results in a higher effective interest rate than the nominal annual rate.
- Present worth and future value formulas allow determining the equivalent value
Using Excel for TVM calculations REV2There are 4 methods to d.docxdickonsondorris
The document provides instructions for using Excel to perform various time value of money (TVM) calculations. It discusses using the financial functions in Excel to calculate present value (PV), future value (FV), internal rate of return (IRR), net present value (NPV), loan payments, effective annual rate, bond valuations, and other TVM problems. Guidelines are provided for inputting the appropriate rate, periods, payment, and future value into the relevant Excel functions.
The document discusses key concepts related to time value of money including:
1) Time value of money measures opportunity cost and the interest rate is the price paid to rent money.
2) Compound interest means interest is earned on prior interest amounts as well as the principal over time.
3) Factors like inflation and risk impact interest rates in the real world compared to theoretical risk-free rates.
This document discusses concepts related to the time value of money, including present and future value calculations. It covers key topics like compounding, discounting, internal rate of return (IRR), and net present value (NPV). Examples are provided to illustrate how to use formulas to calculate future values, present values, loan amortization schedules, and IRR. The goal is to understand how to adjust cash flows for differences in timing and risk.
This chapter discusses how inflation impacts investments and how to calculate real returns after accounting for inflation. It also covers how to solve problems related to annuities, which are a series of equal payments made over a set period of time, and amortized loans, which provide examples of calculating monthly payments over different time periods to reach a purchase goal amount. The document provides step-by-step instructions and formulas for calculating inflation rates, future values adjusted for inflation, real returns, annuity payments, and monthly savings amounts needed over different time periods to reach a purchase goal.
The document summarizes key concepts related to time value of money including:
1) Money today is worth more than money in the future due to factors like interest rates and inflation.
2) Compound interest means interest is earned on both the principal amount and any previous interest earned.
3) Present value calculations determine the current worth of future cash flows while future value calculates the future worth of present cash flows.
4) Annuities represent a stream of regular payments and their present and future values can be calculated using standard formulas.
Time Preference for Money, Required Rate of Return, Time Value Adjustment, Future Value, Future Value of an Annuity, Sinking Fund, Present Value, Present Value of an Annuity, Capital Recovery and Loan Amortisation, Present Value of Perpetuity, Present Value of Growing Annuities, Value of an Annuity Due, Multi-Period Compounding, Continuous Compounding, Net Present Value, Present Value and Rate of Return , Internal Rate of Return , Internal Rate of Return
This chapter discusses net present value (NPV) analysis and time value of money concepts. It introduces formulas for calculating future value, present value, and NPV for single-period and multi-period cash flows. It also covers compounding periods, perpetuities, annuities, and growing cash flows. The key concepts of this chapter are NPV analysis, discounting future cash flows, and accounting for the time value of money.
For this Portfolio Project, you will write a paper about John A.docxevonnehoggarth79783
For this Portfolio Project, you will write a paper about "John Adams" as well as any event in U.S. history that is relevant to your major area of study or of interest to you. You will write about John Adams from the perspective of another historical personality who lived at the same time as the person or event you are going to describe.
For your historical personality, try to select someone from an under-represented population (examples of possible perspectives include that of Anne Hutchinson, Pocahontas, or Sojourner Truth). This analysis is to make you think about how events/people’s actions were interpreted at the time.
Key Points::
Remember that you will be writing from the perspective of a historical person about another person or an event from a period of U.S. history up to Reconstruction. From your historical person’s perspective, provide a thorough summary of the person or event you’ve chosen to write about, including the incidents that took place and any key individuals involved or affected.
Address the general importance of the person or event in the context of U.S. history.
Now, explain specifically how the person or event changed “your” daily life—“you” being the historical persona you have adopted.
Think long-term: How will the person or the event you are describing make a long-term impact in the lives of people who are in the under-represented group to which your historical person/perspective belongs?
Paper Requirements:
Your paper must be four to six pages, not including the required references and title pages.
Use at least five sources, not including the textbook. Include a scholarly journal article. Include at least one
primary
source from those identified in the syllabus.
Definition of a Primary Source
: A primary source is any source, document or artifact that was created at the time of the event. It was usually created by someone who witnessed the event, lived during or even shortly afterwards, or somehow would have first-hand knowledge of that event. A secondary source, by contrast, is written by a historian or someone writing about the event after it happened.
Have an introduction and strong thesis statement. Make use of support and examples supporting your thesis
Finish with a forceful conclusion reiterating your main idea.
Format your paper according to the
CSU-Global Guide to Writing and APA Requirements
(Links to an external site.)
.
.
For this portfolio assignment, you are required to research and anal.docxevonnehoggarth79783
For this portfolio assignment, you are required to research and analyze a TV program that ran between 1955 and 1965.
To successfully complete this essay, you will need to answer the following questions:
What is the background of this show? Explain what years it was on TV, describe the channel it aired on, the main characters, setting, etc..
What social issues and historical events were taking place at the time the show was being broadcast?
Did these issues affect the television show in any way?
Did the television show make an impact on popular culture?
Your thesis for the essay should attempt to answer this question:
Explain the cultural relevance of the show, given the information gathered from the show's background, and cultural history. How can television act as a reflection of the social, political, and cultural current events?
.
More Related Content
Similar to 6.1 Credit PolicyFirms routinely extend credit to their customer.docx
This document provides an overview of key concepts related to the time value of money, including calculating the future and present value of annuities. It defines annuities as equal annual cash flows and provides formulas and examples for determining the future value and present value of annuities using interest tables. It also introduces the concepts of sinking fund factor and capital recovery factor for calculating present and future values.
This document provides an overview of key concepts for calculating present and future values, including:
1) How to calculate present and future values of single cash flows using discount factors and compound interest formulas.
2) How to calculate present value for a stream of multiple cash flows by summing the discounted cash flows.
3) Examples are provided to illustrate calculating present value for investments, loans, perpetuities, annuities, and growing cash flows.
4) Shortcuts for calculating perpetuities and annuities are explained.
5) The differences between nominal interest rates, effective interest rates, and how interest is quoted are defined.
6) Useful spreadsheet functions for present value calculations are listed.
The document discusses the time value of money and how to value cash flows that occur at different points in time. It introduces key concepts like compound interest, discounting, perpetuities, annuities, and net present value. It provides formulas for calculating the present and future value of lump sums, perpetuities, annuities, growing perpetuities, and growing annuities. Tools like spreadsheets and calculators can simplify time value of money calculations. The internal rate of return is the interest rate that makes the net present value of a project's cash flows equal to zero.
The document discusses the cash credit system for working capital loans in India and proposes a solution to optimize interest costs. It presents a mathematical model to determine the fixed and variable components of a working capital loan that would minimize a borrower's total annual interest burden, given their projected monthly borrowing needs. The model solution is to set the fixed component at a level where the monthly borrowing exceeds it for n/12 of the year, where n/12 is equal to the interest rate of the fixed component over the total rate.
The document discusses the time value of money, which refers to the concept that money has greater value when received now rather than in the future due to opportunity costs, inflation, and uncertainty. It provides formulas for calculating future value, present value, and interest rates. It also discusses compound interest and how money can double over time depending on the interest rate and compounding periods. Examples are provided to demonstrate calculations for simple vs compound interest and different compounding periods.
The document discusses financial functions in Excel used to analyze investment projects, including NPV, IRR, XNPV, and XIRR. NPV compares the present value of cash inflows to outflows to determine if a project is profitable. IRR is the discount rate that makes NPV equal to zero. XNPV and XIRR are used for uneven cash flows. Other functions discussed are PMT, PV, FV, NPER, and RATE.
This document provides a summary of key concepts related to liabilities from Chapter 9 of an accounting textbook. It defines current and noncurrent liabilities, and discusses specific current liability accounts like accounts payable, accrued liabilities, and notes payable. It also covers liability ratios like the current ratio and accounts payable turnover ratio. Additionally, it discusses long-term liabilities such as notes payable, bonds, and capital versus operating leases. The chapter explores the time value of money concept of present value as it applies to liabilities.
The document discusses net present value calculations for various cash flow scenarios over multiple time periods, including:
- One-period and multi-period future value, present value, and net present value calculations
- Growing perpetuities, annuities, and growing annuities
- Effective annual interest rates and calculations for different compounding periods
- Examples of valuing cash flows using time value of money formulas and financial calculators
This document discusses the concept of time value of money, which means that a unit of money received today is worth more than the same amount received in the future. It explains the techniques of compounding and discounting, which allow converting cash flows received or paid at different points in time to a common point for comparison. Compounding calculates the future value of an amount invested now, growing at a specified interest rate over time. Discounting calculates the present value of a future cash flow. The document provides examples of using compounding and discounting formulas to solve time value of money problems involving single and multiple cash flows over time.
This document summarizes key concepts related to interest rates, including:
- Annual percentage rates (APRs) understate actual interest earned due to compounding, while effective annual rates (EARs) account for compounding.
- Amortizing loans make monthly payments that include both interest and principal, with the interest portion declining over time as the balance falls.
- Nominal interest rates do not account for inflation, while real rates represent purchasing power growth after adjusting for inflation.
- Riskier loans have higher interest rates than risk-free government bonds to compensate investors for default risk.
This document discusses nominal and effective interest rates, including continuous compounding. It defines nominal and effective interest rates, and how to calculate effective rates for different compounding periods. It provides examples of calculating effective rates for annual, semi-annual, quarterly, and continuous compounding. It also discusses how to handle calculations when the payment period is equal to, longer than, or shorter than the compounding period. This includes using the appropriate effective rate and number of periods in calculations.
This document discusses key concepts related to engineering economics, including capital, interest, cash flow diagrams, present worth, future value, nominal interest rates, effective interest rates, and simple vs compound interest. It provides examples and formulas for calculating future value, present worth, nominal interest rates, and effective interest rates. The key points are:
- Interest rates are used to determine the time value of money and allow economic comparisons of cash flows over different time periods.
- Compound interest accounts for interest earned on both the principal amount and previously accumulated interest.
- More frequent compounding results in a higher effective interest rate than the nominal annual rate.
- Present worth and future value formulas allow determining the equivalent value
Using Excel for TVM calculations REV2There are 4 methods to d.docxdickonsondorris
The document provides instructions for using Excel to perform various time value of money (TVM) calculations. It discusses using the financial functions in Excel to calculate present value (PV), future value (FV), internal rate of return (IRR), net present value (NPV), loan payments, effective annual rate, bond valuations, and other TVM problems. Guidelines are provided for inputting the appropriate rate, periods, payment, and future value into the relevant Excel functions.
The document discusses key concepts related to time value of money including:
1) Time value of money measures opportunity cost and the interest rate is the price paid to rent money.
2) Compound interest means interest is earned on prior interest amounts as well as the principal over time.
3) Factors like inflation and risk impact interest rates in the real world compared to theoretical risk-free rates.
This document discusses concepts related to the time value of money, including present and future value calculations. It covers key topics like compounding, discounting, internal rate of return (IRR), and net present value (NPV). Examples are provided to illustrate how to use formulas to calculate future values, present values, loan amortization schedules, and IRR. The goal is to understand how to adjust cash flows for differences in timing and risk.
This chapter discusses how inflation impacts investments and how to calculate real returns after accounting for inflation. It also covers how to solve problems related to annuities, which are a series of equal payments made over a set period of time, and amortized loans, which provide examples of calculating monthly payments over different time periods to reach a purchase goal amount. The document provides step-by-step instructions and formulas for calculating inflation rates, future values adjusted for inflation, real returns, annuity payments, and monthly savings amounts needed over different time periods to reach a purchase goal.
The document summarizes key concepts related to time value of money including:
1) Money today is worth more than money in the future due to factors like interest rates and inflation.
2) Compound interest means interest is earned on both the principal amount and any previous interest earned.
3) Present value calculations determine the current worth of future cash flows while future value calculates the future worth of present cash flows.
4) Annuities represent a stream of regular payments and their present and future values can be calculated using standard formulas.
Time Preference for Money, Required Rate of Return, Time Value Adjustment, Future Value, Future Value of an Annuity, Sinking Fund, Present Value, Present Value of an Annuity, Capital Recovery and Loan Amortisation, Present Value of Perpetuity, Present Value of Growing Annuities, Value of an Annuity Due, Multi-Period Compounding, Continuous Compounding, Net Present Value, Present Value and Rate of Return , Internal Rate of Return , Internal Rate of Return
This chapter discusses net present value (NPV) analysis and time value of money concepts. It introduces formulas for calculating future value, present value, and NPV for single-period and multi-period cash flows. It also covers compounding periods, perpetuities, annuities, and growing cash flows. The key concepts of this chapter are NPV analysis, discounting future cash flows, and accounting for the time value of money.
