# LESSON 13 TIME VALUE OF MONEY 13.0 AIMS AND OBJECTIVES 13.1 INTRODUCTION CONTENTS

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1 Accounting and Finance for Managers LESSON 13 TIME VALUE OF MONEY CONTENTS 13.0 Aims and Objectives 13.1 Introduction 13.2 Foundations of The Time Vaue of Money 13.3 Cassifications of The Time Vaue of Money Rue of Rue of Frequency of Compounding 13.5 Effective Rate of Interest 13.6 Future Vaue of an Annuity Future Vaue of Annuity Due Sinking Fund Factor Method 13.7 Present Vaue of Singe Cash Fow 13.8 Present Vaue of Annuity 13.9 Capita Recovery Factor Method Let us Sum up Lesson-end Activity Keywords Questions for Discussion Suggested Readings 13.0 AIMS AND OBJECTIVES This esson is intended to discuss the concept of time vaue of money and its roe in studying the viabiity of the project by comparing the initia investment future benefits. After studying this esson you wi be abe to: (i) describe concept and components of the time vaue of money (ii) cassify the time vaue of money and describe rues of 72 and 69 (iii) understand effective rate of interest and future vaue of an annuity 13.1 INTRODUCTION 214 The time vaue of money has gained greater importance in studying the viabiity of the project by comparing the initia investment with the anticipated future benefits. If the anticipated future benefits are more than the initia investment then the investment is found to be viabe in generating the economic benefits.

2 Why the time vaue of money principe is warranted to study under the financia management? The foowing are the many reasons invoved: To determine the rea rate of return With reference to Money empoyment on productive assets In an infationary period, a rupee today has greater purchasing power than rupee in the future The future is uncertain- Individuas prefer current consumption rather than future consumption Time Vaue of Money 13.2 FOUNDATIONS OF THE TIME VALUE OF MONEY There are two, one is the time preference of money and another one is reinvestment opportunity which are identified and inter reated with each other. Eary receipt of money paves way for the reinvestment opportunity but the ater receipt does not carry the things. Time vaue of money normay contains three different components viz: Rea rate of return: It is the return which consider origina return of the investment but it never considers the infation rate. Expected/Anticipated rate of return: It is the positive rate of return normay expected by every one on the amount of investment from the future. Risk premiums: This an aowance is normay given to the investors to compensate the uncertainty CLASSIFICATIONS OF THE TIME VALUE OF MONEY The concept of time vaue of money can be cassified into two major cassifications: Future vaue of money Present vaue of money Future vaue of money: It is further bifurcated into two different categories viz Future vaue of singe sum and Future vaue of an Annuity Present vaue of money: It is further cassified into two major casses viz Present vaue of singe sum and Present vaue of and Annuity Future vaue of singe sum: It coud be found from the inbound reationship in between the future vaue of money and present vaue of money. FV n = PV(1+K) n FV n = Future Vaue of Cash Infow PV = Initia Cash Fow K = Annua Rate of Return N = Life of Investment Iustration 1 If you deposit Rs.1,000 today in a Indian bank which pays 10% interest, find out the future vaue of money after 3 years. 215

3 Accounting and Finance for Managers Future vaue of Rs.1,000 after three years wi be = Rs.1,000(1+.10) 3 = Rs.1,000(1.331)= Rs. 1,331 Doubing period: It is the period which makes the investment as "Doubed" There are two different approaches viz Rue of 72 Rue of Rue of 72 The initia amount of investment gets Doubed within which 72/I I = Interest Rate of the investment Iustration 2 The amount of the investment is Rs.1,000. The annua rate of interest is 12%. When this amount of Rs.1,000 wi get doubed? = 72/12 = 6 years Rue of 69 The amount method is found to crude method in determining the doubing period which has its own imitations. The Rue of 69 was deveoped ony in order to remove the bottenecks associated with the eary mode of doubing period. The rue of 69 is found to be a scientific method as we as rationa method in determining the doubing period of the investment = /I Iustration 3 The amount of the investment is Rs.1,000. The annua rate of interest is 11% When this amount of Rs 1,000 wi get doubed? = /11= yrs 1. State Bank of India announces that your money is getting doubed in 99 months. What is the rate of interest payabe? 2. The next aspect in the Future vaue of money is interest frequency of compounding FREQUENCY OF COMPOUNDING Whenever any compounding is taking pace, the foowing methodoogy has to be adopted for the determination of the future vaue of money. FV = PV(1+k/m) mxn M = Number of Times Compounding is done during the year N = number of years 216 K = compounding rate

