This document contains 18 math problems related to inflation and calculating present and future values with inflation adjustments. The problems cover topics like calculating cost per person for a sewage treatment plant adjusted for inflation, determining life insurance needs to provide a constant annual interest amount after accounting for inflation and interest rates, and calculating internal rates of return on investments when adjusting for inflation.
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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 ...
This is the third presentation for the University of New England Graduate School of Business unit GSB711 - Managerial Finance. It explores the time value of money, using examples to help students clarify this concept.
11.value1.00 pointsSpeedy Delivery Systems can buy a pie.docxsusanschei
11.
value:
1.00 points
Speedy Delivery Systems can buy a piece of equipment that is anticipated to provide a return of 11 percent and can be financed at 8 percent with debt. Later in the year, the firm turns down an opportunity to buy a new machine that would yield a return of 18 percent but would cost 20 percent to finance through common equity. Assume debt and common equity each represent 50 percent of the firm’s capital structure.
a.
Compute the weighted average cost of capital. (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
Weighted average cost of capital
%
b.
Which project(s) should be accepted?
New machine
Piece of equipment
12.
value:
1.00 points
A brilliant young scientist is killed in a plane crash. It is anticipated that he could have earned $310,000 a year for the next 30 years. The attorney for the plaintiff’s estate argues that the lost income should be discounted back to the present at 4 percent. The lawyer for the defendant’s insurance company argues for a discount rate of 9 percent.
What is the difference between the present value of the settlement at 4 percent and 9 percent? Compute each one separately. Use Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Present Value
PV at 4% rate
$
PV at 9% rate
Difference
$
13.
value:
1.00 points
The Goodsmith Charitable Foundation, which is tax-exempt, issued debt last year at 13 percent to help finance a new playground facility in Los Angeles. This year the cost of debt is 20 percent higher; that is, firms that paid 15 percent for debt last year will be paying 18.00 percent this year.
a.
If the Goodsmith Charitable Foundation borrowed money this year, what would the aftertax cost of debt be, based on their cost last year and the 20 percent increase? (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
Aftertax cost of debt
%
b.
If the receipts of the foundation were found to be taxable by the IRS (at a rate of 20 percent because of involvement in political activities), what would the aftertax cost of debt be? (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
Aftertax cost of debt
%
14.
value:
1.00 points
Airborne Airlines Inc. has a $1,000 par value bond outstanding with 20 years to maturity. The bond carries an annual interest payment of $96 and is currently selling for $960. Airborne is in a 40 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar.
a.
Compute the yield to maturity on the old issue and use this as the yield fo.
Math 034 First Letter of Last Name Homework #8 .docxandreecapon
Math 034 First Letter of Last Name
Homework #8 Full Name ___________________________
Due Wednesday 11/4/15 Section _____________________________
1. (Section 7.3) On the basis of how long he has until retirement and his comfort with investment risk, Bill has
decided that he wants to allocate the money in his retirement account as follows: 70% to equities, 25% to fixed
income, and 5% to cash.
a. If he assumes that each asset class provides the low end of the rates of return shown in the table in
Example #1 in the PowerPoint slides from Section 7.3, what overall rate of return would he expect to
earn over the long term?
b. If he assumes that each asset class provides the high end rate of return, what overall rate of return
would he expect to earn over the long term?
2. (Section 7.3) The Northern Tier Real Estate Fund has $84,324,980 in assets and 1,009,880 shares. If Ruth owns
76.387 shares of this fund, what is the value of her investment?
3. (Section 7.3) The net asset value of a mutual fund is $139.56. The fund charges a 2% load. How many shares
will you own if you invest $11,000 in this fund?
4. (Section 7.3) One November 1, 2009, the net asset value of the Phillips International Fund was $52.43. On
November 1, 2015, the net asset value was $28.12. If all dividends were reinvested, each share of the fund on
November 1, 2009 would have grown to 2.486 shares on November 1, 2015. Calculate the average annual rate
of return.
5. (Section 7.3) A mutual fund had annual returns of +10%, +9%, -4%, -8%, and +3% in each of the past 5 years.
