CHAPTER 2
How to Calculate Prent Values
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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 prent value of the
perpetuity)
dimensionless7.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 prent 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 the 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 tho five years).
b. You need to t 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 ×我心中的鲁迅 (60,476 - 55,476) = $7,934.
10. a. FV = 1,000e.12x5 = 1,000e.6 = $1,822.12.
b. PV = 5e-.12 x 8 = 5ebed-.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
雨声像什么>intervieweeb. FV = 10,000,000x(1 + .06/12)(4x12) = 12,704,892
c. FV = 10,000,000xe(4x.06) = 12,712,492
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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:
broth$24.65 = $10 [AF3]
AF3 = 2.465
e.
AF3 = DF1 + DF2 + DF3 = AF2 + DF3
2.465 = 1.724 + DF3
DF3 = 0.741
14. The prent value of the 10-year stream of cash inflows is:
Thus:
NPV = –$800,000 + $886,739.66 = +$86,739.66
At the end of five years, the factory’s value will be the prent value of the five remaining $170,000 cash flows:
15.
16. a. Let St = salary in year t
b.PV(salary) x 0.05 = $38,033.13
Future value = $38,018.96 x (1.08)30 = $382,714.30
c.
17.
Period | | | Prent Value |
0 | | | 400,000.00 |
1 | | +100,000/1.12 = | + 89,285.71 |
2 | | +200,000/1.122 = | +159,438.78 |
3 | | +300,000/1.123 = | +213,534.07 |
| | Total = NPV = $62,258.56 |
| | | |
18. We can break this down into veral different cash flows, such that the sum of the parate cash flows is the total cash flow. Then, the sum of the prent values of the parate cash flows is the prent value of the entire project. (All dollar figures are in millions.)
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▪Cost of the ship is $8 million
PV = $8 million
幼儿英语话剧剧本▪Revenue is $5 million per year, operating expens are $4 million. Thus, operating cash flow is $1 million per year for 15 years.
▪Major refits cost $2 million each, and will occur at times t = 5 and t = 10.
PV = ($2 million)/1.085 + ($2 million)/1.0810 = $2.288 million
▪Sale for scrap brings in revenue of $1.5 million at t = 15.
PV = $1.5 million/1.0815 = $0.473 million
Adding the prent values gives the prent value of the entire project:
NPV = $8 million + $8.559 million $2.288 million + $0.473 million
NPV = $1.256 million
19. a. PV = $100,000
b. PV = $180,000/1.125 = $102,136.83
c. PV = $11,400/0.12 = $95,000
d.
e. PV = $6,500/(0.12 0.05) = $92,857.14
Prize (d) is the most valuable becau it has the highest prent value.
20. Mr. Bast is buying a curity worth $20,000 now. That is its prent value. The unknown is the annual payment. Using the prent value of an annuity formula, we have:
