1. The document discusses the concepts of time value of money, interest rates, and different types of interest including simple and compound interest.
2. It provides formulas for calculating future value and present value using simple and compound interest, and examples of applying these formulas.
3. The document also covers annuities, explaining the differences between ordinary annuities and annuities due. It provides formulas and examples for calculating future and present value of both types of annuities.
1. The chapter discusses the concepts of working capital management, including defining working capital and its components.
2. It analyzes the trade-offs between liquidity, profitability and risk for different levels of current assets. Specifically, it notes profitability varies inversely with liquidity while profitability increases with risk.
3. The chapter also covers approaches to financing current assets, such as hedging short-term assets with short-term financing versus using more long-term financing, and how the current assets decision interacts with the liability structure choice.
The presentation slide is on stock valuation. We have tried to present the various techniques to stock valuation under which different methods are discussed with illustrations. Key concepts:
Zero Growth Model
Balance sheet Technique
Constant Growth Model
Two-stage growth Model
Feel Free to comment.
The document discusses time value of money concepts including present value and future value. It explains that money received today is worth more than the same amount in the future due to factors like risk, inflation, and investment opportunities. It provides formulas for simple and compound interest as well as future and present value calculations. Examples are given to demonstrate compound interest, rule of 72, annuities, and amortizing a loan over time.
Bond valuation involves calculating the present value of a bond's future interest payments and principal repayment. There are several types of bonds that differ in issuer and features. Bonds are issued by corporations and governments to raise funds for projects while managing costs and diversifying sources of capital. Investors face various risks when purchasing bonds like interest rate, default, market and call risks. Key metrics for bonds include current yield, yield to maturity, yield to call and realized yield, which are calculated using principles of time value of money. Bond prices generally move inversely to interest rates and bonds with longer maturities are more sensitive to interest rate changes. Price impacts from interest rate changes are also not symmetrical. Lower coupon bonds experience greater price volatility from
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 summarizes key concepts about bonds from Chapter 7. It defines different types of bonds like debentures, mortgage bonds, and convertible bonds. It also explains important bond terminology such as par value, coupon interest rate, maturity, and bond ratings. Finally, it discusses methods of valuing bonds and factors that influence their value and ratings.
Cost of capital ppt @ bec doms on financeBabasab Patil
The document discusses the cost of capital and how it is calculated. It can be summarized as:
1) The cost of capital is a weighted average of the costs of a firm's capital components (debt, preferred stock, common equity), weighted by the proportion of each in the firm's target capital structure.
2) The cost of each capital component is calculated based on its market yield after adjusting for taxes (for debt) and flotation costs.
3) The weighted average cost of capital (WACC) provides a benchmark to evaluate whether potential projects should be undertaken based on whether their returns exceed the WACC.
This document summarizes key concepts from Chapter 5 of the textbook "Fundamentals of Financial Management" regarding risk and return. It defines return, expected return, risk, and standard deviation as measures of risk. It provides examples of how to calculate expected return and standard deviation for discrete distributions. It also discusses risk attitudes, portfolio return and risk, systematic and unsystematic risk, and the Capital Asset Pricing Model.
1. The chapter discusses the concepts of working capital management, including defining working capital and its components.
2. It analyzes the trade-offs between liquidity, profitability and risk for different levels of current assets. Specifically, it notes profitability varies inversely with liquidity while profitability increases with risk.
3. The chapter also covers approaches to financing current assets, such as hedging short-term assets with short-term financing versus using more long-term financing, and how the current assets decision interacts with the liability structure choice.
The presentation slide is on stock valuation. We have tried to present the various techniques to stock valuation under which different methods are discussed with illustrations. Key concepts:
Zero Growth Model
Balance sheet Technique
Constant Growth Model
Two-stage growth Model
Feel Free to comment.
The document discusses time value of money concepts including present value and future value. It explains that money received today is worth more than the same amount in the future due to factors like risk, inflation, and investment opportunities. It provides formulas for simple and compound interest as well as future and present value calculations. Examples are given to demonstrate compound interest, rule of 72, annuities, and amortizing a loan over time.
Bond valuation involves calculating the present value of a bond's future interest payments and principal repayment. There are several types of bonds that differ in issuer and features. Bonds are issued by corporations and governments to raise funds for projects while managing costs and diversifying sources of capital. Investors face various risks when purchasing bonds like interest rate, default, market and call risks. Key metrics for bonds include current yield, yield to maturity, yield to call and realized yield, which are calculated using principles of time value of money. Bond prices generally move inversely to interest rates and bonds with longer maturities are more sensitive to interest rate changes. Price impacts from interest rate changes are also not symmetrical. Lower coupon bonds experience greater price volatility from
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 summarizes key concepts about bonds from Chapter 7. It defines different types of bonds like debentures, mortgage bonds, and convertible bonds. It also explains important bond terminology such as par value, coupon interest rate, maturity, and bond ratings. Finally, it discusses methods of valuing bonds and factors that influence their value and ratings.
Cost of capital ppt @ bec doms on financeBabasab Patil
The document discusses the cost of capital and how it is calculated. It can be summarized as:
1) The cost of capital is a weighted average of the costs of a firm's capital components (debt, preferred stock, common equity), weighted by the proportion of each in the firm's target capital structure.
2) The cost of each capital component is calculated based on its market yield after adjusting for taxes (for debt) and flotation costs.
3) The weighted average cost of capital (WACC) provides a benchmark to evaluate whether potential projects should be undertaken based on whether their returns exceed the WACC.
This document summarizes key concepts from Chapter 5 of the textbook "Fundamentals of Financial Management" regarding risk and return. It defines return, expected return, risk, and standard deviation as measures of risk. It provides examples of how to calculate expected return and standard deviation for discrete distributions. It also discusses risk attitudes, portfolio return and risk, systematic and unsystematic risk, and the Capital Asset Pricing Model.
This document provides solutions to capital budgeting problems involving techniques like payback period, net present value (NPV), and internal rate of return (IRR). For problem E10-1, the payback periods for two projects are provided. For other problems, the cash flows for projects are input into a financial calculator to calculate NPV or IRR in order to evaluate which projects should be accepted. The solutions demonstrate how to apply these capital budgeting techniques to make investment decisions.
This document discusses the time value of money concepts of simple and compound interest, present and future value, and annuities. It provides formulas and examples for calculating future and present value of single deposits using tables or calculators. It also covers calculating the future value of annuities and using annuity tables. Key concepts covered include compound interest earning interest on interest, and the higher growth it provides over time compared to simple interest.
What is the 'Time Value of Money - TVM'
The time value of money (TVM) is the idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. TVM is also referred to as present discounted value.
BREAKING DOWN 'Time Value of Money - TVM'
Money deposited in a savings account earns a certain interest rate. Rational investors prefer to receive money today rather than the same amount of money in the future because of money's potential to grow in value over a given period of time. Money earning an interest rate is said to be compounding in value.