What was the average rate of return over this period?
6. (Section 7.3) Two years ago, an investment you made in a mutual fund was worth $7,500.00. Today it is worth
$6,195.35. When you complain to your fund manager, he indicates that your annual rate of return for the year
that just ended was 8%. Calculate your annual rate of return for the first year.
7. (Section 8.1) The company you work for provides a lifetime income to its employees on retirement at age 65.
The formula provides 2% for each year of service of the average of the employee’s earnings for the last 3 years
on the job, up to a maximum of 75%. Your company offers employees the choice to retire as early as age 60 or
as late as age 72. Those retiring before age 65 have their calculated benefit reduced by 2.4% for each year they
retire prior to age 65; those retiring later have their benefit increased by 2.2% for each year beyond age 65 that
they work.
a. Suppose you plan to retire this year at age 61. You have 26 years of service to the company and your
last 3 years’ earnings were $55,785, $59,840, and $60,565. Calculate your pension benefit.
b. Suppose you plan to retire this year at age 70. You have 40 years of service to the company and your
last 3 years’ earnings were $67,654, $69,450, and $74,820. Calculate your pension benefit.
8. (Section 8.1) The comp ...
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devry fin 515 week 4 midterm,devry fin 515 week 4 problem set,devry fin 515 week 4,devry fin 515 week 4,devry fin 515,devry fin 515 week 4 tutorial,devry fin 515 week 4 assignment,devry fin 515 week 4 help
devry fin 515 week 4 midterm,devry fin 515 week 4 problem set,devry fin 515 week 4,devry fin 515 week 4,devry fin 515,devry fin 515 week 4 tutorial,devry fin 515 week 4 assignment,devry fin 515 week 4 help
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 ...
This is the third presentation for the University of New England Graduate School of Business unit GSB711 - Managerial Finance. It explores the time value of money, using examples to help students clarify this concept.
11.value1.00 pointsSpeedy Delivery Systems can buy a pie.docxsusanschei
11.
value:
1.00 points
Speedy Delivery Systems can buy a piece of equipment that is anticipated to provide a return of 11 percent and can be financed at 8 percent with debt. Later in the year, the firm turns down an opportunity to buy a new machine that would yield a return of 18 percent but would cost 20 percent to finance through common equity. Assume debt and common equity each represent 50 percent of the firm’s capital structure.
a.
Compute the weighted average cost of capital. (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
Weighted average cost of capital
%
b.
Which project(s) should be accepted?
New machine
Piece of equipment
12.
value:
1.00 points
A brilliant young scientist is killed in a plane crash. It is anticipated that he could have earned $310,000 a year for the next 30 years. The attorney for the plaintiff’s estate argues that the lost income should be discounted back to the present at 4 percent. The lawyer for the defendant’s insurance company argues for a discount rate of 9 percent.
What is the difference between the present value of the settlement at 4 percent and 9 percent? Compute each one separately. Use Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Present Value
PV at 4% rate
$
PV at 9% rate
Difference
$
13.
value:
1.00 points
The Goodsmith Charitable Foundation, which is tax-exempt, issued debt last year at 13 percent to help finance a new playground facility in Los Angeles. This year the cost of debt is 20 percent higher; that is, firms that paid 15 percent for debt last year will be paying 18.00 percent this year.
a.
If the Goodsmith Charitable Foundation borrowed money this year, what would the aftertax cost of debt be, based on their cost last year and the 20 percent increase? (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
Aftertax cost of debt
%
b.
If the receipts of the foundation were found to be taxable by the IRS (at a rate of 20 percent because of involvement in political activities), what would the aftertax cost of debt be? (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
Aftertax cost of debt
%
14.
value:
1.00 points
Airborne Airlines Inc. has a $1,000 par value bond outstanding with 20 years to maturity. The bond carries an annual interest payment of $96 and is currently selling for $960. Airborne is in a 40 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar.
a.
Compute the yield to maturity on the old issue and use this as the yield fo.