Similar to 6.1 Credit PolicyFirms routinely extend credit to their customer.docx (20)
For this Portfolio Project, you will write a paper about John A.docxevonnehoggarth79783
For this Portfolio Project, you will write a paper about "John Adams" as well as any event in U.S. history that is relevant to your major area of study or of interest to you. You will write about John Adams from the perspective of another historical personality who lived at the same time as the person or event you are going to describe.
For your historical personality, try to select someone from an under-represented population (examples of possible perspectives include that of Anne Hutchinson, Pocahontas, or Sojourner Truth). This analysis is to make you think about how events/people’s actions were interpreted at the time.
Key Points::
Remember that you will be writing from the perspective of a historical person about another person or an event from a period of U.S. history up to Reconstruction. From your historical person’s perspective, provide a thorough summary of the person or event you’ve chosen to write about, including the incidents that took place and any key individuals involved or affected.
Address the general importance of the person or event in the context of U.S. history.
Now, explain specifically how the person or event changed “your” daily life—“you” being the historical persona you have adopted.
Think long-term: How will the person or the event you are describing make a long-term impact in the lives of people who are in the under-represented group to which your historical person/perspective belongs?
Paper Requirements:
Your paper must be four to six pages, not including the required references and title pages.
Use at least five sources, not including the textbook. Include a scholarly journal article. Include at least one
primary
source from those identified in the syllabus.
Definition of a Primary Source
: A primary source is any source, document or artifact that was created at the time of the event. It was usually created by someone who witnessed the event, lived during or even shortly afterwards, or somehow would have first-hand knowledge of that event. A secondary source, by contrast, is written by a historian or someone writing about the event after it happened.
Have an introduction and strong thesis statement. Make use of support and examples supporting your thesis
Finish with a forceful conclusion reiterating your main idea.
Format your paper according to the
CSU-Global Guide to Writing and APA Requirements
(Links to an external site.)
.
.
For this portfolio assignment, you are required to research and anal.docxevonnehoggarth79783
For this portfolio assignment, you are required to research and analyze a TV program that ran between 1955 and 1965.
To successfully complete this essay, you will need to answer the following questions:
What is the background of this show? Explain what years it was on TV, describe the channel it aired on, the main characters, setting, etc..
What social issues and historical events were taking place at the time the show was being broadcast?
Did these issues affect the television show in any way?
Did the television show make an impact on popular culture?
Your thesis for the essay should attempt to answer this question:
Explain the cultural relevance of the show, given the information gathered from the show's background, and cultural history. How can television act as a reflection of the social, political, and cultural current events?
.
For this paper, discuss the similarities and differences of the .docxevonnehoggarth79783
For this paper, discuss the similarities and differences of the impacts of the causes of the 2008 Great Recession and the current world crisis with the CoVID-19 virus*
How did the regulations you've studied over the past few chapters and in the Financial Crisis Chapter (Chapter 12) prepare banks and other financial institutions to better weather the effects of the stay-at-home orders and other impacts of the pandemic? Are there other regulations that could be placed on the banking industry that would make sense and help them through these trying times?
*Note: I am not trying to downplay or minimize in any way the "human" impact or any other non-economic impacts of the virus; this paper is just focusing on one component of the costs, among the many different impacts (perhaps much more important impacts)
4 pages 4 resources
.
For this paper, discuss the similarities and differences of the impa.docxevonnehoggarth79783
The document asks the student to discuss the similarities and differences between the impacts of the causes of the 2008 Great Recession and the current CoVID-19 crisis. It prompts the student to consider how banking regulations studied in previous chapters prepared financial institutions for the pandemic's effects and whether additional regulations could help the banking industry weather challenging times. The document notes that the focus is solely on the economic impacts of the virus, not minimizing its human and other non-economic costs.
For this paper choose two mythological narratives that we have exami.docxevonnehoggarth79783
For this paper choose two mythological narratives that we have examined so far in this course, or that you are otherwise personally familiar with. The two myths that you choose should have one or more elements in common, possibly including (but not limited to):
Overarching story (e.g., creation, flood) or story elements (e.g., descent into the underworld, establishment of divine rulership, rapture of mortals by gods, divine disguise)
Narrative structure (e.g., repetitive patterns, discursion)
Themes (e.g., love, jealousy, mortality, revenge, mutability/transformation, limits of human power/knowledge)
Characters (e.g., tricksters)
Cultural functions (e.g., reinforcement of societal norms, explanation of origins of society, explanation of natural phenomena, incorporation in ritual practices, entertainment)
Compare and contrast the two myths you choose, taking into consideration the various elements noted above and any others you deem relevant. (In making comparisons, you do not necessarily need to apply the specifically "comparativist" approach discussed in the course as one historical strand of mythological analysis.)
While you are welcome to reference external sources, this is not a research paper and the use of secondary sources is not required or expected. If you choose to examine a myth not discussed in the course, however, please indicate the source from which you have taken this.
.
For this module, there is only one option. You are to begin to deve.docxevonnehoggarth79783
For this module, there is only one option. You are to begin to develop your diversity consciousness by
identifying a current event in the news pertaining to social inequality in terms social class, gender, or racial ethnicity.
You are to
provide the link to this news article and analyze
the report including in your discussion the following:
What social inequality is being demonstrated in this current even? Describe it
What relationship is going on between the “majority” and “minority group.” Define who is the majority and who is the minority. Describe why you have identified the group as minority and majority.
Who is being marginalized in this event? How? Why do you believe they are being marginalized?
Is any group being “blamed” in this event? Is this “blame” at the individual level or the societal level – or both?
Who has the power in this situation? What is that power?
Who has the privilege in this situation? What is that privilege?
What suggestions do you have that would assist in addressing this social inequality?
What did you learn? (How did this develop your diversity consciousness?)
need to cite using apa and needs to be at least 250 words
.
For this Major Assignment 2, you will finalize your analysis in .docxevonnehoggarth79783
For this Major Assignment 2, you will finalize your analysis in your Part 3, Results section, and finalize your presentation of results from the different data sources. Also, for this week, you will complete the Part 4, Trustworthiness and Summary section to finalize the last part of this Major Assignment 2.
To prepare for this Assignment:
· Review the social change articles found in this week’s Learning Resources.
Part 4: Trustworthiness and Summary
D. Trustworthiness—summarize across the different data sources and respond to the following:
o What themes are in common?
o What sources have different themes?
o Explain the trustworthiness of your findings, in terms of:
§ Credibility
§ Transferability
§ Dependability strategies
§ Confirmability
Summary
· Based on the results of your analyses, how would you answer the question: “What is the meaning of social change for Walden graduate students?”
· Self-Reflection—Has your own understanding of you as a positive social change agent changed? Explain your reasoning.
· Based on your review of the three articles on social change, which one is aligned with your interests regarding social change and why?
By Day 7
Submit
Parts 1, 2, 3, and 4 of your Major Assignment 2.
.
For this Final Visual Analysis Project, you will choose one website .docxevonnehoggarth79783
For this Final Visual Analysis Project, you will choose one website that you visit frequently (it must be a professional business website, not your own personal website). Feel free to use websites such as Nike, Apple, Northwestern Mutual, etc. or a website that applies to your career choices.
Once you choose your website, you will begin to consider the effects the visual elements have on the viewers and
create a thesis statement and outline using the response elements 1-5 below.
For the Thesis & Outline TEMPLATE document click
here
.
APA title page, reference page, and formatting.
Use at least four academic/scholarly sources.
Use properly cited quotes and paraphrases when necessary.
Complete, polished, and error-free cohesive sentences.
Contains an introduction, body, and conclusion.
Sensory Response –
When analyzing the viewer’s sensory response to a particular visual, it is important to consider the visual elements that attract the eyes. Close your eyes when considering a visual. When you open your eyes, what are the first visual elements that you see? When analyzing a viewer’s Sensory Response, you may consider analyzing at least two of the following effects:
Colors
Lines
Shapes
Balance
Contrast
Perceptual Response –
When analyzing a viewer’s perception of visuals, it is important to consider the audience. Consider who is or is not attracted to this type of visual communication. When analyzing a viewer’s Perceptual Response, consider at least two of the following effects:
Target audience specifics (age, profession, gender, financial status, etc.)
Cultural familiarity elements (ethnicity, religious preference, social groups, etc)
Cognitive visuals (viewer’s memories, experiences, values, beliefs, etc.)
Technical Response –
When analyzing a viewer’s response to certain visuals, we need to consider the technical visual aspects that may affect perception. Describe how visuals affect the interpretation of the intended media communication message. Address specific technological elements that impact perception. When analyzing the Technical Response, consider the Laws of Perceptual Organization (similarity, proximity, continuity, common fate, etc), and at least two of the following types of visuals:
Drop-down menus
Hover-over highlighting
Animations
Quality of visuals
Emotional Response
– When analyzing a viewer’s Emotional Response, it is important to consider the targeted audience preferences and emotional intelligence. Discuss what the viewer might want to see and what type of visual presentation will set the tone for that response. When analyzing the Emotional Response, consider the effects of at least two of the following types of visuals:
Mood setting colors
Mood setting lighting
Persuasive images
Positioning of search or purchase buttons
Social media icons and share options
Ethical Response -
When analyzing a viewer’s Ethical Response, it is important to consider the ta.
For this essay, you will select one of the sources you have found th.docxevonnehoggarth79783
For this essay, you will select one of the sources you have found through your preliminary research about your research topic (see Assignment 1.1). Which source you choose is up to you; however, it should be substantial enough that you will be able to talk about it at length, and intricate enough that it will keep you (and your reader) interested. For more info see attached document
.
For this discussion, you will address the following prompts. Keep in.docxevonnehoggarth79783
For this discussion, you will address the following prompts. Keep in mind that the article or video you’ve chosen should not be about critical thinking, but should be about someone making a statement, claim, or argument related to Povetry & Income equality. One source should demonstrate good critical thinking skills and the other source should demonstrate the lack or absence of critical thinking skills. Personal examples should not be used.
1. Explain at least five elements of critical thinking that you found in the reading material.
2.Search the Internet, media, and find an example in which good critical thinking skills are being demonstrated by the author or speaker. Summarize the content and explain why you think it demonstrates good critical thinking skills.
3.Search the Internet, media, or and find an example in which the author or speaker lacks good critical thinking skills. Summarize the content and explain why you think it demonstrates the absence of good, critical thinking skills.
Your initial post should be at least 250 words in length, which should include a thorough response to each question.
Due midnight Thursday April 22,2020
.
For this discussion, research a recent science news event that h.docxevonnehoggarth79783
For this discussion, research a recent science news event that has occurred in the last six months. The event should come from a well-known news source, such as ABC, NBC, CBS, Fox, NPR, PBS, BBC, National Geographic, The New York Times, and so on. Post a link to the news story, and in your initial post:
* Summarize your news story and its contributions to the science or STEM fields
* If your news event is overtly related to globalization, explain how this event contributes to global studies. If your news event does not directly relate to globalization, how could the science behind your event be applied to global studies?
.
For this Discussion, review the case Learning Resources and the .docxevonnehoggarth79783
For this Discussion, review the case Learning Resources and the case study excerpt presented. Reflect on the case study excerpt and consider the therapy approaches you might take to assess, diagnose, and treat the patient’s health needs.
Case: An elderly widow who just lost her spouse.
Subjective: A patient presents to your primary care office today with chief complaint of insomnia. Patient is 75 YO with PMH of DM, HTN, and MDD. Her husband of 41 years passed away 10 months ago. Since then, she states her depression has gotten worse as well as her sleep habits. The patient has no previous history of depression prior to her husband’s death. She is awake, alert, and oriented x3. Patient normally sees PCP once or twice a year. Patient denies any suicidal ideations. Patient arrived at the office today by private vehicle. Patient currently takes the following medications:
•
Metformin 500mg BID
•
Januvia 100mg daily
•
Losartan 100mg daily
•
HCTZ 25mg daily
•
Sertraline 100mg daily
Current weight: 88 kg
Current height: 64 inches
Temp: 98.6 degrees F
BP: 132/86
By Day 3 of Week 7
Post
a response to each of the following:
• List three questions you might ask the patient if she were in your office. Provide a rationale for why you might ask these questions.
• Identify people in the patient’s life you would need to speak to or get feedback from to further assess the patient’s situation. Include specific questions you might ask these people and why.