BREAKING DOWN 'Compound Interest'
Compound Interest Formula
Compound interest is calculated by multiplying the principal amount by one plus the annual interest rate raised to the number of compound periods minus one.The total initial amount of the loan is then subtracted from the resulting value.
The document discusses the fundamental time value of money concepts in finance. It defines future value as the value a sum grows to with interest over time, and present value as the amount needed today to be worth a future sum. The four basic concepts are future and present value of a sum, and future and present value of an annuity. Formulas are provided to calculate these values using interest rate and time period. Examples are worked through to demonstrate calculating future and present value of sums and annuities.
Time Value of Money (Financial Management)Qasim Raza
The document discusses different types of interest rates and annuities. It defines simple interest as interest paid only on the principal amount, while compound interest is interest paid on both previous interest and principal. An annuity is a series of equal payments over a period of time, with ordinary annuities having payments at the end of periods and annuity dues having payments at the beginning. The document also discusses calculating future and present values of these different financial instruments using standard formulas.
Managerial Finance By Gitman Chapter 8 solutionsQaisar Mehar
The document contains solutions to warm-up exercises and problems related to finance topics like expected return, standard deviation, coefficient of variation, portfolio analysis, and risk measurement. For a given portfolio, the expected return is calculated as the weighted average of the returns weighted by their probabilities. The standard deviation and coefficient of variation are computed to assess the risk of different assets and portfolios. Overall, the document demonstrates various calculations for key risk and return metrics used to analyze investments.
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.
This document discusses the time value of money concept in finance. It defines key terms like present value, future value, simple interest, and compound interest. It provides formulas for calculating future value and present value of single deposits. Examples are given to demonstrate calculating interest using simple interest formulas versus compound interest formulas. Tables are presented to allow looking up interest factors instead of using formulas. The document also introduces the concepts of amortization schedules and using a financial calculator for time value of money problems.
Capacity planning involves determining the maximum output rate of a process and ensuring there is enough capacity to meet future demand. It is done both in the long-term, through capacity timing and sizing strategies, and short-term through constraint management. A systematic approach to capacity planning involves estimating future capacity requirements, identifying gaps between requirements and available capacity, developing alternative plans to address gaps, and evaluating alternatives both qualitatively and quantitatively. Tools like waiting line models, simulation, and decision trees can help with complex capacity planning problems.
The document discusses risk and return in investing. It explains that equity investments like stocks historically have higher average returns of over 10% compared to debt investments like bonds that return 3-4%, but stocks are also more volatile. It defines risk as the variability of returns, and introduces the concepts of systematic risk that affects all stocks equally and unsystematic risk that is specific to individual stocks. Diversification can reduce unsystematic risk but not systematic risk. It also discusses measuring market risk through a stock's beta value, which represents its volatility relative to the overall market.
Signaling theory and window of opportunity theory are two theories of capital structure. Signaling theory suggests that managers have better information about a company's prospects than outside investors. Companies with positive prospects will avoid stock offerings, while those with negative prospects will want to issue stock to share losses. The window of opportunity theory proposes that managers time the market when issuing securities, such as issuing equity when stock prices are high and debt when interest rates are low. Capital structure choices also impact lenders and rating agencies.
1. The document discusses risk and return, defining concepts like expected return, risk, standard deviation, beta, and models like the Capital Asset Pricing Model (CAPM).
2. It provides examples of how to calculate expected return, standard deviation, and beta for both discrete and continuous probability distributions.
3. The CAPM model relates a security's expected return to market risk (beta) and the risk-free rate, stating that expected return equals the risk-free rate plus a risk premium based on beta.
cost of capital .....ch ...of financial management ..solution by MIAN MOHSIN ...mianmohsinmumtazshb
The document provides solutions to problems from Chapter 11 on the cost of capital.
It calculates the cost of various sources of capital such as debt, preferred stock, and common equity. It also calculates the weighted average cost of capital (WACC) using different capital structure weights.
Key calculations include:
1) Calculating the cost of debt using the yield to maturity method and the approximation method.
2) Calculating the cost of preferred stock as the dividend yield.
3) Calculating the cost of common equity using the capital asset pricing model.
4) Calculating the WACC using both book value and market value weights for the capital structure.
5) Exploring how
This document provides an introduction and overview of a course on introduction to finance. It includes the course title, code, list of group members, lecturer, and covers key concepts related to time value of money including future value, present value, and calculating interest rates. The document contains examples and explanations of how to calculate future value, present value, and solving for interest rates and time periods using timelines and formulas.
This document discusses concepts related to the time value of money, including present and future value calculations. It covers key topics like compound interest, discounting cash flows, loan amortization schedules, and the internal rate of return. Examples are provided to illustrate how to use formulas to calculate future values, present values, loan payments, and identify the internal rate of return for an investment project. The goal is to understand how to adjust cash flows for differences in timing and risk.
The document discusses various bond valuation concepts like coupon rate, current yield, spot interest rate, yield to maturity, yield to call, and realized yield. It provides examples to calculate these measures and explains how bond prices are determined based on factors like interest rates, time to maturity, and cash flows. Bond duration is introduced as a measure of interest rate risk exposure, and bond risks from default and changes in interest rates are explained.
The document discusses the time value of money concept. It states that time value of money refers to money received today being more valuable than the same amount received in the future. It also underpins the concept of interest. The document then provides techniques for adjusting cash flows for time value of money using discounting and compounding. It explains discounting as calculating the present value and compounding as calculating the future value of cash flows. Specific formulas and examples are given for single cash flows, annuities, and perpetuities under both discounting and compounding.
This document discusses accounts receivable and inventory management. It covers credit and collection policies including average collection period, bad debt losses, credit terms, and cash discounts. It also addresses analyzing credit applicants, determining appropriate inventory levels using methods like economic order quantity, and inventory control techniques like the ABC method. The document provides examples of how firms can evaluate relaxing credit standards and terms to increase sales while managing risks.
Financial Management: Risk and Rates of Returnpetch243
This document discusses risk and rates of return in investments. It defines different types of risk like stand-alone risk and portfolio risk. It shows how to calculate expected returns, standard deviation as a measure of risk, and the coefficient of variation to compare risk-adjusted returns. It introduces the Capital Asset Pricing Model (CAPM) and how it uses beta to measure non-diversifiable market risk and determine required rates of return based on the security market line. It provides examples of calculating betas, expected returns, and portfolio risk measures like standard deviation and required returns.
3 time value_of_money_slides - Basic Financenakomuri
The document discusses the time value of money, which is the basic principle that a dollar received today is worth more than a dollar received in the future due to opportunity costs. It defines key terms like compound interest, future value, present value, and annuities. The five learning objectives are to define the time value of money, understand its significance, learn how to calculate future and present values of cash flows, understand compounding and discounting, and work with annuities and perpetuities.
This document provides an overview of financial statement analysis. It discusses the different types of financial statements, including the balance sheet, income statement, and statement of cash flows. It also presents various ratios used in financial analysis to evaluate a firm's liquidity, leverage, coverage, activity, and profitability. These ratios are calculated for a sample company, Basket Wonders, and compared to industry averages. Trend analyses reveal declining coverage and inventory turnover ratios for Basket Wonders relative to peers. Overall, the document introduces key concepts in financial statement analysis using example ratios.