Math 034 First Letter of Last Name Homework #8 .docxandreecapon
Math 034 First Letter of Last Name
Homework #8 Full Name ___________________________
Due Wednesday 11/4/15 Section _____________________________
1. (Section 7.3) On the basis of how long he has until retirement and his comfort with investment risk, Bill has
decided that he wants to allocate the money in his retirement account as follows: 70% to equities, 25% to fixed
income, and 5% to cash.
a. If he assumes that each asset class provides the low end of the rates of return shown in the table in
Example #1 in the PowerPoint slides from Section 7.3, what overall rate of return would he expect to
earn over the long term?
b. If he assumes that each asset class provides the high end rate of return, what overall rate of return
would he expect to earn over the long term?
2. (Section 7.3) The Northern Tier Real Estate Fund has $84,324,980 in assets and 1,009,880 shares. If Ruth owns
76.387 shares of this fund, what is the value of her investment?
3. (Section 7.3) The net asset value of a mutual fund is $139.56. The fund charges a 2% load. How many shares
will you own if you invest $11,000 in this fund?
4. (Section 7.3) One November 1, 2009, the net asset value of the Phillips International Fund was $52.43. On
November 1, 2015, the net asset value was $28.12. If all dividends were reinvested, each share of the fund on
November 1, 2009 would have grown to 2.486 shares on November 1, 2015. Calculate the average annual rate
of return.
5. (Section 7.3) A mutual fund had annual returns of +10%, +9%, -4%, -8%, and +3% in each of the past 5 years.
What was the average rate of return over this period?
6. (Section 7.3) Two years ago, an investment you made in a mutual fund was worth $7,500.00. Today it is worth
$6,195.35. When you complain to your fund manager, he indicates that your annual rate of return for the year
that just ended was 8%. Calculate your annual rate of return for the first year.
7. (Section 8.1) The company you work for provides a lifetime income to its employees on retirement at age 65.
The formula provides 2% for each year of service of the average of the employee’s earnings for the last 3 years
on the job, up to a maximum of 75%. Your company offers employees the choice to retire as early as age 60 or
as late as age 72. Those retiring before age 65 have their calculated benefit reduced by 2.4% for each year they
retire prior to age 65; those retiring later have their benefit increased by 2.2% for each year beyond age 65 that
they work.
a. Suppose you plan to retire this year at age 61. You have 26 years of service to the company and your
last 3 years’ earnings were $55,785, $59,840, and $60,565. Calculate your pension benefit.
b. Suppose you plan to retire this year at age 70. You have 40 years of service to the company and your
last 3 years’ earnings were $67,654, $69,450, and $74,820. Calculate your pension benefit.
8. (Section 8.1) The comp ...
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
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Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
1. 211
Chapter 15
Inflation
15-1
The first sewage treatment plant for Athens, Georgia cost about $2 million in 1964. The utilized
capacity of the plant was 5 million gallons/day (mgd). Using the commonly accepted value of 135
gallons/person/day of sewage flow, find the cost per person for the plant. Adjust the cost to 1984
dollars with inflation at 6%. What is the annual capital expense per person if the useful life is 30
years and the value of money is 10%?
Solution
Population equivalents = 5 mgd/135 = 37,037
Cost per capita = = $54
1984$, F = 54(F/P, 6%, 20) = $173.18
Annual Cost, A = 173.18(A/P, 10%, 30) = $18.37
15-2
How much life insurance should a person buy if he wants to leave enough money to his family, so
they receive $25,000 per year in interest, of consent Year 0 value dollars? The interest rate
expected from banks is 11%, while the inflation rate is expected to be 4% per year.
Solution
The actual (effective) rate that the family will be getting is
i' = = = 0.0673 = 6.73%
To calculate P, n = ∞ (capitalized cost)
P = = = $371,471
Therefore, he needs to buy about $371,500 of life insurance.