• Explain what, if any, physical exams, and diagnostic tests would be appropriate for the patient and how the results would be used.
• List a differential diagnosis for the patient. Identify the one that you think is most likely and explain why.
• List two pharmacologic agents and their dosing that would be appropriate for the patient’s antidepressant therapy based on pharmacokinetics and pharmacodynamics. From a mechanism of action perspective, provide a rationale for why you might choose one agent over the other.
• For the drug therapy you select, identify any contraindications to use or alterations in dosing that may need to be considered based on the client’s ethnicity. Discuss why the contraindication/alteration you identify exists. That is, what would be problematic with the use of this drug in individuals of other ethnicities?
• Include any “check points” (i.e., follow-up data at Week 4, 8, 12, etc.), and indicate any therapeutic changes that you might make based on possible outcomes that may happen given your treatment options chosen.
Respond to the these discussions. All questions need to be addressed.
Discussion 2 Me
Treatment of a Patient with Insomnia
The case presented this week, is that of a 75-year-old widow who just lost her spouse 10-months ago. Th patient presents with chief complaints of insomnia. Past medical history of DM, HTN, and MDD is reported. Since the passing of her husband, she states her depression has gotten worse .
For this Discussion, give an example of how an event in one part.docxevonnehoggarth79783
For this Discussion, give an example of how an event in one part of the world can cause a response elsewhere in the world:
Reviewing the aspects of your event, analyze the cause and effect of global influences through direct or indirect means.
What aspects of diversity are evident in your event?
How can understanding diversity benefit a society?
.
For this discussion, consider the role of the LPN and the RN in .docxevonnehoggarth79783
For this discussion, consider the role of the LPN and the RN in the nursing process.
How would the LPN and RN collaborate to develop the nursing plan of care to ensure the patient is achieving their goal?
What are the role expectations for the LPN and RN in the nursing process?
Pls include two references and intext citation.
.
For this discussion, after you have viewed the videos on this topi.docxevonnehoggarth79783
For this discussion, after you have viewed the videos on this topic posted in this week's assignment, please answer the questions posted with this week's discussion.
After posting your individual answers to questions, you are required to respond to 2 students answers with meaningful/thoughtful input on their comments. Your responses must be minimum of a paragraph with at least 3 sentences. Your comments to 2 students
Video #1: History of Homosexuality on Film -- https://youtu.be/SeDhMKd83r4
Video #2: The Gay Culture, According to Television -- https://youtu.be/EbdxRZJfRp4
Video #3: Top 10 Groundbreaking Moments for LGBTQ Characters on TV -- https://youtu.be/yXJAzPJFjQ8
Video #4: I'm Gay, But I'm not ... -- https://criticalmediaproject.org/im-gay-but-im-not/
Video #5: Acting Gay - One Word Cut -- https://youtu.be/a4jfiqiIy0A
LGBTQ+ Questions:
· Name some common stereotypes associated with LGBTQ community?
· What role does media play in establishing & perpetuating these stereotypes?
· Name 2 LGBTQ characters, 1 one from current show/movie; 1 from 10-15 years ago
. Are there differences in the characters?
. Have things changed? Evolved? Improved?
· Are LGBTQ characters portrayed differently than straight characters?
· Why do stories involving LGBTQ characters revolve around their sexuality or sexual orientation?
Acting Gay - One Word: What is your one-word association with the saying "Acting Gay"? Why did you choose this word?
Jarrett Kelley
LGBTQ Discussion
COLLAPSE
Top of Form
1. Some common stereotypes that coincide with the LGBTQ community are promiscuous, non-religious, flamboyant, mentally ill, high sex drives, etc.
2. The media plays a role in establishing these stereotypes because the general public is always watching these shows, reading the news, and listening to stories about different cultures and groups and media that they may not see or interact with in their lives. Therefore, media is an outlet to show these things in a easy way to gain knowledge about people without meeting people face-to-face apart of these groups when sometimes the stereotypes shown can't represent everyone in those groups.
3. Currently, in Marvel's Runaways, that ended in December, there are two lesbian superheros that share a kiss at the end of a season. Karolina, one of the characters, wants to get away from her childhood of religious upbringing and wants to pursue her own life with her superpower of glowing colors. Nico is shown with a Gothic appearance and can be seen as aggressive but down to earth as well. The War at Home was a television show on Fox and a character named Kenny, who is sixteen years old, is kicked out of his house by his parents after finding out he is gay.
a. There are some differences in the characters as Karolina is more flamboyant and colorful, compared to Nico who is goth and likes to remain strictly to business. Kenny is quiet most of the time about his life, especially about his gay crush until his p.
For this discussion choose one of the case studies listed bel.docxevonnehoggarth79783
For this "discussion" choose
one
of the case studies listed below and mention which case study number you picked. After completing your readings, you should be able to identify the psychological disorder associated to each. After choosing one case study, identify the diagnosis, symptoms in your words and treatment plan for that diagnosis. Provide
in-text citations and references in APA format
to indicate where you are getting information from regarding diagnosis and treatment options).
This is the Case Study I chose:
Martin is a 21 year-old business major at a large university. Over the past few weeks his family and friends have noticed increasingly bizarre behaviors. On many occasions they’ve overheard him whispering in an agitated voice, even though there is no one nearby. Lately, he has refused to answer or make calls on his cell phone, claiming that if he does it will activate a deadly chip that was implanted in his brain by evil aliens. His parents have tried to get him to go with them to a psychiatrist for an evaluation, but he refuses. He has accused them on several occasions of conspiring with the aliens to have him killed so they can remove his brain and put it inside one of their own. He has stopped attended classes altogether. He is now so far behind in his coursework that he will fail if something doesn’t change very soon. Although Martin occasionally has a few beers with his friends, he’s never been known to abuse alcohol or use drugs. He does, however, have an estranged aunt who has been in and out of psychiatric hospitals over the years due to erratic and bizarre behavior.
The Psychological disorder is: SCHIZOPHRENIA
I have attached the reading as well.
Please Consider the following:
APA Format
Only sources from the text
250 words or more
Please let me know if you need anything else.
.
For this assignment, you will use what youve learned about symbolic.docxevonnehoggarth79783
For this assignment, you will use what you've learned about symbolic interactionism to develop your own analysis.
Your assignment is to select a television program that you know contains social inequality or social class themes. In 3-5 pages make sure to provide the following:
Provide a brief introduction that includes the program's title, describes the type of program, and explains which social theme you are addressing
Describe and explain scenes that apply to the social theme.
Identify all observed body language, facial expressions, gestures, posture stances, modes of dress, nonverbal cues, symbols, and any other observed nonverbal forms of communication in the scenes.
Explain your interpretation of the meanings of the identified nonverbal communications and symbolism.
Summarize how these interpretations are important to the sociological understanding of your chosen social inequality or social class theme.
Suggest how your interpretation of the respective meanings might be generalized to society as a whole.
.
For this Assignment, you will research various perspectives of a mul.docxevonnehoggarth79783
For this Assignment, you will research various perspectives of a multicultural education issue and develop an advocacy plan to effectively communicate and advocate for a culturally responsive solution. During the development of your advocacy plan, synthesize and reflect on the major learning points that are applicable to leading culturally responsive social change in your context.
To prepare for this Assignment, review the issues you identified in the Equity Audit assignment.
Review Chapters 1–5 (pp. 1–64) of “An Introduction to Advocacy: Training Guide.”
Develop and submit your advocacy plan. To complete this Assignment, use the document below:
.
For this assignment, you will be studying a story from the Gospe.docxevonnehoggarth79783
Jesus visited Mary and Martha in Luke 10:38-42. The passage describes Mary sitting at Jesus' feet listening to his teaching while Martha was distracted by her household duties. Jesus affirmed Mary's choice to listen to him over working, showing the importance of prioritizing time with God over other tasks.
For this assignment, you will discuss how you see the Design Princip.docxevonnehoggarth79783
For this assignment, you will discuss how you see the Design Principles used in a 2D print. You can select a 2D print from your home, workplace, or use the CSU Art Appreciation LibGuide to find a print in an online museum. Take a photograph of the print or save an image of the print, and include it in the worksheet.In Unit II, our assignment was to describe an artwork using the Visual Elements. We can think of the Design Principles as a way that the artist organized the Visual Elements. Instead of focusing on the small parts of the artwork (like line, shape, and mass) the Design Principles look at the whole artwork and how all the elements work together. Provide a detailed description of the design principles in your 2D print, using full and complete sentences. For Design Principles, make sure you describe how the artist used the ones in Chapter 5: unity and variety, balance, emphasis, repetition and rhythm, and scale and proportion. Questions to consider are included below:
Unity: what elements work together to make a harmonious whole?
Variety: What creates diversity?
Balance: Is it symmetrical or asymmetrical?
Emphasis: What is the focal point?
Repetition and rhythm: Is an element repeated?
Scale and proportion: Are the objects in proportion to each other?
Be sure to describe exactly where in the artwork you see each Principle. You'll want to describe each artwork using the terms we learned in this unit's reading. Remember to write in complete sentences and use proper grammar.
.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
6.1 Credit PolicyFirms routinely extend credit to their customer.docx
1. 6.1 Credit Policy
Firms routinely extend credit to their customers. This increases
the sales of the firms and enables the customers to buy the
goods even when they do not have any cash available. For
instance a lumberyard may sell building material to a contractor
on 60-day credit. When the contractor finishes his job and gets
paid, he will also pay the bill from the lumberyard. The cost to
the lumberyard for extending credit consists of two items: the
cost of capital made available to the contractor, and second, the
possibility of default. In some cases the seller is unable the
recover the proceeds of a sale from a customer. The seller is
prepared to take this risk.
Suppose the cost of capital to a firm is r. The firm has decided
to make a credit sale to customer for an amount S. The cost of
goods sold is C. The default risk of the firm is expressed in
terms of a discrete probability distribution, Pi that the payment
Si will be received after time i. The firm does not impose any
penalties for late payments. Then we can write the NPV of this
credit policy as
n PiSi
i=1
We can also compare the NPV of two different credit policies
with the help of this expression.
6.2 Analysis of Credit Decisions
The corporations have to make the decision whether to grant
credit to a customer, or to reject his application. This credit
decision is usually based on the previous experience with this
customer. If it is a new customer, the firm must make
appropriate inquiries about the credit history of the new
2. customer. There are well established credit reporting agencies
that will rank the customers according to their creditworthiness.
Based on their recommendations, the company must make its
own credit-granting decision.
One way to analyze credit problems is to compute the NPV of a
credit decision. Let us develop such a model. Suppose a
company sells goods to a customer with value S, while the cost
of goods sold is C. The probability that the customer will
default is p, thus the probability that he will pay on time is 1 −
p. If the customer pays on time, he will do so after time n. Since
the billing cycles are generally in months, we assume that the
time is n months. If the customer defaults, the firm may still be
able to recover a fraction R of the
(
105
)
original sales after time m months. The risk-adjusted cost of
capital to the firm is r, per month. The NPV of this decision is
(
T
re
a
s
u
r
y
M
a
n
a
g
4. NPV(one-time) = − C + (1 + r)n + (1 + r)m = N1
This is a single period decision model. It ignores the possibility
that the customer may come back for additional purchases. The
NPV of the first encounter of the customer is N1.
To make a somewhat better model, we assume that the customer
will buy an amount S every month. The firm will continue to
give the customer credit until he actually defaults. The NPV of
a two-period model will be
NPV(two-time) =
(1 − p)S
+
(
(
1 −
p
)
S
−
C
+
(
1 +
5. r
)
n
+
pRS
m
(
1 +
r
)
) (
(1 + r)n+1
In the above expression, the tan part of the equation represents
the NPV of the first encounter, N1. The blue part of the
equation represents the probability that the customer paid his
bill for the first month. The lavender part of the eqution is the
value of the NPV of the second month. It assumes that the
customer will buy the amount of merchandise in the second
month. The soncd month’s NPV is similar to that for the first
month, except that the terms are multiplied by 1/(1 + r) because
of delay in the event by another month.
We can simplify the above equation as
6. 1−p
NPV(two-
The probabilities in the second and subsequent periods are
conditional probabilities. The probability that the customer pays
in the second month is contingent upon his prompt payment in
the first month, and thus the probability is (1 − p)2. This is the
probability that he will pay in the first month and the second
month.
We now extend the calculation to three periods as
1−p
NPV(three-
The third term, [(1 − p)/(1 + r)]2 in the above equation
represents that fact the third month’s shopping by the customer
is contingent upon the payment for the first two periods; and the
fact that the third month is delayed by two months.
