The Time Value of Money C H A P T E R N I N E


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1 The Time Value of Money C H A P T E R N I N E
2 Figure 91 Relationship of present value and future value PPT 91 $1,000 present value $ 10% interest $1, future value Number of periods
3 Figure 92 Compounding process for annuity PPT 92 Period 0 Period 1 Period 2 Period 3 Period 4 $1,000 x = $1,000 $1,000 for one period 10% FV = $1,100 $1,000for two periods 10% FV = $1,210 $1,000 for three periods 10% FV = $1,331 $4,641
4 Table 91 Relationship of present value to annuity PPT 93 Annual Beginning Interest Annual Ending Year Balance (6 percent) Withdrawal Balance $10, $ $2, $7, , , , , , , , ,
5 Table 92 Payoff table for loan (amortization table) PPT 94 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
6 Review of formulas (a) Formula Appendix FV = PV(1 + i) n Future value single amount.. (91) A PV FV 1 (1 + i) n Present value single amount. (93) B Future value annuity (94a) C Future value annuity in n+ 1 advance (94b) (1+ i) (1+ i) = FV = A FV A A = A BGN (1 + n i) 1 i i PPT n (1 + i) Present value annuity (95a) P V A = A D i
7 Review of formulas (b) Formula Appendix Present value annuity in 1 (1 i) + n 1 advance (95b) (1 + i) PV A = A BGN i Annuity equalling a future i value (96a) A = FV A n C (1 + i) 1 Annuity in advance equalling a i future value (96b) A = FV + (1 + i) (1 + i) BGN A n 1 Annuity equalling a present i value (97a) A = P V D A 1 1 (1 + i) n PPT 95 Annuity in advance equalling a i present value (97b) A BGN = P V A 1 (1 + i) n 1 (1 + i)
8 The present value of a deferred annuity ($1,000 per year to be paid 48 years in the future) (first step) Beginning of fourth period PPT 96 3,993 A 1 A 2 A 3 A 4 A 5 Present $1,000 $1,000 $1,000 $1,000 $1,000 value 0 1* *Each number represents the end of the period; that is, 4 represents the end of the fourth period.
9 The present value of a deferred annuity ($1,000 per year to be paid 48 years in the future) (second step) End of third period Beginning of fourth period PPT 96 $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
10 Chapter 9  Outline LT 91 Time Value of Money Future Value and Present Value Annuities 2 Questions to Ask in Time Value of Money Problems Adjusting for NonAnnual Compounding Compound Interest Tables
11 Time Value of Money LT 92 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 rate
12 Future Value and Present Value LT 93 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
13 Annuity LT 94 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 A good example of an annuity is a lease, where a fixed monthly charge is paid over a number of years
14 2 Questions to Ask in Time Value of Money Problems LT 95 Future Value or Present Value? Future Value: Present (Now) Future Present Value: Future Present (Now) Single amount or Annuity? Single amount: onetime (or lump) sum Annuity: same amount per year for a number of years
15 Adjusting for NonAnnual Compounding LT 96 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
16 Future value of $1 (FV IF ) LT 97 Periods 1% 2% 3% 4% 6% 8% 10% An expanded table is presented in Appendix A
17 Present value of $1 (PV IF ) LT 98 Periods 1% 2% 3% 4% 6% 8% 10% An expanded table is presented in Appendix B
18 Future value of an annuity of $1 (FV IFA ) LT 99 Periods 1% 2% 3% 4% 6% 8% 10% An expanded table is presented in Appendix C
19 Present value of an annuity of $1 (PV IFA ) LT 910 Periods 1% 2% 3% 4% 6% 8% 10% An expanded table is presented in Appendix D
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