15-3
2. 212 Chapter 15 Inflation
A European investor lives near to one of his country’s borders. In Country A (where he lives), an
8% interest rate is offered in banks, and the inflation rate is 3%. Country B, on the other hand, has
an inflation rate of 23%, and banks are offering 26% interest on deposits.
a) What is the real or effective interest rate that this person gets when investing in his Country?
b) This investor believes that the currency of Country B will not change in its value relative to
the value of the currency of Country A during this year. In which country would he get a
larger effective interest rate?
c) Suppose that he invests in a bank in Country B, and that his prediction was wrong. The
currency of Country B was devaluated 20% with respect to the exchange value of Country
A’s currency. What is the effective interest rate that he obtained?
Solution
a) i' = ? if i = 80%, f = 3%
i = i' + f + i'F
.08 = i' + .03 + i'(.03)
i' = 0.0485
= 4.85%
b) if investment in Country A: i'A = 0.0485
if investment in Country B: iB = 26%, fA = 3%
(note that he lives in Country A. Inflation of Country B does not affect him directly)
i'B = = = 0.2233 = 22.33%
He can get a larger effective interest rate in Country B.
c) Let X = amount originally invested in B (measured in currency A).
The amount collected at end of 1 year (measured in currency A) =
= 1.008X
the interest is then i = = 0.008
but during the year the inflation in Country A (where he lives) was 3%, therefore
i = 0.008
f = 0.03
i' = ?
i' = = -0.02136
He actually lost money (negative effective interest rate of - 2.136%).
15-4
Property, in the form of unimproved land, is purchased at a cost of $8,000 and is held for six years
when it is sold for $32,600. An average of $220 each year is paid in property tax and may be
accounted for at an interest of 12%. The income tax rate on the long term capital gain is 15% of
3. Chapter 15 Inflation 213
the gain. Inflation during the period is 7% per year. What is the annual rate of return for this
investment?
Solution
Long term gains = 32,600 - 8,000 = 24,600
Tax on long-term gain = .15 x 24,600 = 3,690
Property tax = 220(F/A, 12%, 6) = 1,785.30
Adjusted FW = 32,600 - 3,690 - 1785.30 = 27,624.70
also FW = 8,000(1 + ieq)6
15-5
The auto of your dreams costs $20,000 today. You have found a way to earn 15% tax free on an
“auto purchase account”. If you expect the cost of your dream auto to increase by 10% per year,
how much would you need to deposit in the “auto purchase account” to provide for the purchase
of the auto 5 years from now?
Solution
Cost of auto 5 years hence: F = P(1 + inflation rate)n
= 20,000 (1 + 0.10)5
= $32,210
Amount to deposit now to have $32,210 five years hence
P = F(P/F, i%, n) = 32,210(P/F, 15%, 5) = $16,014.81
15-6
On January 1, 1975 the National Price Index was 208.5, and on January 1, 1985 it was 516.71.
What was the inflation rate, compounded annually, over that 10-year period? If that rate continues
to hold for the next 10 years, what National Price Index can be expected on January 1, 1995?
Solution
Set NPW = 0
0 = -208.5 + 516.71(P/F, if, 10)
(P/F, if, 10) =
= 0.4035
4. 214 Chapter 15 Inflation
From interest tables the P/F factor at 9% = 0.4224
10% = 0.3855 ∴ 9% < if < 10%
By interpolation if = 9.51%
National Price Index1995 = 516.71(1 + 0.0951)10
= 1,281.69
15-7
An electronics store offers two options to buy a new laptop computer that has a price of $440.00.
A customer can either pay cash and immediately receive a discount of $49.00 or she can pay for
the computer on an installment plan. The installment plan has a nominal rate of 12% compounded
bi-yearly and requires an initial down payment of $44.00 followed by four equal payments
(principle and interest) every six months for two years.
If for the typical customer the cost of money is 5%, what is the maximum effective annual
inflation rate for the next two years that would make paying cash preferred to paying installments?
All figures above are quoted in time zero dollars.