Next, we can extend this analysis to an infinite-period model as
7. follows.
1−p
NPV(infinite-
+ … ∞ ]
For the summation of infinite series, use the equation
which gives
S = a + ax + ax2 + … ∞ =a
1 − x
NPV(infinite-times) =N1
1 − (1 − p)/(1 + r)
After some simplification, it becomes
8. NPV(infinite-
We can do the above summation with the help of Maple. We
type in
sum((1-p)^i/(1+r)^i,i=0..infinity);
–
1 + r p + r
i=0
Simplifying the expression further, we get
(1−p)S
pRS
(6.2)
If we assume that the customer is never going to default, then p
9. = 0. In that case, the above expression simplifies to
(6.3)
This represents the value of a well-established, long-term
customer with perfect credit record.
We use the following symbols in (6.2):
C = cost of goods sold each month
S = sales per month
r = cost of capital to the firm, per month
p = probability that the customer will default in a given month
n = normally the time taken by the customer to pay his bill, in
months
m = time taken by the firm to recover the money in case of
default, in months
R = the fraction of the total sale recovered in case of default
6.3 Valuation of a Credit Card Portfolio
Credit cards have become a permanent fixture on the national
scene. Some of the largest banks, such as Citibank, have
millions of cards in the hands of cardholders. The total credit
card debt for the entire American population is hundreds of
billions of dollars.
There is fierce competition among the card issuers. After
saturating the adult population, the banks are offering credit
cards to students and young adults. To gain customers, many of
10. the card issuers have dropped the annual fees, and they are
offering promotional rates as low as 0% for the first six months.
There is also consolidation in this industry. Many of the smaller
regional banks are out of this business. Most of them have
simply sold their credit card portfolios to national banks. The
Federal Reserve reported that the credit card delinquencies hit
4.86 percent in the first quarter in 2008, while revolving debt—
or the type used in credit purchases—hit
$957.2 billion in March, a 7.9 percent increase. [CNBC, 6/3/08]
We may estimate the value of a credit card portfolio as follows.
Suppose a bank has issued N cards altogether. The bank charges
an annual fee of F per card at the end of each year. Let us
assume that the cost of capital to the bank is r. The bank is able
to collect total fees NF per year from the cardholders. The value
of this perpetuity is
Annual feesV1 =
NF
r(6.4)
Let us assume that n of these cardholders pay off their entire
balance every month near the end of the grace period, and they
do not pay any interest at all. Such customers use the bank’s
capital for their personal use and are thus creating a loss for the
bank. Suppose the average balance on these accounts at the end
of each month is B, and the grace period is g days. The amount
of this monthly loss per card is thus
B−g/365
− B + (1 + r)g/365 = B[(1 + r)
11. − 1]
This monthly loss continues forever, and thus it becomes a
perpetual thing. The value of this perpetuity is calculated by
dividing the above quantity by the monthly cost of capital to the
bank, namely, r/12. Thus, we have the value of perpetuity
B[(1 + r)−g/365 − 1]
r/12=
12B[(1 + r)−g/365 − 1]
r
The total value of n such cards is thus
12nB[(1 + r)−g/365 − 1]
Free ridersV2 =
r(6.5)
The bank does not make a permanent investment in such
customers.
Next, let us consider those cardholders who carry an average
balance C on their cards at the end of each month, and pay
interest on them regularly. The annual rate of interest charged
by the bank on the outstanding balance on an account is R. The
number of such cards is, say m. The annual interest generated
by these accounts is mCR. This is another
12. perpetuity whose present value is given by mCR/r. The
bank has already made an investment mC to finance these
accounts. The NPV these cards is thus
Paying customersV3 = − mC +
mCR
r=
mC(R −r)
r(6.6)
These accounts create value for the bank because the bank
charges a much higher rate of interest R (perhaps 15%) than the
cost of capital for the bank r (around 6%).
We now look at the total annual expenses in maintaining this
credit card operation. This includes printing and mailing of the
bills, administrative expenses, and the losses due to default on
the loans by the cardholders. Assuming these costs average out
to be L at the end of each year, their present value this
perpetuity is
L
Administrative expenses V4 = − r
(6.7)
There is another important source of revenue for the bank.
Whenever a merchant sells something to a customer, who uses a
credit card for the purchase, the merchant must also pay a
percentage of the sale price to the bank. In practice, the bank
collects roughly 1% of the total credit card sales. Suppose the
total monthly sales on all credit cards are NS. The merchants
pay a fraction a of this amount to the bank at the end of every
month. The monthly income to the bank is thus aNS. This
13. equals 12aNS per year. The value of this perpetuity to the bank
is
Merchant feesV5 =
12aNS
r(6.8)
In the above expression S is the average monthly sale per card.
The total NPV of the credit-card portfolio is the sum of the five
components of the value given by equations (6.3-8). Thus
NF12nB[(1 + r)−g/365 − 1]
mC(R −r)
L12aNS
Or,
NPV = r +
r+r− r +r
NPV =
NF + 12nB[(1 + r)−g/365 − 1] + mC(R − r) − L + 12aNS
r(6.9)
If the bank wants to sell this portfolio to another bank, they
must ask for its NPV, plus the amount payable to the bank by
14. the cardholders at a given instant in time. Let us call the total
outstanding balance on all credit cards to be P. The selling price
of the portfolio is thus
Selling price = P +
NF + 12nB[(1 + r)−g/365 − 1] + mC(R − r) − L + 12aNS
r(6.10)
In the above expression we define the symbols as follows:
P = receivables, or the total amount due from the customers at a
given instant
N = n + m = total number of cards issued
n = number of card-holders who pay on time, and do not pay
any interest
B = average monthly balance on such free-rider cards
m = number of card-holders who pay interest every month
C = average monthly balance on these paying-customer cards
F = annual membership fee charged by the bank, at the end of
each year
R = annual rate of interest on the outstanding balance
r = annual cost of capital to the bank
L = annual administrative expenses for credit card portfolio,
including defaults
a = percentage paid by the merchant to the bank on each credit
sale
g = grace period in days
In May 2012, Capital One Financial Corporation purchased the
GM Card credit-card accounts from HSBC Bank Nevada, N.A.
Capital One paid a premium of $2.5 billion on the credit card
loans. According to TREFIS analysis, the stock of Capital One
is worth
15. $58 a share, on May 20, 2013, although in the market it is
trading at about $61 a share. Most of the value of the stock,
61.4%, lies in its credit card operations.
Source: TREFIS, May 20, 2013
6.4 Altman's Zeta Model
Edward Altman (1941-)
A loan officer at a lending institution is evaluating the
creditworthiness of a marginal borrower. A firm is considering
selling goods on credit to another firm that has shaky financial
condition. A security analyst is looking at risky bonds of a firm.
They must all look at the probability of default. In particular,
they are concerned about the possibility of bankruptcy by the
borrower. Edward Altman developed a well-known model for
predicting bankruptcy of firms. The model uses the information
about the financial ratios of the firm and discriminant analysis
to find the probability of bankruptcy.
In the original (1968) model, Altman studies publicly traded
manufacturing companies. He examined companies that went
bankrupt and compared them with those that remained solvent.
He focused on five ratios, shown in the following table, which
seemed to be the most significant factors in predicting
bankruptcy.
(
17. capital Total assets
Accumulated retained earnings Total assets
EBIT Total Assets
Market value of equity Book value of debt
Sales Total assets
Source: Edward I. Altman, Corporate Financial Distress and
Bankruptcy, John Wiley & Sons, (1993), p. 109.
Altman defined the Z-score of a firm as follows:
EBIT
Net working capital
Sales
Z = 3.3 Total Assets + 1.2
Total assets+ 1.0 Total assets
+ 0.6
Market value of equity Book value of debt+ 1.4
Accumulated retained earnings
Total assets(6.11)
where Z is an index of bankruptcy. The value of Z is interpreted
as follows:
sure
IfZ > 2.99, no threat of bankruptcy.
18. This is a statistical model with a fairly good track record. It is
employed by practitioners who have to decide on the possibility
of a firm going bankrupt.
A revised model (1984) looks at non-manufacturing, privately
owned companies. The Z- score in this case is defined as
Net working capital
Accumulated retained earnings
EBIT
Z = 6.56
Total assets+ 3.26
Total assets+ 1.05 Total assets
where Z < 1.23 indicates a bankruptcy prediction,
no bankruptcy.
+ 6.72
Book value of equity
Total liabilities(6.12)
Altman’s model is used by banks and other lenders in evaluating
the creditworthiness of borrowers.
Examples
19. 6.1. Pittston Company has annual sales of $2 million, while the
cost of goods sold is $1.2 million. All sales are cash sales. The
marketing manager at Pittston has come up with the plan of
giving credit to the customers. He believes that this will
increase the sales by 20% without increasing any of the fixed
costs. He thinks that 30% of the customers will pay within 30
days, 30% within 60 days, 38% within 90 days, and 2% of the
customers will default on the payments. The cost of capital to
Pittston is 15%. Should the company introduce the credit sales
system?
To simplify the problem, we consider the cash flows for a single
year. We are just comparing one policy against the other, and if
one policy is better for one year, it will be better for all
subsequent years. First, we find the NPV of the current (cash
only) policy. It comes out to be
NPV(cash) = − 1.2 + 2 = $0.8 million
By extending credit, the sales, and the corresponding cost of
goods sold, will increase by 20%. We can take care of it by
multiplying the entire calculation by a factor of 1.2. Next, the
$2 million in sales comes in three batches, 30%, 30%, and 38%.
This also accounts for the 2% loss by the defaulters. The cash
comes in after 30, 60, and 90 days. We have to discount the
cash by the proper discount factor. This is done as follows:
.3
5 million
20. By comparing the two results, we conclude that Pittston
Company should implement the credit policy. The 20% increase
in the sales, and the extra profits generated by it are sufficient
to offset the delay, and default, in payments. ♥
6.2. Taylor Company has the following credit policy at present:
2/10, net 30 days. At this time, Taylor receives 30% of the sales
within 10 days, and the rest within 30 days. The manager of the
firm believes that if the terms of sales were relaxed, the sales
would increase by 10%. He proposes that Taylor should
eliminate the discount, and allow all customers to pay within 60
days. The cost of capital for the company is 12% and the cost of
goods sold is 65% of the total sales. Should Taylor adopt the
new policy?
The term "2/10, net 30 days" means that those customers who
pay within 10 days of the sale are entitled to a 2% discount,
otherwise they must pay the full amount within 30 days. Many
businesses offer a discount for prompt payment for the sales. It
is a win-win situation: the customers get the merchandise at a
2% discount, and the company improves its cash flow. The
customers, who wait 30 days before they can make a payment,
must pay the full amount.
Let us assume that there are no defaults under either policy.
Suppose the total annual sales are $1 million. Let us find the
NPV of both the policies. For the current policy, we get
.3*.98
.7
NPV(old) = − .65 + 1.1210/365 + 1.1230/365 = $0.3366 million
In the above calculation, .65 stands for $.65 million in cost of
21. goods sold, .3 is 30% of the customers who pay within 10 days,
and they pay only 98% of the bill after taking the 2% discount.
The remaining 70% pay within 30 days.
For the new policy, there is a 10% increase in sales, but the
customers also delay the payments to 60 days. This gives us
Because the NPV of the second policy is higher, Taylor should
accept the new policy. The higher NPV is due to higher sales
and the elimination of the discount. But it is also reduced by the
delay in collecting money for the sales. ♥
6.3. Moosic Auto Parts is considering the credit application of
an established customer, Duryea Garage. The customer buys
$12,000 worth of merchandise annually and pays in cash.
Moosic believes that the customer will buy $12,500 worth of
merchandise if he is given credit under the terms 2/10, net 60
days. The company is not sure for what percentage of the sales
will the customer elect to pay within 10 days. The cost of
capital for Moosic is 14%, and the variable cost factor is 70%.
Should Moosic extend credit to this customer?
To simplify the calculations, we assume that the customer
makes the purchases just once a year. Thus for the current
policy
NPV(cash) = − .7(12,000) + 12,000 = $3600
For the new policy, the customer buys $12,500 in merchandise.
Suppose the customer takes advantage of the discount for a
fraction p of the sales. Then
22. NPV(credit) = − .7(12,500) +
(.98)p(12,500) 1.1410/365+
(1 −p)(12,500) 1.1460/365
= 3483.64266 − 27.53907p
If p = 0, that is, the customer does not take advantage of the
discount and delays the payment for 60 days, then
12‚500
NPV(credit) = − .7(12,500) + 1.1460/365 = $3483.64
Moosic will lose in this arrangement, and the customer will
come out ahead. If p = 1, the customer pays promptly and takes
the discount for all sales, then
NPV(credit) = − .7(12,500) +
.98*12‚500
1.1410/365 = $3456.10.
