Solution manual for
principles of corporate finance
14th edition by richard Brealey,
stewart myers, franklin allen
PDF FORMAT
, CHAPTER 1
Introduction to Corporate Finance
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. real
b. executive airplanes
c. brand names
d. financial
e. bonds
*f. investment or capital expenditure
*g. capital budgeting or investment
h. financing
*Note that f and g are interchangeable in the question.
Est time: 01-05
2. A trademark, a factory, undeveloped land, and your work force (c, d, e, and g) are all real assets.
Real assets are identifiable as items with intrinsic value. The others in the list are financial assets,
that is, these assets derive value because of a contractual claim.
Est time: 01-05
3. a. Financial assets, such as stocks or bank loans, are claims held by investors.
Corporations sell financial assets to raise the cash to invest in real assets such as plant
and equipment. Some real assets are intangible.
b. Capital expenditure means investment in real assets. Financing means raising the cash
for this investment.
c. The shares of public corporations are traded on stock exchanges and can be purchased
by a wide range of investors. The shares of closely held corporations are not publicly
traded and are held by a small group of private investors.
d. Unlimited liability: Investors are responsible for all the firm‘s debts. A sole proprietor has
unlimited liability. Investors in corporations have limited liability. They can lose their
investment, but no more.
Est time: 01-05
,4. Items c and d apply to corporations. Because corporations have perpetual life, ownership can be
transferred without affecting operations, and managers can be fired with no effect on ownership.
Other forms of business may have unlimited liability and limited life.
Est time: 01-05
5. Separation of ownership facilitates the key attributes of a corporation, including limited liability for
investors, transferability of ownership, a separate legal personality of the corporation, and
delegated centralized management. These four attributes provide substantial benefit for
investors, including the ability to diversify their investment among many uncorrelated returns—a
very valuable tool explored in later chapters. Also, these attributes allow investors to quickly exit,
enter, or short sell an investment, thereby generating an active liquid market for corporations.
However, these positive aspects also introduce substantial negative externalities as well. The
separation of ownership from management typically leads to agency problems, where managers
prefer to consume private perks or make other decisions for their private benefit—rather than
maximize shareholder wealth. Shareholders tend to exercise less oversight of each individual
investment as their diversification increases. Finally, the corporation‘s separate legal personality
makes it difficult to enforce accountability if they externalize costs onto society.
Est time: 01-05
6. Shareholders will only vote to maximize shareholder wealth. Shareholders can modify their
pattern of consumption through borrowing and lending, match risk preferences, and hopefully
balance their own checkbooks (or hire a qualified professional to help them with these tasks).
Est time: 01-05
7. If the investment increases the firm‘s wealth, it increases the firm‘s share value. Ms. Espinoza
could then sell some or all these more valuable shares to provide for her retirement income.
Est time: 01-05
8. a. Assuming that the encabulator market is risky, an 8% expected return on
the F&H encabulator investments may be inferior to a 4% return on U.S.
government securities, depending on the relative risk between the two assets.
b. Unless the financial assets are as safe as U.S. government securities, their cost of capital
would be higher. The CFO could consider expected returns on assets with similar risk.
Est time: 06-10
9. Managers would act in shareholders‘ interests because they have a legal duty to act in their
interests. Managers may also receive compensation— bonuses, stock, and option payouts with
value tied (roughly) to firm performance. Managers may fear personal reputational damage from
not acting in shareholders‘ interests. And managers can be fired by the board of directors (elected
by shareholders). If managers still fail to act in shareholders‘ interests, shareholders may sell
their shares, lowering the stock price and potentially creating the possibility of a takeover, which
can again lead to changes in the board of directors and senior management.
Est time: 01-05
,10. Managers that are insulated from takeovers may be more prone to agency problems and
therefore more likely to act in their own interests rather than in shareholders‘. If a firm instituted a
new takeover defense, we might expect to see the value of its shares decline as agency
problems increase and less shareholder value maximization occurs. The counterargument is that
defensive measures allow managers to negotiate for a higher purchase price in the face of a
takeover bid—to the benefit of shareholder value.