Solution
The monthly payments in nominal dollars if the installment plan was selected would be
(-440 + 44)(A/P, 6%, 4) = -$114.28
The breakeven inflation rate is that such that
NPVBUY = NPVINSTALL or NPVBUY - INSTALL = 0
NPVB - I = ((-440 + 49) + 44) + 114.28(P/A, i1/2, 4) = 0
(P/A, i1/2, 4) = 3.0364 therefore the nominal effective semi-annual cost of money would have
to be i1/2 = .115. The nominal effective annual rate would be i = (1.115)2
– 1 = 0.2432
The effective annual inflation rate can now be computed from the formula
(1.2432) = (1.05) (1 + f)
f = .1840
15-8
An automobile that cost $19,500 in 2004 has an equivalent model four years later in 2008 that cost
$22,250. If inflation is considered the cause of the increase, what was the average annual rate of
inflation?
Solution
F = P(1 + if)n
22,250 = 19,500(1 + if)4
5. Chapter 15 Inflation 215
= (1 + if)4
1 + if = (1.141)1/4
1 + if = 1.0335
if = 3.35%
15-9
A machine has a first cost of $100,000 (in today’s dollar) and a salvage value of $20,000 (in then
current dollars) at the end of its ten year life. Each year it will eliminate one full-time worker. A
worker costs $30,000 (today’s dollars) in salary and benefits. Labor costs are expected to escalate
at 10% per year. Operating and maintenance costs will be $10,000 per year (today’s dollars) and
will escalate at 7% per year.
Construct a table showing before-tax cash flows in current dollars, and in today’s dollars. The
inflation rate is 7%.
Solution
End of Current Dollars Today’s
Year Savings O & M Capital Total Dollar’s
0 -100,000 -100,000 -100,000
1 33,000 -10,700 22,300 20,841
2 36,300 -11,449 24,851 21,706
3 39,930 -12,250 27,680 22,595
4 43,923 -13,108 30,815 23,509
5 48,315 -14,026 34,290 24,448
6 53,147 -15,007 38,140 25,414
7 58,462 -16,058 42,404 26,407
8 64,308 -17,182 47,126 27,428
9 70,738 -18,385 52,354 28,477
10 77,812 -19,672 20,000 78,141 39,723
15-10
A project has been analyzed assuming 6% inflation and is found to have a monetary internal rate
of return (IRR) of 22%. What is the real IRR for the project?
Solution
Real IRR = (1.22)/(1.06) - 1 = 0.1509 or 15.09%
15-11
A company requires a real MARR of 12%. What monetary MARR should they use if inflation is
expected to be 7%?
Solution
Monetary MARR = (1.12)(1.07) - 1 = 0.1984 or 19.84%
6. 216 Chapter 15 Inflation
15-12
The real interest rate is 4%. The inflation rate is 8%. What is the apparent interest rate?
Solution
i = i' + f + i'f
= 0.04 + 0.08 + 0.04(0.08) = 12.32%
15-13
A lot purchased for $4,500 is held for five years and sold for $13,500. The average annual
property tax is $45 and may be accounted for at an interest rate of 12%. The income tax rate on
the long term capital gain is 15% of the gain. What is the rate of return on the investment if the
allowance for inflation is treated at an average annual rate of 7%?
Solution
Long term gain = 13,500 - 4,500 = 9,000
Tax on long term gain = (.15)(9,000) = 1,350
Property tax = 45(F/A, 12%, 5) = 285.89
Adjusted FW = 13,500 - 1,350 - 285.89 = 11,864.12
also FW = 4,500(1 + ieq)5
15-14
A solar energy book gives values for a solar system as follows: initial cost, $6,500; initial fuel
savings, $500/year; expected life, 15 years; value of money, 10%; inflation, 12%; and incremental
income tax rate, 25%. If we define the payback condition as the time required for the present
worth of the accumulated benefit to equal the accumulated present worth of the system cost, what
is the time required to reach the payback condition? Since the income tax benefit is related to the
annual interest expense, treat it as a reduction of the annual cost.
