Time Value of Money

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Time Value of Money

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TIME VALUE OF MONEY

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TIME VALUE OF MONEY
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Preference for current consumption

Risk
Investment opportunities



Required rate of return (opportunity cost of
capital) = Risk-free rate + Risk premium

LA

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FUTURE VALUE OF A SINGLE AMOUNT
Suppose you have Rs 1000 today and you deposit it with a financial institution, which pays 10 per cent interest compounded annually. How much would the deposit grow to at the end of three years?

FV n = PV(1+k)n where FV n = Future Value of the initial flow n years hence PV = Initial Cash Flow K = Annual rate of interest N = Life of investment
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FUTURE VALUE OF A SINGLE AMOUNT
 Compound value factor or compound interest factor = (1+k)n  If you deposit Rs 1,000 today in a bank which pays 10% interest compounded annually, how much will the deposit grow to after 8 years and 12 years?  If an investor deposits Rs 20,000 with a bank which is paying interest at 8% on a 15 year time deposit, what will be his accumulated savings at the end of year 15?  For an interest rate of zero per cent, CVF always equals 1, therefore future amount always equals the initial principal
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SEMI-ANNUAL AND OTHER COMPOUNDING

PERIODS


Suppose you deposit Rs 1,000 with a finance company that pays
12% interest semi-annually. How much will the deposit grow to at the end of one year?

FVn = PV(1+k/m)m*n where FVn = Future Value of the initial flow n years hence PV = Initial Cash Flow k = Nominal rate of interest m = Number of times compounding is done during a year n = Number of years for which compounding is done


How much does a deposit of Rs 5,000 grow to at the end of 6 years, if the nominal rate of interest is 12% and the frequency of

compounding is 4 times a year?
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DOUBLING PERIOD


Rule of 72


Doubling period = 72 / Interest rate



Rule of 69


Doubling period = 0.35 + (69 / Interest rate)



Calculate the doubling period for 10% and 15% rate of
interest.

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FUTURE VALUE OF AN ANNUITY
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An annuity is a stream of equal annual cash flows Fixed payment each year for a specified number of years Regular annuity or deferred annuity


Cash flows occur at the end of each period



Annuity due


Cash flows occur at the beginning of each period

Future Value Of Annuity FVAn = A (1+k)n -1 k
Where A = Amount deposited/invested at the end of every year for n years k = Rate of interest n = Duration of the annuity FVAn = Accumulation at the end of n years
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FUTURE VALUE OF AN ANNUITY
 Suppose that a firm deposits Rs 5000 at the end of each year for four years at 6% rate of interest. How much would this annuity accumulate at the end of the fourth year?  Four equal annual payments of Rs 2,000 are made into a deposit account that pays 8% per year. What is the future value of this annuity at the end of 4 years?  Company XYZ is establishing a sinking fund to retire Rs 5,00,000, 8% debentures,10 years from today. The company plans to put a fixed amount into the fund each year for 10 years. The first payment will be made at the end of the current year. The company anticipates that the fund will earn 6% a year. What equal annual contributions must be made to accumulate Rs 5,00,000, 10 years from now? 8 LA

SINKING FUND FACTOR (SFF)
SFF n, i = k (1+k)n -1

 Sinking fund (annuity) = Future Value / CVFA  CVFA = Compound value factor for an annuity

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EFFECTIVE VERSUS NOMINAL RATE
 General relationship between effective and nominal rate of interest is as follows:  r= 1 + k m-1 m where r = effective rate of interest k = nominal rate of interest m = frequency of compounding per year  A bank offers 8% nominal rate of interest with quarterly compounding. What is the effective rate of interest?

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PRESENT VALUE


Concept of present value – exact opposite of that of compound / future value



Money is received at some future date and will be worth less
because the corresponding interest is lost during the period PV of a rupee that will be received in the future will be less than the



value of a rupee in hand today


Given a positive rate of interest, PV of future rupees will always be lower Procedure of finding PVs – Discounting Discounting – concerned with determining the PV of a future amount, assuming that the decision maker has an opportunity to earn a certain return on his money This return – Discounting rate, cost of capital or opportunity cost
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PRESENT VALUE OF A SINGLE AMOUNT


PV = FVn

1 (1+k) n


 

Discounting factor or present value interest factor
PV = Future value X Present value factor of Re 1 Higher the discount rate, lower is the PVF; and longer the period of time, lower is the PVF and vice versa Find the present value of Rs 1,000 receivable 6 years hence if the rate of discount is 10%. Find the present value of Rs 1,000 receivable 20 years hence if the rate of discount is 8%. (Given PVIF 8%,10 = 0.463) Mr X has been given an opportunity to receive Rs 1,060 one year from now. He knows that he can earn 6% interest on his investments. What amount will he be prepared to invest for this opportunity?







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