4 Iustration 4 Time Vaue of Money How much does a deposit of Rs. 5,000 grow to at the end of 6 years. If the nomina rate of interest is 12% and frequency is 4 times a year? The future vaue of Rs. 5,000 wi be = Rs.5,000(1+.12/4) 4 6 = Rs.5,000(2.033)= Rs.10, EFFECTIVE RATE OF INTEREST It is the rate of interest at which mount of the principa grows with regards to the rate of compounding. r = (1+K/m) m - 1 K = Nomina Rate of Interest r = Effective Rate of Interest m = Frequency of Compounding Iustration 5 A bank offers 8% nomina rate of interest with quartery compounding. What is the effective rate of interest? R = (1+.08/4)4-1= =.082 i.e 8.2% 13.6 FUTURE VALUE OF AN ANNUITY Annuity may be a series of either payments or receipts The annuity can be cassified into two categories v Annuity at the end of the period- Reguar / Deferred Annuity v Annuity at the beginning of the period - Annuity Due Annuity at the end of the period A [(1+ K) n 1] FVA n = = Future Vaue Interest Factor Annuity (FVIFA) k Iustration 6 Suppose you deposit Rs.1,000 annuay in a bank for 5 years and your deposits earn a compound interest rate of 10% What wi be vaue of the deposit at the end of 5 years? Assuming the each deposit occurs at the end of the year, the future vaue of this annuity? FVA n = Rs.1,000(FVIFA) for 10% and 5 years = Rs.1,000 5 [(1 +.10) -1].10 = Rs.1, = Rs.6, Future Vaue of Annuity Due A [(1+ K) n 1] FVA n = = (1+k) k 217

5 Accounting and Finance for Managers Iustration 7 If you invest Rs 1,000 at the beginning of every year, for four years. What wi be the vaue of the investment finay. [ (1 +.10) ] 5 1 FVA n = Rs.1,000 (1+.10).10 = Rs.1, = Rs.6, Four annua equa payments of Rs.2,000 are made into a deposit account that pays 8% interest per year. What is the future vaue of this annuity at the end of 4 years? 2. You can save Rs.2,000 a year for 5 years, and Rs.3,000 a year for 3 years thereafter. What wi these savings cumuate to at the end of 8 years. If the rate of interest is 10? Sinking Fund Factor Method It means that the amount to be deposited at the end of every year for the period of "n" years at the rate of interest "K" in order to aggregate Re.1 at the end of the period. A = FVA [K/(1+K) n -1] Iustration 8 How much you shoud save annuay to accumuate Rs.20,000 by the end of 10 years. If the saving earns an interest of 12 %? A = Rs.20,000[.12/(1+.12) 10-1] = Rs.20,000(.05698)=Rs.1,139 The next most important segment is present vaue of money. First we wi discuss the present vaue of singe cash fow 1. How much you shoud save annuay to accumuate Rs.20,000 by the end of 10 years. If the saving earns an interest of 12%? 2. Mr vinay pans to send his son for higher studies abroad after 10 years. He expects the cost of these studies to be Rs.1,00,000. How much shoud he save annuay to have a sum of Rs 1,00,000 at the end of 10 years. If the interest rate is 12%? 13.7 PRESENT VALUE OF SINGLE CASH FLOW It is the process in which the future vaue of singe cash fow is reckoned to "0" time horizon i.e on today. PV n = FV n /(1+R) n Iustration 9 Find the present vaue of Rs.1,000 receivabe 6 years hence if the rate of discount is 6 percent 218 PV n = Rs.1,000/(1+.06) 6 = Rs.1,000(.705) = Rs.705

