Solutions Manual for Principles of Corporate Finance 12th Edition Brealey

SOLUTIONS MANUAL FOR
PRINCIPLES OF CORPORATE
FINANCE 12TH EDITION BREALEY

,Principles of Corporate Finance 12th Edition Brealey Solutions Manual

Chapter 02 - How to Calculate Present Values


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. Ct = PV × (1 + r)t
C8 = $100 × 1.158
C8 = $305.90

Est time: 01-05

2. PV = Ct / DFt
DFt = $125 / $139
DFt = .8993

Est time: 01-05

3. PV = Ct / (1 + r)t
PV = $.099
PV = $172.20

Est time: 01-05

4. a. PV = C1 / (1 + r)1 + C2 / (1 + r)2 + C3 / (1 + r)3
PV = $.15 + $.152 + $.153
PV = $1,003.28

b. NPV = PV – investment
NPV = $1,003.28 – 1,200
NPV = –$196.72

Est time: 01-05


5. 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

6. NPV = C / r – investment


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,Chapter 02 - How to Calculate Present Values


NPV = $138 / .09 − $1,548
NPV = −$14.67

Est time: 01-05


7. PV = C / (r – g)
PV = $4 / (.14 − .04)
PV = $40

Est time: 01-05

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

b. PV7 = (C8 / r)
PV0 approx = (C8 / r) / 2
PV0 approx = ($1 / .10) / 2
PV0 approx = $5

c. A perpetuity paying $1 starting now would be worth $10 (part a), whereas a perpetuity
starting in year 8 would be worth roughly $5 (part b). Thus, a payment of $1 for the next
seven years would also be worth approximately $5 (= $10 – 5).

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

Est time: 06-10

9. 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. a. FV = C × ert
FV = $1,000 × e.12 x 5
FV = $1,822.12

b. PV = C / ert


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, Chapter 02 - How to Calculate Present Values


PV = $5,000,000 / e.12 × 8
PV = $1,914,464

c. PV = C (1 / r – 1 / rert)
PV = $2,000 (1 / .12 – 1 / .12e .12 x 15)

PV = $13,911.69

Est time: 01-05

11.
a. Ct = PV × (1 + r)t
Ct = $10,000,000 x (1.06)4
Ct = $12,624,770

b. Ct = PV × [1+ (r / m)mt
Ct = $10,000,000 × [1 + (.)]12 × 4
Ct = $12,704,892

b. Ct = PV × ert
Ct = $10,000,000 × e.06 × 4
Ct = $12,712,492

Est time: 01-05


12. a. PV = Ct / (1 + r)t
PV = $10,.055
PV = $7,835.26

b. PV = C((1 / r) – {1 / [r(1 + r)t]})
PV = $12,000((1 / .08) – {1 / [.08(1.08)6]})
PV = $55,474.56

c. Ct = PV × (1 + r)t
Ct = ($60,476 − 55,474.56) × 1.086
Ct = $7,936.66

Est time: 06-10

13. a. DF1 = 1 / (1 + r)
r = (1 – .905) / .905
r = .1050, or 10.50%

b. DF2 = 1 / (1 + r)2
DF2 = .1052
DF2 = .8190

c. PVAF2 = DF1 + DF2
PVAF2 = .905 + .819
PVAF2 = 1.7240

d. PVA = C × PVAF3
PVAF3 = $24.65 / $10
PVAF3 = 2.4650



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McGraw-Hill Education.