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Accounting Valuation Models Time value of money a) What is meant by the time value of money? Money received sooner rather than later allows one to use the funds for investment or consumption purposes. b) If I invest \$1,000 today, what amount will I have at the end of one year if the interest rate is 10% compounded annually? Interest = 1,000 x 10% =100 Total =1,000+100= 1,100 Alternative calculation 1,000 x 1.10 =1,100 c) If I invest \$1,000 today, what amount will I have at the end of 3 years if the interest rate is 10% compounded annually? Year 1 Interest = 1,000 x 10% =100 Total =1,000+100 = 1,100 Year 2 Interest = 1,100 x 10% =110 Total =1,100+110 =1,210 Year 3 Interest = 1,210 x 10% =121 Total =1,210+121= 1,331 Alternative calculation =1,000 x 1.10 x 1.10 x 1.10 =1,331 In these two examples, the investment 1,000 is the “Present Value” and the 1,100 is the “Future Value at the end of year 1” and the 1,331 is the “Future Value at the end of year 3” They are all equivalent in value.

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Let FV n denote future value at the end of year n. Let the interest rate be i. FV n,i = PV x (1+i) n That is PV =FV n,i /(1+i) n d) What is the present value of \$10,000 to be received at the end of 3 years, if the interest rate is 5% compounded annually? 10,000/(1+0.05) 3 =8,638.38 Other ways to calculate PV, FV: Business calculator Present Value Interest Factor PVF n,i =1/(1+i) n FVF n,i = (1+i) n
What is an annuity? A recurring periodic series of equal payments, received at equal intervals with interest compounded each period e) If I invest \$2,000 at the end of each year for 3 years, what amount will be the future amount accumulated by the end of year 3, if the interest rate is 8% compounded annually?

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