Chap002 Solutions
CHAPTER 2
How to Calculate Present Values
Answers to Problem Sets
1. If the discount factor is .507, then .507 x 1.126 = $1.
Est time: 01-05
2. DF x 139 = 125. Therefore, DF =125/139 = .899.
Est time: 01-05
3. PV = 374/(1.09)9 = 172.20.
Est time: 01-05
4. PV = 432/1.15 + 137/(1.152) + 797/(1.153) = 376 + 104 + 524 = $1,003.
Est time: 01-05
5. FV = 100 x 1.158 = $305.90.
Est time: 01-05
6. NPV = −1,548 + 138/.09 = −14.67 (cost today plus the present value of the perpetuity). Est time: 01-05
7. PV = 4/(.14 − .04) = $40.
Est time: 01-05
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.
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).
d. PV = C/(r − g) = 10,000/(.10-.05) = $200,000.
Est time: 06-10
9. a. PV = 600,000/(1.055) = `470,115.7 (assuming the cost of the car does not appreciate over those five years).
b. The six-year annuity factor [(1/0.08) – 1/(0.08 x (1+.08)6)] = 4.623. You need to set aside (600,000 × six-year annuity factor) = 600,000 × 4.623 = `2,773,727.8.
c. At the end of six years you would have 1.086 × (3,000,000 – 2,773,727.8) = `359,065.55.
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.
a. FV = 10,000,000 x (1.06)4 = 12,624,770.
b. FV = 10,000,000 x (1 + .06/12)(4 x 12) = 12,704,892.
c. FV = 10,000,000 x e(4 x .06) = 12,712,492.
Est time: 01-05
12.
a.
How to Calculate Present Values
Answers to Problem Sets
1. If the discount factor is .507, then .507 x 1.126 = $1.
Est time: 01-05
2. DF x 139 = 125. Therefore, DF =125/139 = .899.
Est time: 01-05
3. PV = 374/(1.09)9 = 172.20.
Est time: 01-05
4. PV = 432/1.15 + 137/(1.152) + 797/(1.153) = 376 + 104 + 524 = $1,003.
Est time: 01-05
5. FV = 100 x 1.158 = $305.90.
Est time: 01-05
6. NPV = −1,548 + 138/.09 = −14.67 (cost today plus the present value of the perpetuity). Est time: 01-05
7. PV = 4/(.14 − .04) = $40.
Est time: 01-05
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.
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).
d. PV = C/(r − g) = 10,000/(.10-.05) = $200,000.
Est time: 06-10
9. a. PV = 600,000/(1.055) = `470,115.7 (assuming the cost of the car does not appreciate over those five years).
b. The six-year annuity factor [(1/0.08) – 1/(0.08 x (1+.08)6)] = 4.623. You need to set aside (600,000 × six-year annuity factor) = 600,000 × 4.623 = `2,773,727.8.
c. At the end of six years you would have 1.086 × (3,000,000 – 2,773,727.8) = `359,065.55.
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.
a. FV = 10,000,000 x (1.06)4 = 12,624,770.
b. FV = 10,000,000 x (1 + .06/12)(4 x 12) = 12,704,892.
c. FV = 10,000,000 x e(4 x .06) = 12,712,492.
Est time: 01-05
12.
a.