6 Shorter Discounting Periods The discounting may be frequent in times ike intra year compounding, intra month compounding and so on. Subject to v Number of periods in the anaysis- increases v Discount rate appicabe per period decreases Time Vaue of Money v v v Ê 1 ˆ PV= FV Á Ë 1+ k/m mxn M = number of times discounting K = Discount rate Iustration 10 Consider the foowing cash infow of Rs.10,000 at the end of four years. The present vaue of cash infow when the discount rate is 12% and discounting quartery. PV = Rs.10,000 (.623)=Rs.6,230 To get Rs.20,000, how much shoud be invested per year (at the end). The important information of the banking investment reveas the foowing are the rate of interest is 10% and the norma compounding process is once in 6 months PRESENT VALUE OF ANNUITY Present vaue of an annuity - Present vaue of future cash series - To identify the vaue of future cash fows on present vaue PVA n,k = Ê(1 + K) Á Ë K(1 + k) n-1 n ˆ ææ Present vaue factor annuity Iustration 11 If you expect to receive Rs.1,000 annuay for 3 years, each receipt is expected to be at the end of the years. What woud be the present vaue of future cash discount rate of 10%? PVA n,k = Rs.1,000 (2.487)= Rs.2, What is the present vaue of an annuity of Rs.2,000 at 10%? 2. What is the present vaue of a 4 year annuity of Rs.10,000 discounted at 10 %? 3. A 10 payments annuity of Rs.5,000 wi begin 7 years hence. (The first payment occurs at the end of 7 years) what is the vaue of this annuity now if the discount rate is 12 per cent? 13.9 CAPITAL RECOVERY FACTOR METHOD Ê K(1 + k) ˆ A = PVA Á n 1 Ë(1 + K) - ææ Reciproca to Present vaue of an annuity 219

7 Accounting and Finance for Managers Iustration 12 If your father deposits Rs.1,00,000 on retirement in a bank which pays 10% annua interest. How much can be withdrawn annuay for a period of 10 years? A = PVA(1/PVIFA) A = Rs.1,00,000 (1/6.145)= Rs.16,273 Present Vaue of Perpetuity Perpetuity means that series with indefinite duration P? = A PVIFA k,? Iustration 13 The present vaue of perpetuity of 10%, how much shoud be invested on today? A = P?/ PVIFA k,? = Rs.10,000/.10= Rs.1,00, Time vaue of money is appicabe in (a) Pay back period method (b) Accounting rate of return method (c) Discounted cash fows method (d) None of the above 2. Compounding factor is to determine (a) Present vaue (b) Future vaue (c) Present vaue and Future vaue (d) None of the above 3. Annuity due means that (a) Series at the end (b) Series at the beginning (c) Neither at the beginning nor at the end (d) None of the above 4. Capita recovery factor method is to find out the vaue of annuity through (a) (b) (c) Present vaue of an annuity Reciproca to the present vaue of annuity Future vaue of annuity (d) None of the above 5. Rue of 72 is for (a) (b) (c) (d) To determine the present vaue of the cash fows To find out future vaue of cash fows To find out the doubing period None of the above LET US SUM UP 220 The time vaue of money has gained greater importance in studying the viabiity of the project by comparing the initia investment with the anticipated future benefits. Rea rate of return is the return which consider origina return of the investment but it never considers the infation rate. Expected/Anticipated rate of return is the positive rate of return

8 normay expected by every one on the amount of investment from the future. Time Vaue of Money Risk premiums is an aowance is normay given to the investors to compensate the uncertainty LESSON-END ACTIVITY How much woud you invest now at 5% per annum compounded annua if you want to get Rs. 5,00,000 after 20 years KEYWORDS Time vaue of money: Money vaue in terms of time, money vaue in between the present and future Future vaue of money: Present vaue of money in terms of future through compounding process Present vaue of money: Future vaue of money is reckoned to "0" time period horizon FVIF: Future vaue interest factor component for compounding FVIFA: Future vaue interest factor component for compounding the series of cash payments or receipts PVIF: Present vaue interest factor of singe cash fow PVIFA: Present vaue of interest factor of mutipe cash fows Reguar annuity: Series which normay happen at the end of the specified horizon Annuity Due: Series which normay happen at the beginning Doubing period: During which the amount of the investment gets doubed within the given compounding factor component Effective rate of interest: It is the rate of interest which the investment grows QUESTIONS FOR DISCUSSION 1. Define time vaue of money 2. Expain the foundations of the time vaue of money 3. Expain the cassifications of the time vaue of money 4. Iustrate the rue of 69 with ive exampe from the banking industry 5. Expain the appications of the time vaue of money in the banking companies 6. Which method is appied for EMI cacuation by the financing companies? SUGGESTED READINGS R.L. Gupta and Radhaswamy, Advanced Accountancy. V.K. Goya, Financia Accounting, Exce Books, New Dehi. Khan and Jain, Management Accounting. S.N. Maheswari, Management Accounting. S. Bhat, Financia Management, Exce Books, New Dehi. Prasanna Chandra, Financia Management Theory and Practice, Tata McGraw Hi, New Dehi (1994). I.M. Pandey, Financia Management, Vikas Pubishing, New Dehi. Nitin Bawani, Accounting & Finance for Managers, Exce Books, New Dehi. M.P. Pandikumar Accounting & Finance for Managers Exce Books, New Dehi. 221

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