Solution
Annualizing P: A = 6,500(A/P, 10%, 15)
= $854.75
1 + iC = (1.10)(1 + 0.25 × 0.10) = 1.1275
PW of costs = 854.75(P/A, 12.75%, 15) = 5,595.82
7. Chapter 15 Inflation 217
1 + ieq = = 1.018
The solution strategy is to find the time for the PW of benefits to equal PW of cost. When the
combined effect of the two rates on a distributed A amount are opposed then the net effect
retains the direction of the longer rate. The inflation rate is greater than the time value of
money, which is abnormal. To solve this problem, find the PW of benefit, and to do that we
must get FW of the equivalent rate, ieq.
Try 10 years: FW = 500(F/A, 1.8%, 10) = 500 (10.850) = $5,425.06
Try 11 years: FW = 500(F/A, 1.8%, 11) = 500 (12.045) = $6,022.72
10 years < Payback < 11 years By interpolation payback = 10.3 years
15-15
Compute the internal rate of return based on constant (Year 0) dollars for the following after-tax
cash flow given in current or actual dollars. Inflation is assumed to be 7% per year. (Round to the
nearest dollar.)
After Tax Cash Flow
Year In Actual Dollars
1998 (Yr 0) -$10,000
1999 3,745
2000 4,007
2001 4,288
2002 4,588
Solution
After Tax Cash Flow
Year In Constant Dollars
1998 (0) -$10,000
1999 (1) 3,745(1.07)-1
= 3,500
2000 (2) 4,007(1.02)-2
= 3,500
2001 (3) 4,288(1.07)-3
= 3,500
2002 (4) 4,588(1.07)-4
= 3,500
NPW = 0 at IRR
0 = -10,000 + 3,500(P/A, i%, 4)
(P/A, i%, 4) = 10,000/3,500
= 2.857
Searching the interest tables where n = 4, i = IRR = 15%
8. 218 Chapter 15 Inflation
15-16
The capital cost of a wastewater treatment plant for a small town of 6,000 people was estimated to
be about $85/person in 1969. If a modest estimate of the rate of inflation is 5.5% for the period to
1984, what is the per capita capital cost of the treatment plant in 1984?
Solution
F = P(1+ if)n
= 85(1+.055)15
= 85(2.232)
= $189.76
15-17
Minor Oil Co. owns several gas wells and is negotiating a 10-year contract to sell the gas from
these wells to Major Oil Co. They are negotiating on the price of the gas the first year, per
thousand cubic feet (KCF), and on the escalation clause, the percentage rate of increase in the
price every year thereafter. Minor expects the wells to produce 33,000 KCF the first year and to
decline at the rate of 18% every year thereafter. Minor has agreed to spend $500,000 now to lay
pipelines from each well to Major’s nearby refinery. What should the minimum price be the first
year and what should the escalation rate be if Minor wants their revenue each year to remain
constant (uniform) over the life of the contract. Assume an end-of-year convention and a
minimum attractive rate of return (MARR) of 15%.
Solution
Required annual income to earn the 15% MARR on $500,000:
EAB = 500,000(A/P, 15%, 10) = $99,650.
First year price = $99,650/33,000 = $3.02/KCF
Annual production declines (1 - 0.18) of initial rate each year.
Let f = required annual escalation rate
Then (1 - 0.18)(1+f) = 1 to keep the revenue constant
f = - 1
= 0.2195/year
15-18
Jack purchases a lot for $40,000 cash and plans to sell it after 5 years. What should he sell it for if
he wants a 20% before-tax rate of return, after taking the 5% annual inflation rate into account?
Solution
F = 40,000(F/P, 20%, 5)(F/P, 5%, 5)
9. Chapter 15 Inflation 219
= $126,988
15-19
Undeveloped property near the planned site of an interstate highway is estimated to be worth
$48,000 in six years when the construction of the highway is completed. Consider a 15% capital
gains tax on the gain, an annual property tax of 0.85% of the purchase price, an annual inflation
rate of 7%, and an expected return of 15% on the investment. What is the indicated maximum
purchase price now?
