CHAPTER 2
How to Calculate Present Values
Answers to Problem Sets
- If the discount factor is .507, then .507 x 1.126 = $1.
Est time: 01-05
- DF x 139 = 125. Therefore, DF =125/139 = .899.
Est time: 01-05
- PV = 374/(1.09)9 = 172.20.
Est time: 01-05
- PV = 432/1.15 + 137/(1.152) + 797/(1.153) = 376 + 104 + 524 = $1,003.
Est time: 01-05
- FV = 100 x 1.158 = $305.90.
Est time: 01-05
- NPV = −1,548 + 138/.09 = −14.67 (cost today plus the present value of the
perpetuity).
Est time: 01-05
- PV = 4/(.14 − .04) = $40.
Est time: 01-05
- a. PV = 1/.10 = $10.
- Since the perpetuity will be worth $10 in year 7, and since that is roughly
double the present value, the approximate PV equals $5.
You must take the present value of years 1–7 and subtract from the total present value of the perpetuity:
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).
- PV = C/(r − g) = 10,000/(.10-.05) = $200,000.
Est time: 06-10
9. a. PV = 10,000/(1.055) = $7,835.26 (assuming the cost of the car does not
appreciate over those five years).
- The six-year annuity factor [(1/0.08) – 1/(0.08 x (1+.08)6)] = 4.623. You need to set aside (12,000 × six-year annuity factor) = 12,000 × 4.623 = $55,475.
- At the end of six years you would have 1.086 × (60,476 - 55,475) = $7,935.
Est time: 06-10
10. a. FV = 1,000e.12 x 5 = 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.
Est time: 01-05
11.
- FV = 10,000,000 x (1.06)4 = 12,624,770.
- FV = 10,000,000 x (1 + .06/12)(4 x 12) = 12,704,892.
- FV = 10,000,000 x e(4 x .06) = 12,712,492.
Est time: 01-05
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. |