Chap002

CHAPTER 2
How to Calculate Present Values

Answers to Problem Sets

1. If the discount factor is .507, then .507*1.126 = $1

2. 125/139 = .899

3. PV = 374/(1.09)9 = 172.20

4. PV = 432/1.15 + 137/(1.152) + 797/(1.153) = 376 + 104 + 524 = $1,003

5. FV = 100*1.158 = $305.90

6. NPV = -1,548 + 138/.09 = -14.67 (cost today plus the present value of the perpetuity) 7. PV = 4/(.14-.04) = $40

8. a. PV = 1/.10 = $10

b. Since the perpetuity will be worth $10 in year 7, and since that is roughly double the present value, the approximate PV equals $5. PV = (1 / .10)/(1.10)7 = 10/2= $5 (approximately)

c. A perpetuity paying $1 starting now would be worth $10, whereas a perpetuity starting in year 8 would be worth roughly $5. The difference between these cash flows is therefore approximately $5. PV = 10 – 5= $5 (approximately)

d. PV = C/(r-g) = 10,000/(.10-.05) = $200,000.

9. a. PV = 10,000/(1.055) = $7,835.26 (assuming the cost of the car does not appreciate over those five years).

b. You need to set aside (12,000 × 6-year annuity factor) = 12,000 × 4.623 = $55,476.

c. At the end of 6 years you would have 1.086 × (60,476 - 55,476) = $7,934.

10. a. FV = 1,000e.12x5 = 1,000e.6 = $1,822.12.

b. PV = 5e-.12 x 8 = 5e-.96 = $1.914 million

c. PV = C (1/r – 1/rert) = 2,000(1/.12 – 1/.12e .12 x15) = $13,912

11.
a. FV = 10,000,000x(1.06)4 = 12,624,770

b. FV = 10,000,000x(1 + .06/12)(4x12) = 12,704,892

c. FV = 10,000,000xe(4x.06) = 12,712,492

12.
a.
PV = $100/1.0110 = $90.53

b.
PV = $100/1.1310 = $29.46

c.
PV = $100/1.2515 = $ 3.52

d.
PV = $100/1.12 + $100/1.122 + $100/1.123 = $240.18

13. a. r1 = 0.1050 = 10.50%

b.

c. AF2 = DF1 + DF2 = 0.905 + 0.819 = 1.724

d. PV of an annuity = C  [Annuity factor at r% for t years]
Here:
$24.65 = $10  [AF3]
AF3 = 2.465

e. AF3 = DF1 + DF2 + DF3 = AF2 + DF3
2.465 = 1.724 + DF3
DF3 = 0.741

14. The present value of the 10-year