Est time: 01-05
Appendix Questions:
1.Both would still invest in their friend‘s business. A invests and receives $121,000 for his
investment at the end of the year—which is greater than the $120,000 that would be received
from lending at 20% ($100,000 × 1.20 = $120,000). G also invests, but borrows against the
$121,000 payment, and thus receives $100,833 ($121,.20) today.
Est time: 01-05
2. a. He could consume up to $200,000 now (forgoing all future consumption) or up to $216,000
next year ($200,000 × 1.08, forgoing all consumption this year). He should invest all of his wealth
to earn $216,000 next year. To choose the same consumption (C) in both years, C = ($200,000
– C) × 1.08 = $103,846.
Dollars Next Year
220,000
216,000
203,704
200,000
Dollars Now
b. He should invest all of his wealth to earn $220,000 ($200,000 × 1.10) next year. If he
consumes all this year, he can now have a total of $203,703.70 ($200,000 × 1.10/1.08) this year
or $220,000 next year. If he consumes C this year, the amount available for next year‘s
consumption is ($203,703.70 – C) × 1.08. To get equal consumption in both years, set the
amount consumed today equal to the amount next year:
C = ($203,703.70 – C) × 1.08
C = $105,769.20
Est time: 06-10
, 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. 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 accrue 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
3.
Transistors Transistors (1 r)t
2019 1972
32, 000, 000, 000 2, 250 (1 r)48
r 40.94% 59.00% rPredicted
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. 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
9. PV = Ct / (1 + r)t
PV = $.099
PV = $172.20
Est time: 01-05
10. 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
11. 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 = $89.29 + $79.72 + $71.18
PV = $240.18
Est time: 01-05
10
Ct
12. NPV (1.12)
t 0
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
,13. 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 remaining cash flows:
PV = $170,000 × ((1 / .14) – {1 / [.14(1.14)(10 – 5)]})
PV = $583,623.76
Est time: 01-05
14. Use the formula: NPV = –C0 + C1 / (1 + r) + C2 / (1 + r)2
NPV5% = –$700,000 + $30,.05 + $870,.052
NPV5% = $117,687.07
NPV10% = –$700,000 + $30,.10 + $870,.102
NPV10% = $46,280.99
NPV15% = –$700,000 + $30,.15 + $870,.152
NPV15% = –$16,068.05
The figure below shows that the project has a zero NPV at about 13.65%.
NPV13.65% = –$700,000 + $30,.1365 + $870,.13652
NPV13.65% = –$36.83
Est time: 11-15
, 15. a. NPV = –Investment + PVAoperating cash flows – PVrefits + PVscrap value
NPV = –$8,000,000 + ($5,000,000 – 4,000,000) × ((1 / .08) – {1 / [.08(1.08) 15]}) –
($2,000,.085 + $2,000,.0810) + $1,500,.0815
NPV = –$8,000,000 + 8,559,479 – 2,287,553 + 472,863
NPV = –$1,255,212
b. The cost of borrowing does not affect the NPV because the opportunity cost of capital
depends on the use of the funds, not the source.
Est time: 06-10
16. NPV = C / r – investment
NPV = $138 / .09 − $1,548
NPV = −$14.67
Est time: 01-05
17. One way to approach this problem is to solve for the present value of:
(1) $100 per year for 10 years, and
(2) $100 per year in perpetuity, with the first cash flow at year 11.
If this is a fair deal, the present values must be equal, thus solve for the interest rate (r).
The present value of $100 per year for 10 years is:
PV = C × ((1 / r) – {1 / [r × (1 + r)t]})
PV = $100 × ((1 / r) – {1 / [r × (1 + r)10]})
The present value, as of year 0, of $100 per year forever, with the first payment in year 11, is:
PV = (C / r) / (1 + r)t
PV = ($100 / r) / (1 + r)10
Equating these two present values, we have:
$100 × ((1 / r) – {1 / [r × (1 + r)10]}) = ($100 / r) / (1 + r)10
Using trial and error or algebraic solution, r = 7.18%.
