Chapter The Time Value of Money


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1 Chapter The Time Value of Money
2 PPT 92 Chapter 9  Outline Time Value of Money Future Value and Present Value Annuities TimeValueofMoney Formulas Adjusting for NonAnnual Compounding Compound Interest Tables Summary and Conclusions
3 Time Value of Money PPT 93 The basic idea behind the concept of time value of money is: $1 received today is worth more than $1 in the future OR $1 received in the future is worth less than $1 today Why? because interest can be earned on the money The connecting piece or link between present (today) and future is the interest or discount rate
4 Future Value and Present Value PPT 94 Future Value (FV) is what money today will be worth at some point in the future Present Value (PV) is what money at some point in the future is worth today
5 Figure 91 Relationship of present value and future value PPT 95 $1,000 present value $ 10% interest $1, future value Number of periods
6 Future value of $1 (FV IF ) PPT 96 Periods 1% 2% 3% 4% 6% 8% 10% An expanded table is presented in Appendix A
7 Present value of $1 (PV IF ) PPT 97 Periods 1% 2% 3% 4% 6% 8% 10% An expanded table is presented in Appendix B
8 2 Questions to Ask in Time Value of Money Problems PPT Future Value or Present Value? Future Value: Present (Now) Future Present Value: Future Present (Now) 2. Single amount or Annuity? Single amount: onetime (or lump) sum Annuity: equal amount per year for a number of years
9 Annuities PPT 99 Annuity: a stream or series of equal payments to be received in the future The payments are assumed to be received at the end of each period (unless stated otherwise) A good example of an annuity is a lease, where a fixed monthly charge is paid over a number of years
10 Figure 92 Compounding process for annuity PPT 910 Period 0 Period 1 Period 2 Period 3 Period 4 $1,000 for three periods 10% FV = $1,331 $1,000 for two periods 10% FV = $1,210 $1,000 for one period 10% FV = $1,100 $1,000 x = $1,000 $4,641
11 Future value of an annuity of $1 (FV IFA ) PPT 911 Periods 1% 2% 3% 4% 6% 8% 10% An expanded table is presented in Appendix C
12 PPT 912 Present value of an annuity of $1 (PV ) IFA Periods 1% 2% 3% 4% 6% 8% 10% An expanded table is presented in Appendix D
13 Table 91 Relationship of present value to annuity PPT 913 Annual Year Beginning Balance Interest (6 percent) Annual Withdrawal Ending Balance $10, $ $2, $7, , , , , , , , ,
14 Table 92 Payoff table for loan (amortization table) PPT 914 Annual Repayment Period Beginning Balance Annual Payment Interest (8%) on Principal Ending Balance $40,000 $4,074 $3,200 $ 874 $39, ,126 4,074 3, , ,182 4,074 3,055 1,019 37,163
15 Determining the Yield on an Investment (a) PPT 915 Future value single amount.. (91) Formula FV = PV(1+ i) n Appendix A Present value single amount. (93) PV = FV 1 (1 + i) n B Future value annuity (94a) FV = A A (1 + n i) 1 i C Future value annuity in advance (94b) Present value annuity (95a) FV P V A A = A = BGN A n+ 1 (1+ i) (1+ i) i 1 1 (1 + i) i n D
16 Determining the Yield on an Investment (b) Formula Appendix 1 Present value annuity in (1 + i) n 1 (1 + i) advance (95b) PVA = A BGN i Annuity equalling a future i A = FV A n value (96a) (1 + i) 1 C i Annuity in advance equalling a A = FV BGN A (1 + i) n 1 (1 + i) future value (96b) + Annuity equalling a present value (97a) Annuity in advance equalling a A A = BGN present value (97b) n 1 P V = A 1 P V A i 1 (1 + i) (1 + i) n i 1 (1 + i) PPT 916 D
17 PPT 917 Adjusting for NonAnnual Compounding Interest is often compounded quarterly, monthly, or semiannually in the real world Since the time value of money tables assume annual compounding, an adjustment must be made: the number of years is multiplied by the number of compounding periods the annual interest rate is divided by the number of compounding periods
18 The present value of a deferred annuity ($1,000 per year to be paid 48 years in the future) (first step) PPT 918 Beginning of fourth period A 1 A 2 A 3 A 4 A 5 Present $1,000 $1,000 $1,000 $1,000 $1,000 value $3, * *Each number represents the end of the period; that is, 4 represents the end of the fourth period
19 The present value of a deferred annuity ($1,000 per year to be paid 48 years in the future) (second step) PPT 919 End of third period Beginning of fourth period $3,170 $3,993 A 1 A 2 A 3 A 4 A 5 Present (single amount) $1,000 $1,000 $1,000 $1,000 $1,000 value
20 Summary and Conclusions PPT 920 The financial manager uses the time value of money approach to value cash flows that occur at different points in time A dollar invested today at compound interest will grow a larger value in future. That future value, discounted at compound interest, is equated to a present value today Cash values may be single amounts, or a series of equal amounts (annuity)
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