Solution
Let X = purchase cost
1 + ieq = (1.15)(1.07) = 1.231
Annual property tax = .0085X
FW of property tax = .0085X(F/A, 23.1%, 6) = .0909X
Adjusted return = 48,000 - .15(48,000 - X) - .0909X
Also = X(1.231)6
= 3.48X
Therefore 40,800 + .15 X - .0909X = 3.48X
X = $11,927 purchase price
15-20
A solar system costs $6500 initially and qualifies for a federal tax credit (40% of cost, not to
exceed $4,000). The cost of money is 10%, and inflation is expected to be 7% during the life of
the system. The expected life of the system is 15 years with zero salvage value. The homeowner
is in the 40% income tax bracket. The initial fuel saving is estimated at $500 for the first year and
will increase in response to inflation. The annual maintenance cost of the system is established at
5% of the annualized cost of the system. What is the time required for the payback condition to be
reached for this investment?
Solution
Adjust initial cost by tax credit: P = .60(6,500) = 3,900
Annualized cost: A = 3,900(A/P, 10%, 15) = 512.85
1 + ic = = 1.0895 1 +im = 1.05 represents maintenance charge as a rate
PW of costs = 512.85(P/A, 8.95%, 15) = 512.85(8.086) = 4,146.67
1 + ieq = (1 + i)/(1 + if) = 1.10/1.07 = 1.028
Try 9 years: PW = 500 (P/A, 2.8%, n) = 500 (7.868) = $3,934.18
Try 10 years: PW = 500 (P/A, 2.8%, n) = 500 (8.618) = $4,308.97
9 years < Payback < 10 years By interpolation payback = 9.6 years
10. 220 Chapter 15 Inflation
15-21
The net cost of a solar system for a home is $8,000 and it is expected to last 20 years. If the value
of money is 10%, inflation is expected to be 8%, and the initial annual fuel saving is $750, what is
the time for the payback condition to be reached for the system? Assume the homeowner is in the
30% income tax bracket.
Solution
Annualize P: A = 8,000 (A/P, 10%, 20) = 940
1 + ic = (1.10)(1 + .10 x .30) = 1.133
PW of Cost = 940(P/A, 13.3%, 20) = 940(6.900) = 6,486
1 + ieq = (1 + i)/(1 + if) = 1.10/1.08 = 1.0185
Try 9 years: PW = 940(P/A, 1.85%, n) = $6,171
Try 10 years: PW = 940(P/A, 1.85%, n) = $6,790
9 years < Payback < 10 years By interpolation payback = 9.5 years
15-22
An undeveloped percent of land in Gibson County, Tennessee was purchased in 1980 for $4,850.
The property tax was $8 for the first year and is assumed to have increased by $2 per year each
year thereafter. The capital gain tax is 13.6% of long-term capital gain. Inflation for the period is
an 8% annual rate. A 16% rate of return on the investment is desired. What is the required sale
price in 1985?
Solution
1 + ieq = (1.16)(1.08) = 1.2528
FW of property tax = [8 + 2(A/G, 25.28%, 5)] [F/A, 25.28%, 5]
= [8+ 2(3.12)] [8.252]
= 91.74
Let X = selling price
Long-term capital gains tax = 0.136(X - 4,850) = .136X - 659.60
Adjusted return = X - [.136X - 659.60 + 91.74] = .864X + 567.86
Also = 4,850(1.2528) = 14,967.54
.864X + 567.86 = 14,967.54
.864X = 14,399.68
X = $16,666.31 selling price
15-23
The apparent interest rate is 9.18% and the real interest rate is 6%. The inflation rate is
11. Chapter 15 Inflation 221
a. 3.00%
b. 3.18%
c. 5.30%
d. 6.00%
Solution
i = i' + f + i'f
.0918 = .06 + f + .06f
.0318 = 1.06f
f = .03
The answer is a.