The Business,Tex,and financial environmentsZubair Arshad
Here are the likely effects of the occurrences on money and capital markets:
1. The saving rate of individuals in the country declines:
- This would decrease the supply of funds available in financial markets.
- Interest rates would likely rise as demand for funds exceeds reduced supply.
- Investment levels may fall as fewer funds are available for businesses and projects.
2. Individuals increases their savings at saving and loan associations and decreases their savings at banks:
- This would decrease the supply of funds available to banks while increasing the supply available to saving and loan associations.
- Interest rates at banks may rise as their funding decreases. Rates at saving and loan associations may fall as their funding increases.
- Banks would
This document provides solutions to capital budgeting problems involving techniques like payback period, net present value (NPV), and internal rate of return (IRR). For problem E10-1, the payback periods for two projects are provided. For other problems, the cash flows for projects are input into a financial calculator to calculate NPV or IRR in order to evaluate which projects should be accepted. The solutions demonstrate how to apply these capital budgeting techniques to make investment decisions.
This document discusses the time value of money concepts of simple and compound interest, present and future value, and annuities. It provides formulas and examples for calculating future and present value of single deposits using tables or calculators. It also covers calculating the future value of annuities and using annuity tables. Key concepts covered include compound interest earning interest on interest, and the higher growth it provides over time compared to simple interest.
What is the 'Time Value of Money - TVM'
The time value of money (TVM) is the idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. TVM is also referred to as present discounted value.
BREAKING DOWN 'Time Value of Money - TVM'
Money deposited in a savings account earns a certain interest rate. Rational investors prefer to receive money today rather than the same amount of money in the future because of money's potential to grow in value over a given period of time. Money earning an interest rate is said to be compounding in value.
BREAKING DOWN 'Compound Interest'
Compound Interest Formula
Compound interest is calculated by multiplying the principal amount by one plus the annual interest rate raised to the number of compound periods minus one.The total initial amount of the loan is then subtracted from the resulting value.
The document discusses the fundamental time value of money concepts in finance. It defines future value as the value a sum grows to with interest over time, and present value as the amount needed today to be worth a future sum. The four basic concepts are future and present value of a sum, and future and present value of an annuity. Formulas are provided to calculate these values using interest rate and time period. Examples are worked through to demonstrate calculating future and present value of sums and annuities.
Time Value of Money (Financial Management)Qasim Raza
The document discusses different types of interest rates and annuities. It defines simple interest as interest paid only on the principal amount, while compound interest is interest paid on both previous interest and principal. An annuity is a series of equal payments over a period of time, with ordinary annuities having payments at the end of periods and annuity dues having payments at the beginning. The document also discusses calculating future and present values of these different financial instruments using standard formulas.
Managerial Finance By Gitman Chapter 8 solutionsQaisar Mehar
The document contains solutions to warm-up exercises and problems related to finance topics like expected return, standard deviation, coefficient of variation, portfolio analysis, and risk measurement. For a given portfolio, the expected return is calculated as the weighted average of the returns weighted by their probabilities. The standard deviation and coefficient of variation are computed to assess the risk of different assets and portfolios. Overall, the document demonstrates various calculations for key risk and return metrics used to analyze investments.
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.
This document discusses the time value of money concept in finance. It defines key terms like present value, future value, simple interest, and compound interest. It provides formulas for calculating future value and present value of single deposits. Examples are given to demonstrate calculating interest using simple interest formulas versus compound interest formulas. Tables are presented to allow looking up interest factors instead of using formulas. The document also introduces the concepts of amortization schedules and using a financial calculator for time value of money problems.
Capacity planning involves determining the maximum output rate of a process and ensuring there is enough capacity to meet future demand. It is done both in the long-term, through capacity timing and sizing strategies, and short-term through constraint management. A systematic approach to capacity planning involves estimating future capacity requirements, identifying gaps between requirements and available capacity, developing alternative plans to address gaps, and evaluating alternatives both qualitatively and quantitatively. Tools like waiting line models, simulation, and decision trees can help with complex capacity planning problems.
The document discusses risk and return in investing. It explains that equity investments like stocks historically have higher average returns of over 10% compared to debt investments like bonds that return 3-4%, but stocks are also more volatile. It defines risk as the variability of returns, and introduces the concepts of systematic risk that affects all stocks equally and unsystematic risk that is specific to individual stocks. Diversification can reduce unsystematic risk but not systematic risk. It also discusses measuring market risk through a stock's beta value, which represents its volatility relative to the overall market.
Signaling theory and window of opportunity theory are two theories of capital structure. Signaling theory suggests that managers have better information about a company's prospects than outside investors. Companies with positive prospects will avoid stock offerings, while those with negative prospects will want to issue stock to share losses. The window of opportunity theory proposes that managers time the market when issuing securities, such as issuing equity when stock prices are high and debt when interest rates are low. Capital structure choices also impact lenders and rating agencies.
1. The document discusses risk and return, defining concepts like expected return, risk, standard deviation, beta, and models like the Capital Asset Pricing Model (CAPM).
2. It provides examples of how to calculate expected return, standard deviation, and beta for both discrete and continuous probability distributions.
3. The CAPM model relates a security's expected return to market risk (beta) and the risk-free rate, stating that expected return equals the risk-free rate plus a risk premium based on beta.
cost of capital .....ch ...of financial management ..solution by MIAN MOHSIN ...mianmohsinmumtazshb
The document provides solutions to problems from Chapter 11 on the cost of capital.
It calculates the cost of various sources of capital such as debt, preferred stock, and common equity. It also calculates the weighted average cost of capital (WACC) using different capital structure weights.
Key calculations include:
1) Calculating the cost of debt using the yield to maturity method and the approximation method.
2) Calculating the cost of preferred stock as the dividend yield.
3) Calculating the cost of common equity using the capital asset pricing model.
4) Calculating the WACC using both book value and market value weights for the capital structure.
5) Exploring how
This document provides an introduction and overview of a course on introduction to finance. It includes the course title, code, list of group members, lecturer, and covers key concepts related to time value of money including future value, present value, and calculating interest rates. The document contains examples and explanations of how to calculate future value, present value, and solving for interest rates and time periods using timelines and formulas.
This document discusses concepts related to the time value of money, including present and future value calculations. It covers key topics like compound interest, discounting cash flows, loan amortization schedules, and the internal rate of return. Examples are provided to illustrate how to use formulas to calculate future values, present values, loan payments, and identify the internal rate of return for an investment project. The goal is to understand how to adjust cash flows for differences in timing and risk.
The document discusses various bond valuation concepts like coupon rate, current yield, spot interest rate, yield to maturity, yield to call, and realized yield. It provides examples to calculate these measures and explains how bond prices are determined based on factors like interest rates, time to maturity, and cash flows. Bond duration is introduced as a measure of interest rate risk exposure, and bond risks from default and changes in interest rates are explained.