Est time: 06-10
principles of corporate finance
14th edition by richard Brealey,
stewart myers, franklin allen
PDF FORMAT
, CHAPTER 1
Introduction to Corporate Finance
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. real
b. executive airplanes
c. brand names
d. financial
e. bonds
*f. investment or capital expenditure
*g. capital budgeting or investment
h. financing
*Note that f and g are interchangeable in the question.
Est time: 01-05
2. A trademark, a factory, undeveloped land, and your work force (c, d, e, and g) are all real assets.
Real assets are identifiable as items with intrinsic value. The others in the list are financial assets,
that is, these assets derive value because of a contractual claim.
Est time: 01-05
3. a. Financial assets, such as stocks or bank loans, are claims held by investors.
Corporations sell financial assets to raise the cash to invest in real assets such as plant
and equipment. Some real assets are intangible.
b. Capital expenditure means investment in real assets. Financing means raising the cash
for this investment.
c. The shares of public corporations are traded on stock exchanges and can be purchased
by a wide range of investors. The shares of closely held corporations are not publicly
traded and are held by a small group of private investors.
d. Unlimited liability: Investors are responsible for all the firm‘s debts. A sole proprietor has
unlimited liability. Investors in corporations have limited liability. They can lose their
investment, but no more.
Est time: 01-05
,4. Items c and d apply to corporations. Because corporations have perpetual life, ownership can be
transferred without affecting operations, and managers can be fired with no effect on ownership.
Other forms of business may have unlimited liability and limited life.
Est time: 01-05
5. Separation of ownership facilitates the key attributes of a corporation, including limited liability for
investors, transferability of ownership, a separate legal personality of the corporation, and
delegated centralized management. These four attributes provide substantial benefit for
investors, including the ability to diversify their investment among many uncorrelated returns—a
very valuable tool explored in later chapters. Also, these attributes allow investors to quickly exit,
enter, or short sell an investment, thereby generating an active liquid market for corporations.
However, these positive aspects also introduce substantial negative externalities as well. The
separation of ownership from management typically leads to agency problems, where managers
prefer to consume private perks or make other decisions for their private benefit—rather than
maximize shareholder wealth. Shareholders tend to exercise less oversight of each individual
investment as their diversification increases. Finally, the corporation‘s separate legal personality
makes it difficult to enforce accountability if they externalize costs onto society.
Est time: 01-05
6. Shareholders will only vote to maximize shareholder wealth. Shareholders can modify their
pattern of consumption through borrowing and lending, match risk preferences, and hopefully
balance their own checkbooks (or hire a qualified professional to help them with these tasks).
Est time: 01-05
7. If the investment increases the firm‘s wealth, it increases the firm‘s share value. Ms. Espinoza
could then sell some or all these more valuable shares to provide for her retirement income.
Est time: 01-05
8. a. Assuming that the encabulator market is risky, an 8% expected return on
the F&H encabulator investments may be inferior to a 4% return on U.S.
government securities, depending on the relative risk between the two assets.
b. Unless the financial assets are as safe as U.S. government securities, their cost of capital
would be higher. The CFO could consider expected returns on assets with similar risk.
Est time: 06-10
9. Managers would act in shareholders‘ interests because they have a legal duty to act in their
interests. Managers may also receive compensation— bonuses, stock, and option payouts with
value tied (roughly) to firm performance. Managers may fear personal reputational damage from
not acting in shareholders‘ interests. And managers can be fired by the board of directors (elected
by shareholders). If managers still fail to act in shareholders‘ interests, shareholders may sell
their shares, lowering the stock price and potentially creating the possibility of a takeover, which
can again lead to changes in the board of directors and senior management.
Est time: 01-05
,10. Managers that are insulated from takeovers may be more prone to agency problems and
therefore more likely to act in their own interests rather than in shareholders‘. If a firm instituted a
new takeover defense, we might expect to see the value of its shares decline as agency
problems increase and less shareholder value maximization occurs. The counterargument is that
defensive measures allow managers to negotiate for a higher purchase price in the face of a
takeover bid—to the benefit of shareholder value.