This is still not profitable for the company. In fact, the
customer will always try to pay within 10 days. The company
should not implement the new policy.
The company loses primarily because of the 2% discount, and
the 10-day delay in collecting for the sales. The increase in
sales, $500 per year, is not enough to make this policy
worthwhile. ♥
23. Suppose the marketing manager comes with a higher sales
estimate for the customer. He believes that this customer will
now buy S dollars worth of auto parts annually because of the
2% discount for prompt payments. What is the minimum sales
for the customer that will make the new discount policy
profitable for Moosic?
The NPV with new sales figure S will be
(.98)S NPV(credit) = − .7S + 1.1410/365 = .276488 S
Equating it with the previous cash NPV, we get
.276488 S = 3600
Solving for S, we get S = 13,020
Therefore, the customer must buy at least $13,020 worth of
parts to make this new policy to be profitable for Moosic. ♥
6.4. Avoca Company has the following credit policy 2/10, net
30. Avoca also charges 1% per month interest on all accounts
after 30 days. The sales collection schedule of the company is
according to the following table:
Collection within
10 days
30 days
60 days
90 days
Percentage20%30%40%10%
To improve the collection rate, Avoca is thinking of imposing a
24. higher interest rate, 1.5% on all accounts paid after 30 days. It
will continue the 2/10, net-30 policy. Avoca believes that the
new policy will change the collection schedule as follows:
Collection within
10 days
30 days
60 days
90 days
Percentage20%50%20%10%
There will be no change in the total sales as a result of this new
policy. The cost of capital for Avoca is 15%. Should it try the
new policy?
In this problem, we consider only the net present value of the
change in the policy. We ignore such variables as the cost of
goods sold, and the value of the collection after ten days,
because they are the same in both cases.
Suppose the total sales are $1 million. For the current policy,
the present value of sales, in
$million, is
.2*.98
.3
.4(1.01)
.1(1.01)2
25. PV(current) = 1.1510/365 + 1.1530/365 + 1.1560/365 +
1.1590/365 = $.985203 million
For the proposed policy, the PV of sales is
.2*.98
.5
.2(1.015)
.1(1.015)2
PV(new) = 1.1510/365 + 1.1530/365 + 1.1560/365 +
1.1590/365 = $.987462 million
The second policy is only slightly better. The difference
is .987462 − .985203 =
$0.002259 million = $2259. Avoca should implement the new
policy. ♥
6.5. Wilkes Corporation is reviewing the credit application of a
customer. The company expects to sell $3000 worth of
merchandise every month and expects to receive the payment
for it within the 30-day grace period. The cost of goods sold is
$2000. There is a 15% probability that the customer may not be
able to pay his bill in a certain month. In that case, the company
will be able to collect 10% of the balance 4 months after the
sale. The risk-adjusted discount rate is 12%. Should Wilkes give
credit to this customer?
To calculate the NPV of this decision, we use the equation
27. The customer will add $3585 to the value of the firm. Because
the NPV is positive, Wilkes should give credit to the customer.
♥
When the customer becomes well established and has a perfect
credit record, then we may assume that p = 0. In that case we
may use (6.3)
(6.3)
This dramatically increases the value of the customer to the
firm. Thus, the firms keep a wary eye on potentially delinquent
customers. ♥
6.6. Throop Corporation is reviewing the credit application of a
customer. The customer is expected to buy $4000 worth of
merchandise every month and is expected to pay for it within
the 30-day grace period. The cost of goods sold is $2500. There
is a 10% probability that he may not be able to pay his bill in a
certain month. In that case the company will be able to collect
10% of the balance 6 months after the sale. The risk- adjusted
discount rate is 12%. Should Throop give credit to this
customer?
28. To calculate the NPV of this decision, we use the equation
pRS
(6.2)
Putting the numbers, C = 2500, p = .1, S = 4000, r = .01, n = 1,
R = .1, m = 6,
1.011 +
1.016
29. The NPV is positive, thus Throop should give credit to the
customer. ♥
6.7. Dupont National Bank issues credit cards with the
following terms. There is no interest charge if the entire bill is
paid within 25 days. Interest at the rate of 15% per annum is
added to the outstanding balance if the bill is paid after 25 days.
The new balance also includes any purchases made during the
month. This procedure continues until the entire bill is paid.
The cost of capital to the bank is 7%. The balance on a credit
card, on the average, is $1000 at the end of a month. Eighty
percent of the cardholders pay off their entire balance within 25
days, while the remaining carry the average balance.
Under proposed terms, Dupont wants to reduce the interest rate
to 10% on the unpaid balance. It expects that 50% of the
cardholders will now carry the balance, while the other 50%
will still pay in full within 25 days. Dupont expects the balance
of each bill will rise to $1100. Should Dupont introduce the new
terms?
Let us find the value of an average card for the bank. If a
cardholder is carrying a constant balance of $1000 every month,
and the interest rate is 15% per annum, then he is paying $150
per year in interest charges. From the point of view of the bank,
it is carrying a perpetual bond whose annual interest payment is
$150. The cost of capital to the bank is 7%. Recalling the value
of a perpetual bond as
B = C/r(6.3)
where B is the value of the bond, C is the annual interest
payment, and r is the discount rate, or the cost of capital. This
comes out to be 150/.07 = $2142.86. The bank has invested
30. $1000 in this card, namely the balance carried by the
cardholder.
For the bank, the NPV of this credit card balance is
therefore −1000 + 150/.07 =
$1142.86. At the moment, we shall ignore the credit risk of the
cardholder that the bank must also take into consideration.
Twenty percent of the cardholders are in this category.
Next, we analyze the burden on the bank due to a customer who
pays on time. This person is using $1000 of bank's money free
for 25 days, every month. The NPV for one month is thus
1000
− 1000 + 1.0725/365
To find its value as a perpetuity, we divide this by the monthly
discount rate, namely
.07/12. This comes out to be
Eighty percent of the customers are paying within the grace
period. Combining these two numbers, we can find the NPV of
the average card under the old terms as follows:
150/.07) = −$405.50
31. With the new policy, the interest rate is 10% charged on the
unpaid balances. The average balance rises to $1100. Thus, the
annual interest collected on each $1100 balance will be $110.
The value of a perpetual bond with $110 annual interest is
110/.07 =
$1571.43. The bank has invested $1100 in this bond. Thus the
NPV of this bond is –1100
+ 1571.43 = $471.43. We also include the factor .5 as 50%,
representing the percentage of customers who are paying their
bills every month, and the others who are not paying. The NPV
of an average card under the new terms is thus
+ 110/.07) = −$200.21
Suppose we want to use (6.9),
NF + 12nB[(1 + r)−g/365 − 1] + mC(R − r) − L + 12aNS
NPV =
r(6.9)
In (6.9), we let N = 1, n = .8, m = .2, F = 0, C = 1000, R = .15, r
= .07, L = 0, a = 0, B =
1000, g = 25, then
NPV(old) =
32. 12*.8*1000*[1.07−25/365 – 1] + .2*1000*(.15 − .07)
.07= –$405.50
For the new policy, we put N = 1, n = .5, m = .5, F = 0, C =
1100, R = .1, r = .07, L = 0,
a = 0, B = 1100, g = 25, then
12*.5*1100*[1.07−25/365 − 1] + .5*1100*(.1 − .07)
NPV(old) =
.07= −$200.21
This analysis reveals that the credit card operations for the bank
are unprofitable. Each card represents a negative value of about
$405 under the old policy, and negative $200 with the new
policy. This means that the bank has improved the operations,
but they are not profitable yet. ♥
6.8. Scranton National Bank has a portfolio of 20,000 credit
card accounts. The bank charges $25 annual fee on these cards.
There is a 25-day grace period on the accounts, and after that
the cardholders pay interest at the rate of 1.25% per month on
the unpaid balance. Half of the cardholders pay their balance in
full every month, and their average monthly bill is $1000. The
remaining cardholders carry an average balance of $1500
continuously. The operating expenses for the credit card
portfolio, including defaults, are
$150,000 annually. The merchants who accept his card do not
pay any fee to the bank. The cost of capital to the bank is 8%.
Citibank plans to buy Scranton's credit card portfolio. How
much should Citibank pay, excluding the receivables?
33. We use the following equation to find the selling price of the
portfolio,
NF + 12nB[(1 + r)−g/365 − 1] + mC(R − r) − L + 12aNS
Selling price = P +
r(6.10)
In the above expression, a = 0, P = 0, N = 20,000, F = $25, m =
10,000, n = 10,000, C =
$1500, B = $1000, R = .15, r = .08, g = 25 days, L = $150,000.
Putting these numbers, we find the selling price as follows.
NPV =
20‚000(25) + 12(10‚000)(1000)[1.08−25/365 − 1] +
10‚000(1000)(.15 − .08) − 150‚000
.08
= $5,238,847
Suppose the total outstanding balance for all credit cards is $20
million on the day the final deal is signed, then Citibank should
pay Scranton National Bank at least $25.239 million for the
credit card portfolio. ♥
6.9. Peckville National Bank has a portfolio of 30,000 credit
card accounts. The bank charges $25 annual fee on these cards.
There is a 25-day grace period on the accounts, and after that
the cardholders pay interest at the rate of 1% per month on the
unpaid balance. Half of the cardholders pay their balance in full
every month, and their monthly bill is $600, on the average. The
remaining cardholders carry an average balance of
$1200 continuously. The average monthly sale for all cards is
34. $800. The operating expenses for the credit card portfolio,
including defaults, are $120,000 annually. The cost of capital to
the bank is 7%. The outstanding balance of all credit cards is
$27 million.
The merchants pay 1% of the sales to the Bank. Citibank plans
to buy Peckville's credit card portfolio. How much should
Citibank pay, including the receivables?
We may start by using the expression
NF + 12nB[(1 + r)−g/365 − 1] + mC(R − r) − L + 12aNS
Selling price = P +
r(6.10)
In this formula, we have P = $27 million, N = 30,000, F = $25,
m = 15,000, n = 15,000, a = .01, R = .12, r = .07, g = 25 days, B
= $600, S = $800, L = $120,000. Substituting these values, we
get
Selling price = 27,000,000 +
30‚000(25) + 12(15‚000)(600)[1.07–25/365 − 1] +
.07
= 82,866,703
Thus selling price = $82.867 million. ♥
6.10. Archbald Bank is analyzing its credit card portfolio. It
classifies its cardholders into two types: 5000 "free riders", and
10,000 "paying customers." The free riders charge
$300 worth of merchandise every month, on the average, and
35. pay off the full balance after 25 days. The paying customers
charge $100 a month, on the average, but they continuously
carry a balance of $400 of debt. The cost of capital to the bank
is 9%, and it charges 15% interest on the unpaid balance. The
participating merchants pay 1% of the sales, charged on a credit
card, to the bank at the end of each month. Find the value of
this credit-card operation to the bank.
First, we look at the merchant fees. The total monthly sales =
5000*300 + 10,000*100 =
$2,500,000. This produces a revenue of $25,000 at the end of
each month for the bank. To find the value of this income
stream, we discount it at the monthly discount rate of 9/12 =
.75%. This comes out to be
∞ 25000
25000
i=1
Second, we consider the cost of having the free riders. When a
person charges $300 and pays for it after 25 days, the PV of this
transaction to the bank is
300
PV = − 300 + 1.0925/365 = − 1.7655586
If this person keeps on doing this, month after month, the PV of
this to the bank becomes
∞ 1.7655586
36. 1.7655586
i=1
1.0075i= −
.0075= − 235.4078133
The PV to the bank, for all 5,000 such cardholders, is
PV = − 235.4078133*5,000 = − $1,177,039(2)
Third, we evaluate those people who carry a balance of $400
every month. They pay interest at the rate of 400*.15/12 = $5
per month. There are 10,000 such cardholders and their total
contribution to the bank is $50,000 a month. The value of this
income stream to the bank is
∞ 50‚000
i=1
50‚000
.0075 = $6,666,667(3)
The net present value of the credit card operation to the bank is
thus the sum of the three parts of the operation outlined above.
NPV = 3,333,333 − 1,177,039 + 6,666,667 = $8,822,961
This comes out to be around $8.823 million. However, because
of the administration costs, defaults by cardholders, and
fraudulent use of the cards, the actual value is much less.
