Corporate Finance Solutions Chapter 4 - Time Value of Money

Solutions to Chapter 4

The Time Value of Money

Note: Unless otherwise stated, assume that cash flows occur at the end of each year.

1. a. 100/(1.08)10 = $46.32

b. 100/(1.08)20 = $21.45

c. 100/(1.04)10 = $67.56

d. 100/(1.04)20 = $45.64

3. With simple interest, you earn 4% of $1000, or $40 each year. There is no interest on interest. After 10 years, you earn total interest of $400, and your account accumulates to $1400. With compound interest, your account grows to 1000 ( (1.04)10 = $1480. Therefore $80 is interest on interest.

5.

Present Value Years Future Value Interest Rate*

a. $400 11 $684 5% = ()1/11 – 1

b. $183 4 $249 8% = ()1/4 – 1

c. $300 7 $300 0% = ()1/7– 1

To find the interest rate, we rearrange the equation

FV = PV ( (1 + r)n to conclude that r = ()1/n - 1

To use a financial calculator for (a) enter PV= (-)400, FV = 684, PMT = 0, n = 11

and compute the interest rate.

7. PV = 200/1.05 + 400/1.052 + 300/1.053

= 190.48 + 362.81 + 259.15 = $812.44

9. a. PV = 100 × PVIFA(.08,10) = 100 × 6.7101 = 671.01

b. PV = 100 × PVIFA(.08,20) = 100 × 9.8181 = 981.81

c. PV = 100 × PVIFA(.04,10) = 100 × 8.1109 = 811.09

d. PV = 100 × PVIFA(.04,20) = 100 × 13.5903 = 1,359.03

|11. | | | |Per Period Rate, | |

| | | | |APR/m | |

| | |APR |Compounding Period | |Effective annual rate |

| | | | | | |

| |a. |12% |1 month (m = 12/yr) |.12/12...