The document discusses the time value of money concept. It states that time value of money refers to money received today being more valuable than the same amount received in the future. It also underpins the concept of interest. The document then provides techniques for adjusting cash flows for time value of money using discounting and compounding. It explains discounting as calculating the present value and compounding as calculating the future value of cash flows. Specific formulas and examples are given for single cash flows, annuities, and perpetuities under both discounting and compounding.
This document discusses accounts receivable and inventory management. It covers credit and collection policies including average collection period, bad debt losses, credit terms, and cash discounts. It also addresses analyzing credit applicants, determining appropriate inventory levels using methods like economic order quantity, and inventory control techniques like the ABC method. The document provides examples of how firms can evaluate relaxing credit standards and terms to increase sales while managing risks.
Financial Management: Risk and Rates of Returnpetch243
This document discusses risk and rates of return in investments. It defines different types of risk like stand-alone risk and portfolio risk. It shows how to calculate expected returns, standard deviation as a measure of risk, and the coefficient of variation to compare risk-adjusted returns. It introduces the Capital Asset Pricing Model (CAPM) and how it uses beta to measure non-diversifiable market risk and determine required rates of return based on the security market line. It provides examples of calculating betas, expected returns, and portfolio risk measures like standard deviation and required returns.
3 time value_of_money_slides - Basic Financenakomuri
The document discusses the time value of money, which is the basic principle that a dollar received today is worth more than a dollar received in the future due to opportunity costs. It defines key terms like compound interest, future value, present value, and annuities. The five learning objectives are to define the time value of money, understand its significance, learn how to calculate future and present values of cash flows, understand compounding and discounting, and work with annuities and perpetuities.
This document provides an overview of financial statement analysis. It discusses the different types of financial statements, including the balance sheet, income statement, and statement of cash flows. It also presents various ratios used in financial analysis to evaluate a firm's liquidity, leverage, coverage, activity, and profitability. These ratios are calculated for a sample company, Basket Wonders, and compared to industry averages. Trend analyses reveal declining coverage and inventory turnover ratios for Basket Wonders relative to peers. Overall, the document introduces key concepts in financial statement analysis using example ratios.
The Business,Tex,and financial environmentsZubair Arshad
Here are the likely effects of the occurrences on money and capital markets:
1. The saving rate of individuals in the country declines:
- This would decrease the supply of funds available in financial markets.
- Interest rates would likely rise as demand for funds exceeds reduced supply.
- Investment levels may fall as fewer funds are available for businesses and projects.
2. Individuals increases their savings at saving and loan associations and decreases their savings at banks:
- This would decrease the supply of funds available to banks while increasing the supply available to saving and loan associations.
- Interest rates at banks may rise as their funding decreases. Rates at saving and loan associations may fall as their funding increases.
- Banks would
Financial management concerns the acquisition, financing, and management of a firm's assets to maximize shareholder wealth. It involves three key decisions: investment decisions about what assets to acquire and invest in; financing decisions about how to finance those assets; and asset management decisions about efficiently managing existing assets. The goal of financial management is to maximize shareholder value by increasing the share price. While alternative goals like profit or earnings per share maximization are imperfect, shareholder wealth maximization properly accounts for factors like risk, timing of returns, and dividend policy. In the modern corporation, management acts as an agent for shareholders.
Distribution Customer Service and LogisticsZubair Arshad
Logistics involves transporting, storing, and handling goods to meet customer needs. Physical distribution is another term for logistics. Physical distribution provides goods at the right time and place for customers and allows possession of goods. It typically accounts for half of total marketing costs. More efficient physical distribution can increase profits, lower prices, or improve service. The document discusses key aspects of physical distribution like transportation, storage, coordination, and use of technology.
This document discusses various concepts related to the valuation of long-term securities such as bonds, preferred stock, and common stock. It begins by defining different concepts of value such as liquidation value, going-concern value, book value, market value, and intrinsic value. It then covers the valuation of different types of bonds including perpetual bonds, coupon bonds, zero-coupon bonds, and the adjustments needed for semiannual compounding. The valuation of preferred stock is presented as a perpetuity. Common stock valuation is discussed using the dividend valuation model and its variations such as the constant growth model, zero growth model, and growth phases model. Examples are provided to illustrate the application of these valuation models.
The document provides an overview of key concepts related to the time value of money, including compound and simple interest, present and future value calculations, and annuities. It outlines learning objectives, defines key terms, shows examples of calculations, and provides guidance on using formulas and tables to solve time value of money problems for single deposits, annuities, and other scenarios.
This document provides an introduction to investment terminology and concepts. It defines key terms like finance, investment, investor, and differentiates investment from speculation and gambling. It also outlines the major participants in the financial system including households, businesses, governments, banks, insurers, pension funds, and mutual funds. Finally, it describes different types of financial securities and markets.
Computer hardware devices include webcams, scanners, mice, speakers, trackballs, and light pens. Webcams connect via USB or network and are used for video calls and conferencing. Scanners optically scan images and documents into digital formats. Mice are pointing devices that detect motion to move a cursor. Speakers have internal amplifiers and audio jacks. Trackballs contain ball and sensors to detect rotation for cursor movement. Light pens allow pointing directly on CRT displays.
https://rb.gy/n89u77
Discuss the role of time value in finance, the use of computational tools, and the basic patterns of cash flow. Understand the concepts of future value and present value, their calculation for single amounts, and the relationship between them.
The document describes key concepts related to the time value of money, including compound and simple interest, present and future value calculations, and valuation of annuities. It defines ordinary and annuity due cash flows and provides formulas and examples for calculating future and present value of single amounts, as well as future and present value of annuities using interest tables.
The document discusses the time value of money and compound interest. It explains key concepts like simple vs compound interest, present and future value, and ordinary annuities. Examples are provided to demonstrate how to calculate future and present value of single deposits and annuities using formulas, tables and calculators. The reader will learn how interest allows money to grow over time and the importance of compounding interest.
This document provides an overview of chapter 3 which covers the time value of money. It discusses key concepts like simple and compound interest, present and future value, and annuities. The learning objectives are to understand how interest rates can be used to adjust the value of cash flows over time and calculate future and present values for various cash flow scenarios. Formulas, examples, and the use of interest tables and calculators are presented.
This document provides an overview of discounted cash flow valuation concepts including time value of money, compounding and discounting rates, and calculations for present and future value of single and multiple cash flows. Key points covered include:
- Calculating future and present value of single cash flows
- Differences between simple and compound interest
- Effective annual rates for different compounding periods
- Formulas and examples for perpetuities, growing perpetuities, and ordinary annuities
- Learning objectives are to understand time value concepts and perform cash flow calculations for valuation
This document discusses the time value of money concept through examples of simple and compound interest, present and future value calculations for single amounts, annuities, and mixed cash flows. It provides formulas, examples, and guidelines for solving time value of money problems involving deposits, loans, and returns over time discounted or compounded at given interest rates.