15-24
An investor is considering the purchase of a bond. The bond has a face value of $1,000, an
interest rate of 6%, pays interest once a year, and matures in 8 years. This investor’s real MARR
is 25%. If the investor expects an inflation rate of 4% per year for the next 8 years, how much
should he be willing to pay for the bond?
a. $250.50
b. $367.50
c. $384.74
d. $1,000.00
Solution
In order to earn a real 25% return with inflation of 4%, the nominal MARR must be
equal to (1.25)(1.04) - 1 = 30%,
NPV = 0 at IRR
0 = -F.C. + 60(P/A, 30%, 8) + 1,000(P/F, 30%, 8)
F.C. = $250.50
The answer is a.
15-25
An investment in undeveloped land of $9,000 was held for four years and sold for $21,250.
During this time property tax was paid that was, on the average, 0.4% of the purchase price.
Inflation in this time period averaged 7% and the income tax was 15.2% of the long-term capital
gain. What rate of return was obtained on the investment?
Solution
Long-term capital gains tax = 0.152(21,250 - 9,000) = $1,862
12. 222 Chapter 15 Inflation
Property tax = .004 × 9,000 = $36/year
FW of property tax = 36(F/A, ieq, 4)
1 + ieq = = 1.2115 (1st
estimate)
FW of property tax = 36(F/A, 21.15%, 4) = 36(5.47) = $197
1 + ieq = = 1.2084 (2nd
estimate)
Rate of return = -1 = 12.9%
15-26
A company has designed a VLSI circuit and a production system to manufacture it. It is believed
that it can sell 100,00 circuits per year if the price in then-current dollars is cut 20% per year (for
example, if the unit price in the first year is $100, then the price in years 2 through 5 would be
$80, $64, $51.20, and $40.96). The required revenue for the five years is $2,500.00 per year in
today’s dollars. The real and monetary costs of capital are 8.8% and 16.416%, respectively. What
should the then-current dollar selling price be in each of the years 1 through 5?
Solution
Let R be the required revenue in year 1, then the required revenue in years 2 through 5 is .8R,
.64R, .512R, and .0496R. Since these are in then-current $,
(2,500,000)(P/A, 8.8%, 5) = R(1.16416)-1
+ 0.8R(1.16416)-2
+ .064R(1.16416)-3
+ 0.512R(1.16416)-4
+ 0.4096R(1.16416)-5
9,774,800 = 2.32523R
R = 4,203,804 or a unit price of $42.04 in year 1
$33.63 in year 2
$26.90 in year 3
$21.52 in year 4
$17.22 in year 5
15-27
An electronic device cost $1,250 in 2001. If inflation has averaged 2% each year, the price of the
device in 2008 is closet to
a. $1,400
b. $1,408
c. $1,425
d. $1,436
Solution
13. Chapter 15 Inflation 223
F = (1 + f)n
F = (1 +.02)7
= $1,435.86
The answer is d.
15-28
A bond that pays no interest is called a zero-coupon bond. A $10,000 zero-coupon bond that
matures in ten years can be purchased today. If the expected annual rate of inflation is 3% and the
buyer’s unadjusted MARR is 8%, what is the maximum that should be paid for the bond?
Solution
i = i' + f + i'f
= .08 + .03 + .08(.03)
= .1124
P = 10,000(1 + .1124)-10
= $3,446.59
15-29
Sylvia B. bought an 8% tax-free municipal bond. The cost of the bond was $10,000 and it will
pay $800 each year for 20 years. The bond will mature at that time and return the original
$10,000. If inflation is expected to average 3% during the period, what is the inflation adjusted
rate of return?
a. 2.40%
b. 4.85%
c. 8.00%
d. 11.24%
Solution
i = 8% f = 3%
i = i' + f + i'f
.08 = i' + .03 + i'(.03)
i' = .0485 = 4.85%
The answer is b.
15-30
A vacant lot is purchased for $20,000. After five years the lot is to be offered for sale. If the
buyer requires a before tax return on investments of 15% and inflation has averaged 4% per year
over the five-year period the required selling price is nearest to
a. $30,650
b. $31,500
c. $48,950
14. 224 Chapter 15 Inflation
d. $62,750
Solution
F = 20,000(F/P, 4%, 5)(F/P, 15%, 5)
= $48,947.74
The answer is c.