Est time: 01-05
Appendix Questions:
1.Both would still invest in their friend‘s business. A invests and receives $121,000 for his
investment at the end of the year—which is greater than the $120,000 that would be received
from lending at 20% ($100,000 × 1.20 = $120,000). G also invests, but borrows against the
$121,000 payment, and thus receives $100,833 ($121,.20) today.
Est time: 01-05
2. a. He could consume up to $200,000 now (forgoing all future consumption) or up to $216,000
next year ($200,000 × 1.08, forgoing all consumption this year). He should invest all of his wealth
to earn $216,000 next year. To choose the same consumption (C) in both years, C = ($200,000
– C) × 1.08 = $103,846.
Dollars Next Year
220,000
216,000
203,704
200,000
Dollars Now
b. He should invest all of his wealth to earn $220,000 ($200,000 × 1.10) next year. If he
consumes all this year, he can now have a total of $203,703.70 ($200,000 × 1.10/1.08) this year
or $220,000 next year. If he consumes C this year, the amount available for next year‘s
consumption is ($203,703.70 – C) × 1.08. To get equal consumption in both years, set the
amount consumed today equal to the amount next year:
C = ($203,703.70 – C) × 1.08
C = $105,769.20
Est time: 06-10
, 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. 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 accrue 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
3.
Transistors Transistors (1 r)t
2019 1972
32, 000, 000, 000 2, 250 (1 r)48
r 40.94% 59.00% rPredicted
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. 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
9. PV = Ct / (1 + r)t
PV = $.099
PV = $172.20
Est time: 01-05
10. 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
11. 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 = $89.29 + $79.72 + $71.18
PV = $240.18
Est time: 01-05
10
Ct
12. NPV (1.12)
t 0
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
,13. 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 remaining cash flows:
PV = $170,000 × ((1 / .14) – {1 / [.14(1.14)(10 – 5)]})
PV = $583,623.76
Est time: 01-05
14. Use the formula: NPV = –C0 + C1 / (1 + r) + C2 / (1 + r)2
NPV5% = –$700,000 + $30,.05 + $870,.052
NPV5% = $117,687.07
NPV10% = –$700,000 + $30,.10 + $870,.102
NPV10% = $46,280.99
NPV15% = –$700,000 + $30,.15 + $870,.152
NPV15% = –$16,068.05
The figure below shows that the project has a zero NPV at about 13.65%.
NPV13.65% = –$700,000 + $30,.1365 + $870,.13652
NPV13.65% = –$36.83
Est time: 11-15
, 15. a. NPV = –Investment + PVAoperating cash flows – PVrefits + PVscrap value
NPV = –$8,000,000 + ($5,000,000 – 4,000,000) × ((1 / .08) – {1 / [.08(1.08) 15]}) –
($2,000,.085 + $2,000,.0810) + $1,500,.0815
NPV = –$8,000,000 + 8,559,479 – 2,287,553 + 472,863
NPV = –$1,255,212
b. The cost of borrowing does not affect the NPV because the opportunity cost of capital
depends on the use of the funds, not the source.
Est time: 06-10
16. NPV = C / r – investment
NPV = $138 / .09 − $1,548
NPV = −$14.67
Est time: 01-05
17. One way to approach this problem is to solve for the present value of:
(1) $100 per year for 10 years, and
(2) $100 per year in perpetuity, with the first cash flow at year 11.
If this is a fair deal, the present values must be equal, thus solve for the interest rate (r).
The present value of $100 per year for 10 years is:
PV = C × ((1 / r) – {1 / [r × (1 + r)t]})
PV = $100 × ((1 / r) – {1 / [r × (1 + r)10]})
The present value, as of year 0, of $100 per year forever, with the first payment in year 11, is:
PV = (C / r) / (1 + r)t
PV = ($100 / r) / (1 + r)10
Equating these two present values, we have:
$100 × ((1 / r) – {1 / [r × (1 + r)10]}) = ($100 / r) / (1 + r)10
Using trial and error or algebraic solution, r = 7.18%.
Est time: 06-10