The document provides an overview of time value of money concepts including compound and simple interest, present and future value calculations, and annuities. It defines key terms, shows examples of calculations using formulas and tables, and step-by-step solutions to practice problems involving deposits, loans, and determining unknown values. The document aims to help readers understand how to adjust cash flows to a single point in time using interest rates and calculate future and present values.
The document discusses the concepts of time value of money, interest, and annuities. It defines key terms like present value, future value, simple interest, compound interest, and ordinary annuity. It provides examples of calculating simple interest, compound interest, future value, present value, and future value of annuities using standard formulas. Various questions and solutions are given to illustrate time value of money calculations.
Here are the steps to solve this problem:
FV = PV(1 + r/n)nt
FV = $4,000(1 + 0.09)11
FV = $4,000(2.1435)
FV = $8,574
The future value of $4,000 invested for 11 years at 9% compounded annually is $8,574.
The document discusses time value of money concepts including future value, present value, compound interest, and annuities. It provides examples of using the compound interest formula and financial calculators to solve for future value, present value, interest rates, number of periods, and payment amounts of cash flows. It also discusses amortization tables and constructing an amortization schedule for a loan.
This document discusses the time value of money concepts of interest, present value, and future value. It provides examples of calculating simple and compound interest, as well as the present and future value of single deposits and annuities. Formulas for simple and compound interest, present value, future value, ordinary annuities, and annuities due are presented along with examples of applying the concepts and formulas to story problems. Tables of interest rate factors are also included to allow for lookup of present and future values.
Time value of money approaches in the financial managementHabibullah Qayumi
The document discusses the time value of money concept. It explains that money received sooner rather than later allows one to use the funds for investment or consumption purposes. A dollar today is worth more than a dollar tomorrow because it can earn interest if invested. The time value of money depends on interest rates and the number of time periods. Formulas for simple and compound interest, future value, present value, and interest rates are provided. Examples are given to illustrate how to calculate future and present values using the time value of money formulas.
This document discusses the time value of money concepts including simple and compound interest, future and present value, and annuities. It provides formulas, examples, and explanations of how to calculate future and present value for single deposits and annuities using a financial calculator or tables. Key points covered include the differences between simple and compound interest, ordinary annuities versus annuities due, and using the future and present value of interest factors tables to solve time value of money problems.
This document provides an overview of time value of money concepts including simple and compound interest, future and present value, and annuities. Key points covered include:
- Compound interest earns interest on previous interest amounts as well as the principal, resulting in higher total returns over time compared to simple interest.
- Future value and present value formulas allow calculating the value of a single deposit or withdrawal at a future or present point in time using a given interest rate.
- Annuities represent a series of equal periodic cash flows, and formulas are provided to calculate the future and present value of ordinary annuities and annuities due.
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.
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 is a lecture on time value of money which explains the topic time value of money in a very easy and simple way... it also explains some examples on the topic... plus definition of rate of return, real rate of return, inflation premium, nominal interest rate,market risk, maturity risk,liquidity risk,and default risk,
This document provides an overview of key concepts related to accounting and the time value of money. It discusses the basic premise that a dollar today is worth more than a dollar in the future due to interest-earning potential. It also covers compound interest calculation methods and the use of interest tables to solve for unknown variables. Specific topics covered include single-sum problems involving future and present value, annuities, and the calculation of future and present value for both ordinary annuities and annuities due. Worked examples are provided throughout to illustrate the application of time value of money formulas and tables.
- Time value of money refers to the concept that money received today is worth more than the same amount in the future due to its potential to earn interest.
- There are four key financial concepts related to time value of money: future value of a single amount, present value of a single amount, future value of an annuity, and present value of an annuity.
- Compounding interest over long periods of time can significantly increase the value of an investment through the power of compounding, as demonstrated by the example of $1 growing to over $2000 in the stock market over 75 years.
Discover 100 ways to lose 100 pounds, feel better & become healthier without taking any magical pills, buying an expensive gym membeship or going on a dangrious fed diet. Inside this ebook you will discover the topics about what you should always do before you sit down to eat if you really want to lose weight fast! what foods are good to eat!-and what foods you should stay away from at all costs!
Place and Development of Channel SystemsZubair Arshad
This document discusses channel systems and place decisions in marketing. It covers several key points:
Place decisions are an important part of marketing strategy and are guided by ideal place objectives. The channel system can be direct or indirect, and the best system achieves ideal market exposure through intensive, selective, or exclusive distribution. Channel relationships must be managed through issues like conflict handling and common objectives. Vertical arrangements between different levels of a channel may be legal, while horizontal arrangements between competitors at the same level are illegal. Finally, complex channel systems can range from traditional to vertically integrated systems that focus on the final customer.
The document outlines the process of listening which includes 5 stages: receiving, understanding, remembering, evaluating, and responding. It describes each stage in more detail. Receiving means hearing sound waves with the ears. Understanding is learning what the speaker means and their thoughts and feelings. Remembering is adding what was understood to long-term memory, though interpretation can differ from the original message. Evaluating is judging the message and potentially the speaker's emotions. Responding is providing verbal or non-verbal feedback to complete the listening process.
This document defines oral presentations and discusses their key elements and factors. It covers the different types of presentations; elements to consider like purpose, audience and content; and the process from planning to delivery. It provides seven factors for effective delivery, including starting confidently, understanding audience mood, using proper voice, body language, visual aids, timing, and concluding strongly.
The document provides tips for becoming a better listener, including focusing fully on the speaker, maintaining eye contact, avoiding distractions, asking follow up questions, not passing judgement, and avoiding giving unsolicited advice. The overall message is that truly listening involves understanding the emotions behind what is said rather than just the words, and allowing the speaker to communicate freely without feeling the need to one-up or fix their problems. Developing these active listening skills can significantly improve understanding in interpersonal interactions.
The document provides information about different types of job interviews. It discusses one-on-one interviews, group interviews, panel interviews, telephone interviews, and video conferencing interviews. For each type of interview, it provides tips on how to prepare and how to conduct yourself. Overall, the document aims to help job applicants understand various interview formats and how to make a strong impression during the interview process.
This document provides guidance on effective interview skills by outlining 8 key areas that should be assessed during an interview: 1) presentation and manner, 2) attitude, stability and maturity, 3) communication skills, 4) motivation and ambition, 5) leadership potential, 6) problem solving skills, 7) business understanding and interest, and 8) general interests. For each area, it describes positive indicators that should be demonstrated by the candidate as well as negative indicators that should be avoided. The overall purpose is to evaluate important qualifications and fit of a candidate for a given position.
The document discusses several common barriers to effective listening:
1) Making assumptions and joining conversations with predetermined attitudes rather than an open mind.
2) Being preoccupied with one's own thoughts and unable to focus attentively on the other person.
3) Jumping to conclusions about what the other person will say rather than letting them finish their thoughts.
4) Selectively listening only to information that confirms one's own beliefs rather than considering different opinions.
This document discusses different types of listening:
- Informative listening focuses on understanding the core message.
- Appreciative listening involves listening to music or speakers for pleasure.