37. 1. Interpreting Bond Yields. Suppose you buy a 7 percent
coupon, 20-year bond today when it’s first issued. If interest
rates suddenly rise to 15 percent, what happens to the value of
your bond? Why?
2. Bond Yields. The Timberlake-Jackson Wardrobe Co. has 10
percent coupon bonds on the market with nine years left to
maturity. The bonds make annual payments. If the bond
currently sells for $1,145.70, what is its YTM?
3. Coupon Rates. Osborne Corporation has bonds on the market
with 10.5 years to maturity, an YTM of 9.4 percent, and a
current price of $945. The bonds make semiannual payments.
What must the coupon rate be on the bonds?
4. Stock Values. The next dividend payment by Mosby, Inc.
will be $2.45 per share. The dividends are anticipated to
maintain a 5.5 percent growth rate, forever. If the stock
currently sells for $48.50 per share, what is the required return?
5. Stock Values. Ziggs Corporation will pay a $3.85 per share
dividend next year. The company pledges to increase its
dividend by 4.75 percent per year, indefinitely. If you require a
12 percent return on your investment, how much will you pay
for the company’s stock today?
6. Growth Rates. The stock price of Jenkins Co. is $53.
Investors require a 12 percent rate of return on similar stocks.
If the company plans to pay a dividend of $3.15 next year, what
growth rate is expected for the company’s stock price?
PLEASE REPLY IN HIGLITE TO EACH QUESTION ON THIS
SHEET IN SENTENCE FORM, FOLLOWING EACH
PROBLEM AS: 2003 WORD .doc.
Please also SEPARATELY include the Excel Sheet showing
how each problem was solved.
AGAIN, PLEASE USE THIS SHEET TO ADD THE WRITTEN
SOLUTIONS TO.
5.1 Cash Management
38. The management of cash, or treasury management, is perhaps
the most important aspect of working capital management of a
firm. There should always be an adequate amount of cash
available to the corporation. If there is an unexpected shortage
of cash, the company must also have proper means to raise the
needed cash. This requires careful planning and cash budgeting.
Cash is a necessary resource in business, but too much of it is
also wasteful. Usually corporations keep cash in a checking
account, or several accounts, and the excess cash in marketable
securities through a brokerage firm.
These days it is possible to keep both the checking account and
the brokerage account at a single institution. For instance, a
corporation can have checking and brokerage accounts at PNC
Bank. It is also possible to have both these accounts at a
brokerage firm, such as Merrill Lynch. There are some
restrictions, however, on the checking accounts maintained at a
broker. At one time, the banks were not allowed to sell stocks,
and the brokers could not give check-writing privileges to
customers. However, the current trend is to blur the distinction
between banks and brokers. The policy of the Federal Reserve is
to move in that direction.
Large corporations, such as Walmart, Ford, or Microsoft, have
billions of dollars in cash. They have full-time staff who track
the cash flows and cash balances constantly. Even smaller
companies have to watch their cash accounts carefully.
5.2 Baumol Model (1952)
Perhaps the earliest quantitative analysis of the cash
management of a firm was done by William Baumol in 1952.
We study his approach more in a historical context, rather than
a practical tool to manage cash and marketable securities at a
firm.
39. (
82
)
William Baumol (1922- )
We assume that the corporation maintains two accounts: the
checking account for daily expenditure of cash, and the
brokerage account to keep the marketable securities.
In another paper in 1956, James Tobin (1918-2002), extended
this model. In the Baumolmodel, also called Baumol-Tobin
model, we consider two costs associated with managing cash:
the holding cost, and the ordering cost. The first cost is due to
the fact that the cash kept in a checking account, readily
available for any use, is not earning a
rate of return consonant with other operations of the firm. The
economists call this the opportunity cost, because the
opportunity to invest this cash in the business is lost. To
minimize this loss, the firm invests the surplus cash in
marketable securities, such as Treasury bills, and keeps them in
a brokerage account.
(
T
re
a
41. Cash inflow
Brokerage Account
x
Checking Account
Cash outflow
Fig. 5.1: Cash flow in the Baumol model of cash management.
The company maintains a checking account and a brokerage
account. The company deposits all incoming cash in a brokerage
account, which is invested in high-grade bonds and Treasury
securities. The company transfers $x at regular intervals from
the brokerage account to the checking account. It writes checks
to pay all the bills.
The second cost is that of converting marketable securities into
cash. This includes the transactions cost of selling these
securities, the cost of sending the order to the broker, and the
cost of transferring the money from the broker to the local bank
where the checking account is maintained.
Fig. 5.2: An example of a firm that pays out $10,000 uniformly
every week in bills. It starts with $10,000 in the checking
account, and when the balance drops to zero, it replenishes the
cash by another deposit of
$10,000. The average amount in the checking account is thus
$5000.
42. Let us find an optimal way to manage cash. Suppose a company
needs a total amount of cash C in a whole year to pay all its
bills by check. This could be the amount paid to the workers,
suppliers, utilities, rent, and so on. Rather than keeping the
entire amount in a checking account, the company invests most
of the money in marketable securities. When the cash in the
checking account is depleted, it sells an amount x of these
securities and
puts the money in the checking account from which it writes
checks to pay the bills. When the money is exhausted, it
replenishes the checking account by selling another x dollars’
worth of marketable securities. The number of times this
process is repeated in a year is C/x.
The maximum amount of money in the checking account is x,
and the minimum zero. Assuming that the money is used
uniformly, then the average amount of money in the checking
account is x/2. The cost of keeping this amount in the checking
account for a year depends on the return generated by the next
available investment opportunity of these funds, namely,
marketable securities. Suppose this rate is r per annum. Then
the carrying cost of cash, that is, the cost of maintaining cash in
the checking account per year is rx/2.
Next, we look at the ordering cost. This equals the commission
charged by the broker to sell the securities, plus the costs
related to the order of the sale and transfer of the money,
perhaps by wire, to the checking account. Suppose this cost is b
every time this procedure is repeated. The total number of
transfers per year is C/x, and so the total ordering cost per year
is bC/x.
The total of carrying and ordering cost is rx/2 + bC/x per year.
43. To minimize this cost, we have to differentiate the cost function
with respect to x, which is an independent variable.
Let the total cost of cash management per year be T, where
T = rx/2 + bC/x
dTrbC
Then
dx = 2 − x2
At the optimal point, the total cost T is minimized, and its
derivative is zero. Thus
Solving for x, we find
rbC
2 − x2 = 0
2bC
Optimal amount of transfer,x =
r(5.1)
Equation (5.1) implies that to minimize the total cost of
managing cash and marketable securities, the optimal amount of
transfer from brokerage account to the checking account is x =
2bC/r . The equation also implies the following:
44. (1) The optimal transfer x, is directly proportional to the total
spending per year, C
(2) The optimal transfer x, is directly proportional to the
transfer cost, b
(3) The optimal transfer x, is inversely proportional to the
interest rate, r
We can also calculate the following costs.
Total ordering cost, per year = (transaction cost per
transfer)(number of transfers per
year) = bC/x = bC
r
2bC =
rbC
2
Total interest forgone, per year = (average balance in the
checking account)(rate of
interest) = xr/2 =
2bC
rr/2 =
rbC
2
Note that the two costs are equal. Add them to find the total
cost as
45. Total cost of cash management system, per year =
rbC
2 +
rbC
2 =2rbC(5.2)
Example
5.1. Alabama Corporation has to pay $32 million in bills
annually. It has managed to stretch them out uniformly
throughout the year. Alabama has a checking account at a bank
in Scranton, and keeps its excess cash in the form of high grade
bonds in a brokerage account in Philadelphia. The checking
account pays no interest, and the average transaction cost in the
brokerage account is $125. The average interest on the bond
portfolio is 8.5%. Explain how Alabama should optimize its
cash system.
Put b = 125, C = 32,000,000, r = .085, in the equation
2bC
x =r(5.1)
2(125)(32‚000‚000)
x =.085= $306,786
Alabama should keep at most $306,786 in the checking account,
and keep replenishing it when the money runs out. Alabama has
to do it 32,000,000/306,786 = 104.31 times a year. This is
equivalent to one transaction every 365/104.31 = 3.5 days,
twice a week. ♥
5.2. Alaska Corporation spends $25 million a year to pay its
bills. The cost of ordering the sale of securities is $100 per
46. order. The securities are earning 6% per annum. How often
should Alaska sell the securities, and in what amount, in order
to keep its checking account running at the optimal level?
Putting b = 100, C = 25,000,000, and r = .06, in (5.1), we find
2*100*25‚000‚000
x =.06= $288,675
The number of orders per year is 25,000,000/288,675 = 86.6025.
This is equivalent to an order every 365/86.602 = 4.21 days, on
the average.
The ordering cost per year is 86.6025(100) = $8660.25. The
carrying cost is (288,675/2).06 = $8660.25. The ordering cost is
equal to the carrying cost at the optimal point. ♥
The Baumol-Tobin model (5.1) is derived under the following
simplifying assumptions:
1. The company knows its cash expenditures in advance. There
is no uncertainty in these cash payments. These expenses occur
uniformly with time.
2. The cash outflow from the company remains constant with
time, that is, it is not increasing or decreasing.
Alternatively, we can use NPV of cash management to find the
optimal solution. The company has to convert marketable
securities into cash, C/x times per year. The time interval
between two conversions is x/C years. At each order point, the
cash required is x, and the transaction cost is b. The carrying
cost for the first cycle is given by
(av
47. of first cycle, in years) That is,(x/2)(r)(x/C) = rx2/(2C).
The total cost for the first cycle = transaction cost + carrying
cost = b + rx2/2C.
Assuming that this cost is incurred at the end of the first cycle,
the present value of the cost of the first cycle is thus
PV cost of one cycle =
b + rx2/(2C)
(1 + r)x/C
where r is the rate of return available on the marketable
securities. The company will continue to use this procedure as
long as possible, provided the cash flows remain constant. The
present value of the total cost for infinite many cycles is
∞ b + rx2/(2C)
i=1
(1 + r)ix/C
Carrying out the summation and simplifying, we get
2bC + rx2
PV of infinite cycles = 2[(1 + r)x/C − 1]
Differentiate the above expression with respect to x, and set it
equal to zero.
2rxC[1 − (1 + r)x/C] + (2bC + rx2) ln(1 + r) (1 + r)x/C
48. 2[C(1 + r)x/C − 1]2= 0
Or, 2rxC[1 − (1 + r)x/C] + (2bC + rx2) ln(1 + r) (1
+ r)x/C = 0
Put b = 100, C = 25,000,000, and r = .06, in the above equation,
which gives 3,000,000x(1.06x/25,000,000 – 1) −
1.06x/25,000,000 ln(1.06) (5,000,000,000 + .06x2) = 0
Solving for x, we get x = $288,772. This is quite close to the
result obtained by using (5.1), namely, $288,675. Theoretically,
the second method is superior to the previous one because it
looks at the time value of the cash flows, but practically, the
difference is very small.
5.3 Miller-Orr Model (1966)
Another method used for estimating the optimal amount of cash
for a firm was developed by Merton Miller and Daniel Orr.
Miller-Orr model assumes that the cash inflows and outflows
are completely random. It further assumes that the mean cash
flow is zero, and variance of the cash flows is known.
Merton Miller (1923-2000)
From a practical point of view the company maintains a
checking account where all incoming cash and checks are
deposited daily. The company also writes checks on this
account to pay all bills as they come due. The firm monitors two
items on a daily basis:
the net cash flow in the account, and the cash balance in the
49. account. The cash balance should not be too high, because that
is wasteful, and it should not be too low, otherwise the checks
written by the company may start to bounce.
Cash inflow
Checking Account
Cash outflow
Brokerage Account
Fig. 5.3: Cash flow in the Miller-Orr cash management system.
All incoming cash is deposited in a checking account and the
company pays the bills out of this account. When there is too
much cash in the checking account, the companys transfers $2x
from the checking to a brokerage account. When there is not
enough cash in the checking account, an amount $x is
transferred from the brokerage account to the checking account.
The money manager at the firm first decides the minimum
amount of cash that the checking account must have. Let us say,
this amount is L.
When the balance in the checking account drops to L, the
manager sells x amount of marketable securities and puts the
50. cash in the checking account. The balance now becomes L + x,
which is supposed to be the optimal amount of cash in the
account. When the cash in the account rises to a level equal to L
+ 3x, the manager buys securities worth 2x, so that the cash
balance drops down once again to the optimal level L + x. In
this way the cash in the checking account remains between the
limits L + x and L + 3x.
The amount x depends upon the following factors:
1. The transactions cost, b. This is the cost of converting excess
cash into securities, or converting securities back into cash.
