SOLUTION MANUAL
SOLUTION MANUAL
, CHAPTER 2
How to Calculate Present Values
The values shown in the solutions may be rounded for display purposes. However, the answers were
derived using a spreadsheet without any intermediate rounding.
Answers to Problem Sets
1. a. False. The opportunity cost of capital varies with the risks associated with each individual
project or investment. The cost of borrowing is unrelated to these risks.
b. True. The opportunity cost of capital depends on the risks associated with each project and
its cash flows.
c. True. The opportunity cost of capital is dependent on the rates of returns shareholders can
earn on the own by investing in projects with similar risks
d. False. Bank accounts, within FDIC limits, are considered to be risk-free. Unless an investment
is also risk-free, its opportunity cost of capital must be adjusted upward to account for
the associated risks.
Est time: 01-05
2. The opportunity cost of capital refers to the rate of return a firm’s shareholders could earn on their
own by investing at the same level of risk. Thus, when a firm considers a new project, it is the risk
level of the project that determines opportunity cost of capital for that project.
Est time: 01-05
3. a. In the first year, you will earn $1,000 × 0.04 = $40.00
b. In the second year, you will earn $1,040 × 0.04 = $41.60
c. By the end of the ninth year, you will accrued a principle of $1,040 × (1.049) = $1,423.31.
Therefore, in the Tenth year, you will earn $1,423.31 × 0.04 = $56.93
Est time: 01-05
4. The “Rule of 72” is a rule of thumb that says with discrete compounding the time it takes for an
investment to double in value is roughly 72/interest rate (in percent).
Therefore, without a calculator, the Rule of 72 estimate is:
Time to double = 72 / r
Time to double =
Time to double = 18 years , so less than 25 years.
If you did have a calculator handy, this estimate is verified as followed:
Ct = PV × (1 + r)t
t = ln2 / ln1.04
t = 17.67 years
Est time: 01-05
,5. a. Using the inflation adjusted 1958 price of $1,060, the real return per annum is:
$450,300,000 = $1,060 × (1 + r)(2017-1958)
r = [$450,300,000/$1,060](1/59 ) – 1 = 0.2456 or 24.56% per annum
b. Using the inflation adjusted 1519 price of $575,000, the real return per annum is:
$450,300,000 = $575,000 × (1 + r)(2017-1519)
r = [$450,300,000/$575,000](1/498 ) – 1 = 0.0135 or 1.35% per annum
Est time: 01-05
6. Ct = PV × (1 + r)t
C8 = $100 × 1.158
C8 = $305.90
Est time: 01-05
7. a. Ct = PV × (1 + r)t
C10 = $100 × 1.0610
C10 = $179.08
b. Ct = PV × (1 + r)t
C20 = $100 × 1.0620
C20 = $320.71
c. Ct = PV × (1 + r)t
C10 = $100 × 1.0410
C10 = $148.02
d. Ct = PV × (1 + r)t
C20 = $100 × 1.0420
C20 = $219.11
Est time: 01-05
8. Ct = PV × (1 + r)t
C2016 = $100 × 1.345
C2016 = $432.04
Est time: 01-05
9. a. PV = Ct × DFt
DFt = $125 / $139
DFt = .8993
b. Ct = PV × (1 + r)t
$139 = $125 × (1+r)5
r = [$139/$125](1/5) – 1 = 0.0215 or 2.15%
Est time: 01-05
, 10. PV = Ct / (1 + r)t
PV = $.099
PV = $172.20
Est time: 01-05
11. PV = C1 / (1 + r)1 + C2 / (1 + r)2 + C3 / (1 + r)3
PV = $.15 + $.152 + $.153
PV = $1,003.28
NPV = PV – investment
NPV = $1,003.28 – 1,200
NPV = –$196.72
Est time: 01-05
12. The basic present value formula is: PV = C / (1 + r)t
a. PV = $.0110
PV = $90.53
b. PV = $.1310
PV = $29.46
c. PV = $.2515
PV = $3.52
d. PV = C1 / (1 + r) + C2 / (1 + r)2 + C3 / (1 + r)3
PV = $.12 + $.122 + $.123
PV = $240.18
Est time: 01-05
10
Ct
13. NPV
t 0 (1.12)t
NPV = –$380,000 + $50,.12 + $57,.122 + $75,.123 + $80,.124 +
$85,.125 + $92,.126 + $92,.127 + $80,.128 + $68,.129
+ $50,.1210
NPV = $23,696.15
Est time: 01-05
14. a. NPV = – Investment + C × ((1 / r) – {1 / [r(1 + r)t]})
NPV = –$800,000 + $170,000 × ((1 / .14) – {1 / [.14(1.14)10]})
NPV = $86,739.66
b. After five years, the factory’s value will be the present value of the five remaining year’s
of cash flows.