- Critical listening judges credibility and logic to make informed decisions.
- Discriminative listening identifies subtle cues like tone of voice or pauses.
- Empathic listening focuses on understanding the speaker's feelings without interrupting.
- Good listeners pay attention without interrupting while bad listeners are distracted or interrupt.
"Does Foreign Direct Investment Negatively Affect Preservation of Culture in the Global South? Case Studies in Thailand and Cambodia."
Do elements of globalization, such as Foreign Direct Investment (FDI), negatively affect the ability of countries in the Global South to preserve their culture? This research aims to answer this question by employing a cross-sectional comparative case study analysis utilizing methods of difference. Thailand and Cambodia are compared as they are in the same region and have a similar culture. The metric of difference between Thailand and Cambodia is their ability to preserve their culture. This ability is operationalized by their respective attitudes towards FDI; Thailand imposes stringent regulations and limitations on FDI while Cambodia does not hesitate to accept most FDI and imposes fewer limitations. The evidence from this study suggests that FDI from globally influential countries with high gross domestic products (GDPs) (e.g. China, U.S.) challenges the ability of countries with lower GDPs (e.g. Cambodia) to protect their culture. Furthermore, the ability, or lack thereof, of the receiving countries to protect their culture is amplified by the existence and implementation of restrictive FDI policies imposed by their governments.
My study abroad in Bali, Indonesia, inspired this research topic as I noticed how globalization is changing the culture of its people. I learned their language and way of life which helped me understand the beauty and importance of cultural preservation. I believe we could all benefit from learning new perspectives as they could help us ideate solutions to contemporary issues and empathize with others.
Independent Study - College of Wooster Research (2023-2024) FDI, Culture, Glo...AntoniaOwensDetwiler
"Does Foreign Direct Investment Negatively Affect Preservation of Culture in the Global South? Case Studies in Thailand and Cambodia."
Do elements of globalization, such as Foreign Direct Investment (FDI), negatively affect the ability of countries in the Global South to preserve their culture? This research aims to answer this question by employing a cross-sectional comparative case study analysis utilizing methods of difference. Thailand and Cambodia are compared as they are in the same region and have a similar culture. The metric of difference between Thailand and Cambodia is their ability to preserve their culture. This ability is operationalized by their respective attitudes towards FDI; Thailand imposes stringent regulations and limitations on FDI while Cambodia does not hesitate to accept most FDI and imposes fewer limitations. The evidence from this study suggests that FDI from globally influential countries with high gross domestic products (GDPs) (e.g. China, U.S.) challenges the ability of countries with lower GDPs (e.g. Cambodia) to protect their culture. Furthermore, the ability, or lack thereof, of the receiving countries to protect their culture is amplified by the existence and implementation of restrictive FDI policies imposed by their governments.
My study abroad in Bali, Indonesia, inspired this research topic as I noticed how globalization is changing the culture of its people. I learned their language and way of life which helped me understand the beauty and importance of cultural preservation. I believe we could all benefit from learning new perspectives as they could help us ideate solutions to contemporary issues and empathize with others.
BONKMILLON Unleashes Its Bonkers Potential on Solana.pdfcoingabbar
Introducing BONKMILLON - The Most Bonkers Meme Coin Yet
Let's be real for a second – the world of meme coins can feel like a bit of a circus at times. Every other day, there's a new token promising to take you "to the moon" or offering some groundbreaking utility that'll change the game forever. But how many of them actually deliver on that hype?
Abhay Bhutada, the Managing Director of Poonawalla Fincorp Limited, is an accomplished leader with over 15 years of experience in commercial and retail lending. A Qualified Chartered Accountant, he has been pivotal in leveraging technology to enhance financial services. Starting his career at Bank of India, he later founded TAB Capital Limited and co-founded Poonawalla Finance Private Limited, emphasizing digital lending. Under his leadership, Poonawalla Fincorp achieved a 'AAA' credit rating, integrating acquisitions and emphasizing corporate governance. Actively involved in industry forums and CSR initiatives, Abhay has been recognized with awards like "Young Entrepreneur of India 2017" and "40 under 40 Most Influential Leader for 2020-21." Personally, he values mindfulness, enjoys gardening, yoga, and sees every day as an opportunity for growth and improvement.
2. Elemental Economics - Mineral demand.pdfNeal Brewster
After this second you should be able to: Explain the main determinants of demand for any mineral product, and their relative importance; recognise and explain how demand for any product is likely to change with economic activity; recognise and explain the roles of technology and relative prices in influencing demand; be able to explain the differences between the rates of growth of demand for different products.
5 Tips for Creating Standard Financial ReportsEasyReports
Well-crafted financial reports serve as vital tools for decision-making and transparency within an organization. By following the undermentioned tips, you can create standardized financial reports that effectively communicate your company's financial health and performance to stakeholders.
Solution Manual For Financial Accounting, 8th Canadian Edition 2024, by Libby...Donc Test
Solution Manual For Financial Accounting, 8th Canadian Edition 2024, by Libby, Hodge, Verified Chapters 1 - 13, Complete Newest Version Solution Manual For Financial Accounting, 8th Canadian Edition by Libby, Hodge, Verified Chapters 1 - 13, Complete Newest Version Solution Manual For Financial Accounting 8th Canadian Edition Pdf Chapters Download Stuvia Solution Manual For Financial Accounting 8th Canadian Edition Ebook Download Stuvia Solution Manual For Financial Accounting 8th Canadian Edition Pdf Solution Manual For Financial Accounting 8th Canadian Edition Pdf Download Stuvia Financial Accounting 8th Canadian Edition Pdf Chapters Download Stuvia Financial Accounting 8th Canadian Edition Ebook Download Stuvia Financial Accounting 8th Canadian Edition Pdf Financial Accounting 8th Canadian Edition Pdf Download Stuvia
2. 2
The Time Value of Money
The Interest Rate
Simple Interest
Compound Interest
Amortizing a Loan
3. 3
The Interest Rate
Which would you prefer -- $10,000 today or $10,000 in 5 years?
years
Interest is the money paid for the use of money.
Obviously, $10,000 today.
today
You already recognize that there is TIME VALUE TO MONEY!!
MONEY
4. 4
Why TIME?
Why is TIME such an important
element in your decision?
TIME allows you the opportunity to
postpone consumption and earn
INTEREST.
INTEREST
5. 5
Types of Interest
Simple Interest
Interest paid (earned) on only the original
amount, or principal borrowed (lend).
Compound Interest
Interest paid (earned) on any previous
interest earned, as well as on the
principal borrowed (lent).
6. 6
Simple Interest Formula
Formula
SI = P0(i)(n)
SI:
Simple Interest
P0:
Deposit today (t=0)
i:
Interest Rate per Period
n:
Number of Time Periods
7. 7
Simple Interest Example
Assume that you deposit $1,00 in an
account earning 8% simple interest for
10 years. What is the accumulated
interest at the end of the 10nd year?
SI
= P0(i)(n)
= $1,00(.08)(10)
= $80
8. 8
Simple Interest (FV)
What is the Future Value (FV) of the
FV
deposit?
FV
= P0 + SI
= $1,00 + $80
= $180
Future Value is the value at some future
time of a present amount of money, or a
series of payments, evaluated at a given
interest rate.
9. 9
Simple Interest (PV)
What is the Present Value (PV) of the
PV
previous problem?
The Present Value is simply the
$1,00 you originally deposited.
That is the value today!
Present Value is the current value of a
future amount of money, or a series of
payments, evaluated at a given interest
rate.
10. 10
Compound interest
Interest that is earned on a given
deposit and has become part of
principal at the end of a specified
period
Future value of a present amount at a
future date, found by applying
compound interest over a specified
period of time.
11. 11
The equation for future value
FV=PV*(1+i)n
If Fred places $100 in a savings account paying 8% interest compounded
annually, at the end of 1 year he will have $108 in the
account.<100*(1.08)=$108>
If Fred were to leave this money in the account for another year, he would
be paid interest at the rate of 8% on the new principal of $108.At the end of
this second year there would be $116.64 in the
account.<108*(1.08)=116.64> or <100*(1.08)2=116.64>
12. 12
General Future
Value Formula
FV1 = P0(1+i)1
FV2 = P0(1+i)2
etc.
General Future Value Formula:
FVn = P0 (1+i)n
or
FVn = P0 (FVIFi,n) -- See Table I
13. 13
Valuation Using Table I
FVIFi,n is found on Table I at the end
of the book or on the card insert.
Period
1
2
3
4
5
6%
1.060
1.124
1.191
1.262
1.338
7%
1.070
1.145
1.225
1.311
1.403
8%
1.080
1.166
1.260
1.360
1.469
15. 15
Story Problem Example
Julie Miller wants to know how large her deposit
of $10,000 today will become at a compound
annual interest rate of 10% for 5 years.
years
0
10%
1
2
3
4
5
$10,000
FV5
16. 16
Story Problem Solution
Calculation based on general formula:
FVn = P0 (1+i)n
FV5 = $10,000 (1+ 0.10)5
= $16,105.10
Calculation based on Table I:
FV5 = $10,000 (FVIF10%, 5)
= $10,000 (1.611)
= $16,110 [Due to Rounding]
17. 17
Present value of a single
amount
The current dollar value of a
future amount-the amount of
money that would have to be
invested today at a given interest
rate over a specified period to
equal the future amount.
18. 18
Concept of present value
The process of finding present
value is often referred to as
discounting cash flows. It is
concerned with answering the following
question:" if I can earn i percent on my
money, what is the most I would be willing
to pay now for an opportunity to receive
FV n dollars n periods from today?”
20. 20
Present Value
Single Deposit (Graphic)
Assume that you need $1,000 in 2 years.
Let’s examine the process to determine
how much you need to deposit today at a
discount rate of 7% compounded
annually.
0
7%
1
2
$1,000
PV0
PV1
22. 22
General Present
Value Formula
PV0 = FV1 / (1+i)1
PV0 = FV2 / (1+i)2
etc.
General Present Value Formula:
PV0 = FVn / (1+i)n
or
PV0 = FVn (PVIFi,n) -- See Table II
23. 23
Valuation Using Table II
PVIFi,n is found on Table II at the end
of the book or on the card insert.
Period
1
2
3
4
5
6%
.943
.890
.840
.792
.747
7%
.935
.873
.816
.763
.713
8%
.926
.857
.794
.735
.681
25. 25
Story Problem Example
Julie Miller wants to know how large of a
deposit to make so that the money will
grow to $10,000 in 5 years at a discount
rate of 10%.
0
10%
1
2
3
4
5
$10,000
PV0
26. 26
Story Problem Solution
Calculation based on general formula:
PV0 = FVn / (1+i)n
PV0 = $10,000 / (1+ 0.10)5
= $6,209.21
Calculation based on Table I:
PV0 = $10,000 (PVIF10%, 5)
= $10,000 (.621)
= $6,210.00 [Due to Rounding]
28. 28
Future value relationship
Higher the interest rates, higher the
future value
Longer the period of time, higher the
future value
For an interest rate of 0% the FV is
always equal to its PV(1.00). But for
any interest rate greater than zero,
future value is greater than the
present value
30. 30
Present value relationship
The higher the discount rate, the
lower the present value
The longer the period of time, the
lower the present value
At the discount rate 0%,the
present value is always equal to
its future value
31. 31
Types of Annuities
An Annuity represents a series of equal
payments (or receipts) occurring over a
specified number of equidistant periods.
Ordinary Annuity: Payments or receipts
Annuity
occur at the end of each period.
Annuity Due: Payments or receipts
Due
occur at the beginning of each period.
33. 33
Parts of an Annuity
(Ordinary Annuity)
End of
Period 1
0
End of
Period 2
End of
Period 3
1
2
3
$100
$100
$100
Today
Equal Cash Flows
Each 1 Period Apart
34. 34
Parts of an Annuity
(Annuity Due)
Beginning of
Period 1
Beginning of
Period 2
0
1
2
$100
$100
Beginning of
Period 3
$100
Today
3
Equal Cash Flows
Each 1 Period Apart
35. 35
Overview of an
Ordinary Annuity -- FVA
Cash flows occur at the end of the period
0
1
2
n
. . .
i%
R
R
R
R = Periodic
Cash Flow
FVAn = R(1+i) + R(1+i) +
... + R(1+i)1 + R(1+i)0
n-1
n-2
FVAn
n+1
36. 36
Example of an
Ordinary Annuity -- FVA
Cash flows occur at the end of the period
0
1
2
3
$1,000
$1,000
4
$1,000
7%
$1,070
$1,145
FVA3 = $1,000(1.07)2 +
$1,000(1.07)1 + $1,000(1.07)0
= $1,145 + $1,070 + $1,000
= $3,215
$3,215 = FVA3
37. 37
Future value interest factor
for an ordinary annuity
FVIFi,n=1/i*<(1+i)n-1>
FVA=PMT*(FVIFAi,n)
38. 38
Hint on Annuity Valuation
The future value of an ordinary
annuity can be viewed as
occurring at the end of the last
cash flow period, whereas the
future value of an annuity due
can be viewed as occurring at
the beginning of the last cash
flow period.
40. 40
Overview View of an
Annuity Due -- FVAD
Cash flows occur at the beginning of the period
0
1
2
3
R
R
R
i%
R
. . .
FVADn = R(1+i)n + R(1+i)n-1 +
... + R(1+i)2 + R(1+i)1
= FVAn (1+i)
n-1
n
R
FVADn
41. 41
numerical
Martin has $10000 that she can deposit in any of three
saving counts for a 3 year period. Bank A compounds
interest on an annual basis, bank B compounds interest
twice each year, Bank C compounds interest each quarter.
All three banks have a stated annual interest rate of 4%
What amount would Ms.Martin have at the end of third
year?
On the basis of your findings in banks, which bank should
she prefer.