This includes the brokerage commissions, and the value of the
time of the person managing the money. If the cost per
transaction is high, one should move large amounts of cash at
each transaction.
2. The daily variance of the cash flows, σ2. The greater is the
variance of the cash flows, the greater should be the amount
transferred each time. If the cash flows are very predictable, or
known with certainty, then there is no need for the movement of
large blocks of money.
3. The daily interest rate, r. One can easily see that if the
interest rates are high, one should keep as little money in the
checking account as possible. This means that for high interest
rates, x should be small.
Cash, $
L + 3x
51. L + 4/3 x L + x
L
Time
Fig. 5.4. The cash balances in the Miller-Orr model for cash
management.
The mathematical derivation of the optimal transfer amount x is
somewhat complicated, but the result is that
(
) (
)x =
(5.2)
Further, the model specifies the follows values: The minimum
amount of cash = L
The optimal amount of cash = L + x
52. The maximum amount of cash = L + 3x The average amount of
cash = L + (4/3)x
To use equation (5.2) in practice, one has to develop estimates
for the three parameters, b,
again. They expect to spend
$25 million in cash payments annually. Suppose the standard
$6 million, on an annual basis. The cost of each transaction is
still $100, and the rate of return on the marketable securities is
6%. Putting these values in (5.2), we find
(
2
1
/
3
4*.06
So this is what Alaska Corporation should do. They should start
with a cushion of, say,
$50,000, and add $355,689 to it. The starting balance is then
$405,689. Then they should keep putting collections in this
account, and also write checks out of it. If the collections are
running at a faster pace, the balance in the account will keep on
53. rising. When it reaches 50,000 + 3*355,689 = $1,117,067, they
should buy 2*355,689 = $711,378 worth of securities and the
bring the balance down to 1,117,067 − 711,378 = $405,689.
This is the optimal amount of money in the checking account.
On the other hand, if the disbursements are going ahead faster
than the collections, the balance in the account will drop
gradually. When it reaches $50,000, they should sell
$355,689 worth of securities and replenish the cash balance,
bringing it to its optimal level of $405,689 once again.
Example
5.3. Arizona Company uses the Miller-Orr model to manage
cash. The ending balance in their checking account, including
checks and deposits, for 10 consecutive business days is:
Day
Balance
Day
Balance
1$15,625622,725
212,225719,000
313,825817,775
417,375912,125
521,9001010,225
The cost of each transaction is $100, whereas the return on
securities is 5%. They would like to maintain a minimum
balance of $5,000. How should they manage their cash?
First we have to find the variance of the cash flows. We may do
so by augmenting the above table as following.
We calculate the net cash flow each day by subtracting the first
day's balance from the second day's balance, and so on. Then we
add these daily net cash flows, and divide the total by 9. The
54. average net cash flow per day is therefore −5400/9 = −600. We
can also check the result by calculating the difference in the
balance on the first and the tenth day, and dividing by 9. This
comes out to be (10,225 − 15,625)/9 = −600, as before.
Day
Balance
Net Cash
Flow
Difference
(Difference)2
1
$15,625
2
12,225
12,225 – 15,625 =
–3,400
–3,400 + 600
7,840,000
3
13,825
13,825 – 12,225 =
1,600
1,600 + 600
4,840,000
4
17,375
17,375 – 13,825 =
3,550
3,550 + 600
17,222,500
56. Total
–5,400
95,547,500
Next we find the difference between the individual daily net
cash flows and the average. This is set up in the next column.
Then we find the square of all these differences and place them
in the next column marked (Difference)2. Then we add the
numbers in this column and divide the result by 8, because we
have lost another degree of freedom. The final result,
95,547,500/8 gives us the variance of the net cash flows. The
resulting number is σ2 = 11,943,437.5, on a daily basis.
The interest rate is the daily interest rate, because we are
dealing with daily cash flows. That is, r = .05/365. We also
know that b = 100. Putting these numbers in (5.2), we find
4*.05/365
They should start out with the optimal balance of 5,000 +
18,700 = $23,700. If the account balance drops to $5,000, they
should sell $18,700 worth of securities and put the money in the
checking account. If the account balance rises to 5,000 +
57. 3*18,700 =
$61,100, they should take 2*18,700 = $37,400 out of it and buy
securities from this money. This brings the level back to the
optimal point at $23,700. The average balance in this account is
5,000 + (4/3)*(18,700) = $19,933. ♥
5.4. Arkansas Company's checking account balance on 12
successive business days is given in the table below. It uses the
Miller-Orr model for cash management. Arkansas requires a
minimum balance of $3,000 in its checking account. The return
on the securities is 8%, and the cost of each transaction is $150.
How should it set up its cash system?
Day
Balance
Day
Balance
Day
Balance
Day
Balance
1$15,6254$17,3757$19,00010$10,225
212,225521,900817,7751114,000
313,825622,725912,1251215,000
To do the problem with the help of Maple, we type in the
following. The lines starting with the symbol # are comment
lines. They are not part of the instructions for the computer, but
are merely an aid to understand the program.
# n is the number of data items n:=12;# a is an array to store the
data, with size n a:=array(1..n):# put the data in
placea[1]:=15625.: a[2]:=12225.: a[3]:=13825.:
a[4]:=17375.:a[5]:=21900.: a[6]:=22725.: a[7]:=19000.:
a[8]:=17775.:a[9]:=12125.: a[10]:=10225.: a[11]:=14000.:
a[12]:=15000.:print (a);#ncf is an array to store the net cash
58. flows, with size n-1 ncf:=array(1..n-1);# The next statement
fills out the net cash flows for i to n-1 do ncf[i] := -a[i]+a[i+1]
od;# avncf is the average net cash flow avncf:=(a[n]-a[1])/(n-
1);# diffsq is an array to store (difference)^2, with size n-1
diffsq:=array(1..n-1);# fill in the data for (difference)^2for i to
n-1 do diffsq[i]:=(ncf[i]-avncf)^2 od;# var is the variance =
(sigma)^2var:=sum(diffsq[j],j=1..n-1)/(n-2);
# x is the Miller-Orr order quantity x:=(3*b*var/4/r)^(1./3);
subs(b=150,r=.08/365,x);
There are several do statements in the above program. They
give instructions to repeat a certain operation a given number of
times. Each do statement must end with od, which is do spelled
backwards. One must follow the syntax carefully.
The final result of the above calculations is x = $18,020. The
company should start with a cash balance of $21,020, replenish
cash when the balance drops to $3000, and buy
$36,040 worth of securities when the balance reaches $57,060.
♥
5.5. California Company maintains a checking account and a
brokerage account to manage its cash. It writes $45,000 in
checks every week on the average, and the standard deviation of
net cash flows is $15,000 per week. California keeps the excess
cash in the brokerage account that pays 5.25% in interest. The
cost of transferring money between the accounts is $200 per
transaction. California maintains a minimum of $30,000 in the
checking account. Using Miller-Orr model, explain how it
should manage its cash in an optimal manner. In particular:
A. What is the minimum balance in the checking account that
triggers a transfer of money from the brokerage to checking
account? How much money is transferred?
59. B. What the maximum balance in the checking account that
requires a transfer of money from the checking to the brokerage
account, and how much is this amount?
C. What is the interest forgone each year?
A. The minimum balance in the checking account is $30,000.
Use the formula
(
3
b
σ
)2 1/3
(
(5.2)
and put the numerical values for b = 200, σ2 = 15,0002 =
225,000,000, r = .0525/52. Note that we have weekly cash
flows, and thus we must use the weekly rate of interest. This
gives us x = (3*200*225,000,000/4/.0525*52)1/3 = $32,214.
Thus the amount of money transferred is $32,214. ♥
B. Since California would like to keep a minimum of $30,000 in
the checking account, they should start out by keeping 30,000 +
32,214 = $62,214 in this account, which is at the optimal level.
60. They should put the rest of the cash in the brokerage account.
When the amount in the checking account drops to $30,000,
then they should replenish it with
$32,214 additional cash from the brokerage account. The
maximum amount of money in the checking account should be
30,000 + 3*32,214 = $126,642. At that point California should
transfer $64,428 from the checking to brokerage account. ♥
C. The company keeps on the average 30,000 + (4/3)*32,214 =
$72,952 in the checking account. The annual interest foregone
is 72,952*.0525 = $3,830. ♥
5.6. Colorado Company uses Miller & Orr model for its cash
management by maintaining a checking account and a brokerage
account. It writes $65,000 in checks on the average per week,
and the standard deviation of its net cash flows is $25,000 per
week. Colorado requires a minimum of $40,000 in the checking
account. Colorado keeps the excess cash in the brokerage
account that pays 4.75% in interest. The cost of transferring
money between the accounts is $150 per transaction. Explain
how it should manage its cash in an optimal manner. In
particular:
A. What is the minimum balance in the checking account that
triggers a transfer of money from the brokerage to checking
account? How much money is transferred? Minimum balance =
$40,000. We use the formula,
(
3
b
σ
)2 1/3
61. (
(5.2)
and put the numerical values for b = 150, σ2 = 25,0002 =
625,000,000, r = .0475/52. This gives us x =
(3*150*625,000,000/4/.0475*52)1/3 = $42,538. Colorado
should transfer
$42,538 from the brokerage account to checking account. ♥
B. Find the maximum balance in the checking account that
requires a transfer of money from the checking to the brokerage
account, and the amount of this transfer.
The maximum amount in the checking account is 40,000 +
3*42,538 = $167,614. At that time they should transfer
2*42,538 = $85,076 from the checking account to the brokerage
account. ♥
C. What is the interest forgone per year?
The average cash in the checking account is 40,000 +
4*42,538/3 = $96,717. The interest on this amount is
.0475*96,717 = $4,594. ♥
5.4 Speeding Up Collections
The business firms like to get hold of cash from their customers
as soon as possible. Traditionally, the customers pay their bills
by mailing a check. This delays the actual payment because of
62. slow mail, depositing the check, and then clearance of the check
before the funds become available to the payee.
To speed up the collections, the firms with lots of customers,
such as the utility companies, or credit card companies, have
devised several schemes. The two important ones are electronic
collections, and lock-box arrangements.
(a) Electronic Collections
It is possible to transfer funds electronically from bank to bank
by using a system known as the federal wire. This enables the
payer to send the money securely, and precisely at a given time.
In order to collect bills when they are due, some corporations
and banks will enter into an agreement with the buyer to
transfer the money directly from the checking account of the
buyer to their own account. For example, when an insurance
company sells a policy, it may allow the buyer of the policy the
option of monthly payments, whereas the money will be
transferred directly from the account of the policyholder to the
account of the insurance company. The main advantage of this
method is that the insurance company will get the installments
on time, and the policyholder does not have to worry about
writing checks and mailing them.
(b) Lock-box Arrangement
Did you ever notice that your credit card bill, or the telephone
bill, has a post office box as the return address? To speed up the
collections, many corporations, such as Citibank, or Discover
Card, or Sears, who have accounts all over USA, will set up
lock-box arrangements. For example, Sears may have return
addresses with post office numbers in Boston, Atlanta, Chicago,
Houston and San Francisco. Customers in the neighboring states
will send their bills to the nearest post office address. Once the
checks from the customers reach the post office, they are
immediately deposited in a local bank. That bank, in turn, will
63. credit the national account of Sears on a daily basis. This can
reduce the collection period by two to four days.
Sears had annual revenue of $51.78 billion in 12 months ending
January 21, 2008. This comes out to be about $4.315 billion a
month. Suppose Sears is able to reduce the collection period by
4 days each month by using a lock-box arrangement, and its cost
of capital is 12%, then this arrangement is saving them
4315*.12*4/365 = $5.675 million every month. This adds up to
$68 million every year.
One of the optimization problems in cash management is to
properly plan the location and the number of the lock-boxes.
5.5 Treasury Bills
Part of the efficient cash management system of a company is to
invest the free cash in interest-bearing securities, which are
very liquid, and also very safe. The best securities for this
purpose are short-maturity Treasury securities. They are also
known as Treasury bills.
The United States government, through the Department of
Treasury, sells bonds with various times to maturity. Because
the US government, through its power to tax people, has always
been able to pay the interest and principal back to the investors,
such investments are known as risk-free securities. These
securities have various times to maturity ranging from a few
days up to 30 years.
The Treasury Department auctions these securities every week.
These securities are sold at a discount from their face value. In
other words, you can buy a $1000 T-bill for perhaps $990.
When this T-bill matures, you can cash it in for $1,000. Thus
the difference, $10, is the interest earned on the $990
64. investment.
After they have been issued by the Federal Government, the
Treasury bills are then traded in the capital markets. The market
value of these securities changes daily due to the fluctuations in
the interest rates. The market value also drifts slowly towards
the face value of the bonds with the passage of time.
The Wall Street Journal provides two discounts for these
securities. The asked discount gives the purchase price, and the
bid discount the selling price of the T-bill. The discount is
quoted as a percentage of the face amount, but it is annualized
with a 360-day year. The relationship between the dollar
discount and the percentage discount is thus
We can express it as
dFn D = 360
65. The market price of the bond isB = F − D,
(
) (
(5.3)
Once we know the market price of a T-bill, we can also
calculate its bond equivalent yield, which is defined as
Using (5.3), we get
66. (
(
) (
365d
Or,BEY = 360 − nd(5.4)
Another way to look at these securities is to consider them as
zero-coupon bonds. Their present value and the future value are
related by the expression
F = B(1 + r)T(5.5)
Here F is the final value, or face value of the bond, B is its
present value, r is the implied rate of interest on the bond, and
T is the time to maturity in years.
The US Treasury also issues bonds with maturity longer than
one year. These securities carry a coupon and their interest is
paid semiannually. The bonds with maturity less than 5 years
are called notes, while the securities with maturity longer than 5
years are known as bonds.
67. At one time, prices for long-term bonds were quoted in the
newspaper in 32nds of dollars. For example, on May 25, 1994,
the notes maturing in October 1999 with 6% coupon had bid
price listed as 96:16 and asked price 96:18. This means that an
investor can sell such bonds for 9616/32 percent of their face
value and another investor can buy them for 9618/32 percent of
the face amount. For example, one has to pay $96,562.50 to buy
a bond with $100,000 face amount. An investor who is holding
a similar bond can sell it for $96,500. The difference between
these numbers, $62.50, is the profit of the dealer in such bonds.
These days, all prices are quoted in decimals. For instance, on
December 30, 2007, the 3.875% Treasury note, maturing on
February 15, 2013, was selling for 95.08% of its face value. It
paid interest semiannually. Its current yield was 4.076% and the
yield to maturity was 4.957%.
Examples
5.7. A Treasury bill with face value $100,000 will mature in 73
days. Glenn Corporation has bought the bill at a discount of
6.08%. How much did it pay for the T-bill?
Using (5.3), we get
B = 100,000(1 – 0.0608*73/360) = $98,767.11 ♥
5.8. For the T-bill in the previous problem, what is its yield to
maturity considering it to be a zero coupon bond and annual
compounding?
Using the relation (5.5), we have
100,000 = 98,767.11(1 + r)73/365
68. which gives the zero-coupon yield,
r = 6.40% ♥
The zero-coupon yield is higher than quoted discount of 6.08%
because of two reasons. First, the yield is compounded for a full
year, and not just for 73 days, and second, the year is now
counted as being equal to 365 days, and not 360 days. There is
also an inherent inconsistency in this calculation because the
year is being considered to be equal
to 360 days in the first part and then equal to 365 days in the
second part. Anyway, that is the common practice.
5.9. For the T-bill in the previous problem, what is its bond
equivalent yield? We find the bond equivalent yield by using
(5.4). This comes out to be
365*.0608
Bond equivalent yield = 360 – 73*.0608 = 6.24% ♥
5.10. For a T-bill that matures after 135 days, the bid discount
is 3.51% and the asked discount 3.49%. Calculate the buying
and selling price of a bill with face value $100,000. By using
the average of the bid and asked discount, find the zero-coupon
yield and the bond equivalent yield.
Using (5.3), we get
Asked price = buying price = 100,000[1 − .0349(135/360)] =
$98,691.25 ♥
Bid price = selling price = 100,000[1 − .0351(135/360)] =
69. $98,683.75 ♥
Using the mean value of the bid-asked spread = ½(3.49% +
3.51%) = 3.50%, we find
B = 100,000[1 − .035(135/360)] = $98,687.50
For zero-
– 1 = 3.64% ♥
365*.035
For bond equivalent yield, r = 360 – 135*.035 = 3.60% ♥
5.6 Other short-term investments
Besides the Treasury securities, the corporations also invest in
the following:
(a) Repurchase Agreements ("Repos")
Suppose Akron Corporation has Treasury securities with face
amount $1 million. Their market value is, say $960,000.
Suppose Akron needs $960,000 right away, but they also expect
to receive $960,000 after two weeks.
One possibility is to sell these securities on the open market and
get the needed cash. Another possibility is that Akron may sell
these securities for their market value to another corporation,
Toledo Company, with the agreement that Akron will
repurchase these securities after 14 days for $962,000. This
enables Akron to effectively borrow
70. $960,000 for 14 days by paying $2000 in interest costs. The
effective annual interest rate comes out to be
2000*365
r = 960‚000*14 = 5.431%
The advantage to Akron for this arrangement is that its interest
cost is fixed at $2000. It does not have to worry about the
interest-rate fluctuations in the bond market. Toledo corporation
has the advantage of investing at a fixed rate in a risk-free
environment. The interest rate in this case will be slightly
higher than that offered by the Treasury bills.
In the above example, Toledo Corporation is entering into a
reverse-repo agreement, whereby it can invest its spare cash for
a short time. The advantage of a repo or a reverse- repo
arrangement is that a company can borrow or lend money,
without taking any risks, for a fixed period of time, at a fixed
rate.
(b) Certificates of Deposit (CDs)
Certificates of deposit, CD's, are issued by banks at relatively
higher rate of interest, but the investors must put the money for
a fixed period of time. For individual investors, these CD's are
insured by FDIC up to $100,000. The corporations may also buy
"jumbo" CD's, with a minimum of $100,000, and usually in
denomination of $1 million each. The corporations are able to
lock in a fixed rate of return for their idle cash for a set period
of time. However, these CD’s are not federally insured and they
do carry a certain risk.
(c) Money Market Funds
Many mutual fund companies also offer money-market funds.
These funds simply take the money from individual investors
and corporations, and buy jumbo CD's with the pool of money.
71. The managers at the mutual fund company, such as Fidelity
Money MarketFund, select the CD's that are issued by
financially secure banks. They also buy the CD's with staggered
maturity dates. Another feature of the money market funds is
that their share value is fixed daily at $1 per share. The interest
on the account is generally credited once a month.
For a corporation, it is an excellent cash-management tool. The
spare cash earns a fairly high rate of interest, it is kept in a very
safe investment, and it is totally liquid. The fund also offers
check-writing privileges, meaning that the cash is available
immediately.
5.7 Choice of Marketable Securities
The corporations investing in marketable securities look at three
main characteristics of these investments: (a) Maturity, (b)
Credit risk, and (c) Income taxes.
If a company needs cash immediately, it should preferably keep
it in a money-market account. If a company will need the cash
after, say, six months, it is better off buying a
CD that will mature after six months. The cash needs must be
matched with maturity date of the investments.
The marketable securities are issued by other commercial
entities. The risk of the securities depends on the financial
wherewithal of the issuing corporations. The firm that is
purchasing marketable securities must look at the credit quality
of the instruments that it is buying. Of course, lower grade
investments have a higher degree of risk, but they also provide
higher rate of return.
Some companies buy the preferred stock of other companies for
72. investment purposes. This is because the dividends on this type
of stock quite secure, and most of this dividend income is tax
exempt. Consider the following example.
Suppose a company is in the 32% tax bracket. It buys a
preferred stock with a dividend yield of 5%. Suppose 70% of
the dividend income is tax exempt. What is the pre-tax rate of
return on another investment that will provide the same after-
tax return?
Suppose the required return is x. Suppose the firm invests
$100,000 and it gets 100,000x in dividends. It pays 32% in
taxes, which gives 100,000x(1 − .32) = $68,000x after taxes.
Suppose the company invests $100,000 in 5% preferred stock.
The dividend is $5000. 70% of this amount is tax free, or only
30% is taxable. The tax is thus .32(.3)(5000) =
$480. After paying taxes, the net amount is 5000 − 480 = $4520.
Equating the two possibilities, we get
68,000 x = 4520
Or, x = 4520/68,000 = 6.647%
You may simplify the calculation as
x(1 − .32) = .05 − .05(1 − .7)(.32)
This gives x = 6.647%. Therefor, another investment whose
return is fully taxable, must provide 6.647% return to compete
with the 5% return, of which 70% is tax free.
6.1
Collection and NPV from the credit policy of 2/10, net 30 and
73. 1% per month interest on all accounts after 30 days.
OLD POLICY
Collection within
10 days
30 days
60 days
90 days
Percentage
10%
30%
40%
20%
Discount/interest
-2%
0%
1%
1%
Collection
10%*(1-2%)
30%
40%+(40%*1%)
20%+(20%*1%*2)
0.098
0.3
0.404
0.204
Discount Rate
12%
pa
76. Yes, it should try the new policy
For calculating the NPV first the collections have to be
determined after taking into account the discounts given on
payment within 10 days and interest charged on payment made
after 30 days.
After that, the discount rate considered by the company is
12%p.a and days in a year are assumed to be 365. So using this
rate the present value of the collection is calculated and a sum
total of the amount gives the Net Present Value. The same
method applies for both, the old policy as well as the new credit
policy.
Since the NPV of the new credit policy is higher the new credit
policy should be implemented.
6.2
Cash Sale
Annual Sale
5
COGS
-3.2
78. 60 days
90 days
Bad Debt
Total
6.25*20%
6.25*40%
6.25*37%
6.25*3%
1.25
2.5
2.3125
0.1875
6.25
Discount Rate
12%
pa
-4
PV
1.25/(1+12%)^30/365
2.5/(1+12%)^60/365
2.3125/(1+12%)^90/365
0
1.238
2.454
2.249
0.000
5.941
COGS
79. -4.000
NPV
1.941
After calculating the present value of cash flows from credit
sale at a discounted rate of 12% with days in a year taken at 365
days is calculated.
Since the NPV of credit sale is higher than that of cash sale,
Credit sale should be encouraged.
The minimum increase in sale to justify credit sale should be
such that the NPV of Credit sale is at least equal to NPV of
Cash Sale
NPV
1.800
COGS
4.000
PV of Sale
5.800
82. The following equation to find the selling price of the portfolio,
NF + 12nB[(1 + r)−g/365 − 1] + mC(R − r) − L + 12aNS
Selling price = P +
r(6.10)
In the above expression, a = 0, P = 0, N = 10,000, F = $25, m =
10,000, n = 10,000, C =
$1200, B = $800, R = .15, r = .08, g = 25 days, L = $100,000.
Putting these numbers, we find the selling price as follows.
NPV =10‚000(25) + 12(10‚000)(800)[1.08−25/365 − 1] +
10‚000(1200)(.15 − .08) − 100‚000
.08
=3.971
Since the amount offered by Mellon Bank at $5 mn is higher
than the NPV of $3.971 of credit card portfolio, First National
Bank of Jermyn should accept the offer.
SOLUTIONS
5.1. Campbell Corporation uses Baumol model to manage cash.
The cost of transferring money from a money-market fund,
which pays 6% interest on balances, to a checking account is
$32 per transaction. Campbell needs $13 million annually to pay
its bills. Find the annual cost of interest forgone.
$3533 ♥
83. Solution
:
Annual requirement of cash (A) = $ 13 million
Transaction cost (T) = $ 32 per transaction
Opportunity cost of holding cash (R) = 6%
According to Baumol model to manage cash
Total cost = Transaction cost + Opportunity cost
Let C* be the optimum cash balance that minimizes the cost of
holding cash
Transaction cost = A x T
C*
Opportunity cost = C* x R
2
Total cost = A x T + C* x R
C* 2
Differentiating with respect to C* we get
0 = - A x T + 1 x R
C*2 2
84. - A x T = 1 x R
C*2 2
C* = √(2AT) / R
Therefore
C* = √(2*13,000,000* 32) / 0.06
C* = √13866666666.67
C* = $ 117756.81
The annual cost of interest foregone is the opportunity cost
Opportunity cost = C* x R
2
=($ 117756.81/2) *0.06
= $ 3533
The annual cost of interest foregone is $ 3533.
141
85. 5.2. Genentech Corporation, by analyzing its weekly balances in
its checking account, has determined that the variance of cash
flows is $3,000,000. Further, the cost of transferring money
from the checking account to a money market account is $65 per
transfer. The interest on the checking account is 1%, while that
on the market account is 6%. Genentech wants to keep $5,000
as a minimum balance in the checking account. Find the annual
cost of interest forgone.
$606 ♥