SOLUTION MANUAL
, CHAPTER 2
How to Calculate Present Values
The values shown in the solutions may be rounded for display purposes. However, the answers were
derived using a spreadsheet without any intermediate rounding.
Answers to Problem Sets
1. a. False. The opportunity cost of capital varies with the risks associated with each individual
project or investment. The cost of borrowing is unrelated to these risks.
b. True. The opportunity cost of capital depends on the risks associated with each project and
its cash flows.
c. True. The opportunity cost of capital is dependent on the rates of returns shareholders can
earn on the own by investing in projects with similar risks
d. False. Bank accounts, within FDIC limits, are considered to be risk-free. Unless an investment
is also risk-free, its opportunity cost of capital must be adjusted upward to account for
the associated risks.
Est time: 01-05
2. The opportunity cost of capital refers to the rate of return a firm’s shareholders could earn on their
own by investing at the same level of risk. Thus, when a firm considers a new project, it is the risk
level of the project that determines opportunity cost of capital for that project.
Est time: 01-05
3. a. In the first year, you will earn $1,000 × 0.04 = $40.00
b. In the second year, you will earn $1,040 × 0.04 = $41.60
c. By the end of the ninth year, you will accrued a principle of $1,040 × (1.049) = $1,423.31.
Therefore, in the Tenth year, you will earn $1,423.31 × 0.04 = $56.93
Est time: 01-05
4. The “Rule of 72” is a rule of thumb that says with discrete compounding the time it takes for an
investment to double in value is roughly 72/interest rate (in percent).
Therefore, without a calculator, the Rule of 72 estimate is:
Time to double = 72 / r
Time to double =
Time to double = 18 years , so less than 25 years.
If you did have a calculator handy, this estimate is verified as followed:
Ct = PV × (1 + r)t
t = ln2 / ln1.04
t = 17.67 years
Est time: 01-05
,5. a. Using the inflation adjusted 1958 price of $1,060, the real return per annum is:
$450,300,000 = $1,060 × (1 + r)(2017-1958)
r = [$450,300,000/$1,060](1/59 ) – 1 = 0.2456 or 24.56% per annum
b. Using the inflation adjusted 1519 price of $575,000, the real return per annum is:
$450,300,000 = $575,000 × (1 + r)(2017-1519)
r = [$450,300,000/$575,000](1/498 ) – 1 = 0.0135 or 1.35% per annum
Est time: 01-05
6. Ct = PV × (1 + r)t
C8 = $100 × 1.158
C8 = $305.90
Est time: 01-05
7. a. Ct = PV × (1 + r)t
C10 = $100 × 1.0610
C10 = $179.08
b. Ct = PV × (1 + r)t
C20 = $100 × 1.0620
C20 = $320.71
c. Ct = PV × (1 + r)t
C10 = $100 × 1.0410
C10 = $148.02
d. Ct = PV × (1 + r)t
C20 = $100 × 1.0420
C20 = $219.11
Est time: 01-05
8. Ct = PV × (1 + r)t
C2016 = $100 × 1.345
C2016 = $432.04
Est time: 01-05
9. a. PV = Ct × DFt
DFt = $125 / $139
DFt = .8993
b. Ct = PV × (1 + r)t
$139 = $125 × (1+r)5
r = [$139/$125](1/5) – 1 = 0.0215 or 2.15%
Est time: 01-05
, 10. PV = Ct / (1 + r)t
PV = $.099
PV = $172.20
Est time: 01-05
11. PV = C1 / (1 + r)1 + C2 / (1 + r)2 + C3 / (1 + r)3
PV = $.15 + $.152 + $.153
PV = $1,003.28
NPV = PV – investment
NPV = $1,003.28 – 1,200
NPV = –$196.72
Est time: 01-05
12. The basic present value formula is: PV = C / (1 + r)t
a. PV = $.0110
PV = $90.53
b. PV = $.1310
PV = $29.46
c. PV = $.2515
PV = $3.52
d. PV = C1 / (1 + r) + C2 / (1 + r)2 + C3 / (1 + r)3
PV = $.12 + $.122 + $.123
PV = $240.18
Est time: 01-05
10
Ct
13. NPV
t 0 (1.12)t
NPV = –$380,000 + $50,.12 + $57,.122 + $75,.123 + $80,.124 +
$85,.125 + $92,.126 + $92,.127 + $80,.128 + $68,.129
+ $50,.1210
NPV = $23,696.15
Est time: 01-05
14. a. NPV = – Investment + C × ((1 / r) – {1 / [r(1 + r)t]})
NPV = –$800,000 + $170,000 × ((1 / .14) – {1 / [.14(1.14)10]})
NPV = $86,739.66
b. After five years, the factory’s value will be the present value of the five remaining year’s
of cash flows.