42. 42
NUMERICALS
Ramish wishes to choose the better of two equally costly cash
flow streams: annuity X and annuity Y.X is an annuity due with a
cash inflow of $9000 for each of 6 years is an ordinary annuity
with cash inflow of 410000 or each of 6 years. Assume that he can
earn 15% on his investment.
On a subject basis, which annuity do you think is more attractive
and why?
Find the future value at the end of year 6,for both annuity x and Y.
43. 43
NUMERICALS
what is the present value of $ 6000 to be received at the end
of 6 years if the discount rate is 12%?
$100 at the end of three years is worth how much today,
assuming a discount rate of
100%
10%
0%
44. 44
Example of an
Annuity Due -- FVAD
Cash flows occur at the beginning of the period
0
1
2
3
$1,000
$1,000
4
$1,070
7%
$1,000
$1,145
$1,225
FVAD3 = $1,000(1.07)3 +
$1,000(1.07)2 + $1,000(1.07)1
= $1,225 + $1,145 + $1,070
= $3,440
$3,440 = FVAD3
48. 48
PV of an ordinary annuity
Braden company a small producer of toys wants to determine the
most it should pay to purchase a particular ordinary annuity. the
annuity consist of cash flows of 700v at the end of each year for 5
years. The firm requires the annuity to provide a minimum return
of 8%.
49. 49
Long method for finding the
present value of an ordinary
annuity
Year
CF
PVIF8%,n
(1)
(2)
1
700
0.926
2
700
0.857
3
700
0.794
4
700
0.735
5
700
0.681
present value of annuity=2795.10
PVIF=1/i*(1-1/(1+i)n)
PV
(1*2)
648.20
599.90
555.80
514.50
476.70
50. 50
Finding present value of an
Ordinary Annuity -- PVA
Cash flows occur at the end of the period
0
1
2
n
n+1
. . .
i%
R
R
R
R = Periodic
Cash Flow
PVAn
PVAn = R/(1+i)1 + R/(1+i)2
+ ... + R/(1+i)n
51. 51
Example of an
Ordinary Annuity -- PVA
Cash flows occur at the end of the period
0
1
2
3
$1,000
$1,000
$1,000
7%
$ 934.58
$ 873.44
$ 816.30
$2,624.32 = PVA3
PVA3 =
$1,000/(1.07)1 +
$1,000/(1.07)2 +
$1,000/(1.07)3
= $934.58 + $873.44 + $816.30
= $2,624.32
4
52. 52
Hint on Annuity Valuation
The present value of an ordinary
annuity can be viewed as
occurring at the beginning of the
first cash flow period, whereas
the present value of an annuity
due can be viewed as occurring
at the end of the first cash flow
period.
54. 54
Overview of an
Annuity Due -- PVAD
Cash flows occur at the beginning of the period
0
1
2
PVADn
n
. . .
i%
R
n-1
R
R
R
R: Periodic
Cash Flow
PVADn = R/(1+i)0 + R/(1+i)1 + ... + R/(1+i)n-1
= PVAn (1+i)
55. 55
Example of an
Annuity Due -- PVAD
Cash flows occur at the beginning of the period
0
1
2
$1,000
3
$1,000
7%
$1,000.00
$ 934.58
$ 873.44
$2,808.02 = PVADn
PVADn = $1,000/(1.07)0 + $1,000/(1.07)1 +
$1,000/(1.07)2 = $2,808.02
4
57. 57
Steps to Solve Time Value
of Money Problems
1. Read problem thoroughly
2. Determine if it is a PV or FV problem
3. Create a time line
4. Put cash flows and arrows on time line
5. Determine if solution involves a single
CF, annuity stream(s), or mixed flow
6. Solve the problem
7. Check with financial calculator (optional)
58. 58
Mixed Flows Example
Julie Miller will receive the set of cash
flows below. What is the Present Value
at a discount rate of 10%?
10%
0
1
10%
$600
PV0
2
3
4
5
$600 $400 $400 $100
59. 59
How to Solve?
1. Solve a “piece-at-a-time” by
piece-at-a-time
discounting each piece back to t=0.
2. Solve a “group-at-a-time” by first
group-at-a-time
breaking problem into groups
of annuity streams and any single
cash flow group. Then discount
each group back to t=0.
63. 63
Frequency of
Compounding
General Formula:
FVn = PV0(1 + [i/m])mn
n:
Number of Years
m:
Compounding Periods per Year
i:
Annual Interest Rate
FVn,m: FV at the end of Year n
PV0:
PV of the Cash Flow today
64. 64
Impact of Frequency
Julie Miller has $1,000 to invest for 2
years at an annual interest rate of
12%.
Annual
FV2
= 1,000(1+ [.12/1])(1)(2)
1,000
= 1,254.40
Semi
FV2
= 1,000(1+ [.12/2])(2)(2)
1,000
= 1,262.48
66. 66
Present value of perpetuity
An annuity with an infinite life,
providing continual annual cash
flow
PVIF=1/i
67. 67
Effective Annual
Interest Rate
The annual rate of interest actually
paid or earned
The actual rate of interest earned
(paid) after adjusting the nominal
rate for factors such as the number
of compounding periods per year.
(1 + [ i / m ] )m - 1
69. 69
BW’s Effective
Annual Interest Rate
Basket Wonders (BW) has a $1,000
CD at the bank. The interest rate
is 6% compounded quarterly for 1
year. What is the Effective Annual
Interest Rate (EAR)?
EAR
EAR = ( 1 + 6% / 4 )4 - 1
= 1.0614 - 1 = .0614 or 6.14%!
70. 70
Loan amortization
The determination of the equal
periodic loan payments
necessary to provide lender with
a specified interest return and to
repay the loan principal over a
specified period.
71. 71
Steps to Amortizing a Loan
1.
Calculate the payment per period.
2.
Determine the interest in Period t.
(Loan balance at t-1) x (i% / m)
3.
Compute principal payment in Period t.
(Payment - interest from Step 2)
4.
Determine ending balance in Period t.
(Balance - principal payment from Step 3)
5.
Start again at Step 2 and repeat.
72. 72
Amortizing a Loan Example
Julie Miller is borrowing $22,000 at a
compound annual interest rate of 12%.
Amortize the loan if annual payments are
made for 5 years.
Step 1: Payment
PV0 = R (PVIFA i%,n)
$22,000
= R (PVIFA 12%,5)
$22,000
= R (3.605)
R = $22,000 / 3.605 = $5351
73. 73
Amortizing a Loan Example
End of Payment
Year
0
---
Interest Principal Ending
(Pmt-int) Balance
----$22,000
1
$5351
2640
2711
19289
2
5351
2315
3036
16253
3
5351
1951
3400
12853
4
5351
1542
3809
9044
5
5351
1085
4266
4778
6
5351
573
4778
0
74. 74
Usefulness of Amortization
1.
2.
Determine Interest Expense -Interest expenses may reduce
taxable income of the firm.
Calculate Debt Outstanding -- The
quantity of outstanding debt
may be used in financing the
day-to-day activities of the firm.