Chapter 16 In Class Problems - Solutions
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Solutions for Chapter 16 In-class Practice Problems
1. You own 25% of Unique Vacations, Inc. You have decided to retire and want to sell your shares in this closely held, all equity firm. The other shareholders have agreed to have the firm borrow $1.5 million to purchase your 1,000 shares of stock. What is the total value of this firm today if you ignore taxes?
Price per share
=
$
1,500,000
1,000
=
$
1,500
Current noof shares
=
1,000
0.25
=
4,000
[
(
4,000
−
1000
)
∗
$
1,500
]
+
$
1,500,000
=
$
6,000,000
∨
simply
4,000
∗
$
1,500
=
$
6,000,000
2. Your firm has a debt-equity ratio of .75. Your pre-tax cost of debt is 7% and your required return on assets is 15%. What is your cost of equity if you ignore taxes? r
E
=
r
A
+
(
r
A
−
r
D
)
D
E
=
0.15
+
(
0.15
−
0.07
)
0.75
1
=
0.21
=
21%
3. Bigelow, Inc. has a cost of equity of 13.56% and a pre-tax cost of debt of 7%. The required return on the assets is 11%. What is the firm’s debt-equity ratio based on MM Proposition II with no taxes? r
E
=
0.1356
=
r
A
+
(
r
A
−
r
D
)
D
E
=
0.11
+
(
0.11
−
0.07
)
D
E
→
D
E
=
0.64
4. Gail’s Dance Studio is currently an all equity firm that has 80,000 shares of stock outstanding with a market price of $42 a share. The current cost of equity is 12% and the tax rate is 34%. Gail is considering adding $1 million of debt with a coupon rate of 8% to her capital structure. The debt will be sold at par value. What is the levered value of the equity? V
L
=
V
U
+
D T
C
=(
80,000
∗
$
42
)+
(
1,000,000
∗
0.34
)
=
3,700,000
V
L
=
FirmValue
=
V
E
+
V
D
→
V
E = $3.7m − $1m = $2.7m
5. Hey Guys!, Inc. has debt with both a face and a market value of $3,000. This debt has a coupon rate of 7% and pays interest annually. The expected earnings before interest and taxes is $1,200, the tax rate is 34%, and the unlevered cost of capital is 12%. What is the firm’s cost of equity? V
U
=
EBIT
(
1
−
T
C
)
R
U
=
1,200
∗
(
1
−
0.34
)
0.12
=
$
6,600
V
L
=
V
U
+
D T
C
=
6,600
+
(
3,000
∗
0.34
)
=
$
7,620
V
L
=
FirmValue
=
V
E
+
V
D
→V
E
=
V
L
−
V
D
=
$
7,620
−
$
3,000
=
$
4,620
r
E
=
r
U
+
(
r
U
−
r
D
)
D
E
(
1
−
T
c
)
=
0.12
+
(
0.12
−
0.07
)
3,000
4,620
∗(
1
−
0.34
)=
0.1414
=
14.14%
6. Bertha’s Boutique has 2,000 bonds outstanding with a face value of $1,000 each and a coupon rate of 9%. The interest is paid semi-annually. What is the amount of the annual interest tax shield if the tax rate is 34%? Annual Intrerest tax Shield
=
D
∗
R
D
∗
T
c
→
(
2000
∗
1,000
)∗
0.09
∗
0.34
=
61,200
7. A firm has debt of $5,000, equity of $16,000, a cost of debt of 8%, a cost of equity of 12%, and a tax rate of 34%. What is the firm’s weighted average cost of capital? WACC
=
E
V
r
E
+
D
V
r
D
(
1
−
T
C
)
=
16,000
21,000
∗
12%
+
5,000
21,000
∗
8%
∗
(
1
−
0.34
)
=
10.40%
8.
If a firm is unlevered and has a cost of equity capital 12%, what would its cost of equity be if its debt-equity ratio became 2? The expected cost of debt is 8%. r
E
=
r
A
+
(
r
A
−
r
D
)
D
E
∗(
1
−
T
c
)=
0.12
+
(
0.12
−
0.08
)
2
1
=
0.20
=
20%
9. A firm has zero debt in its capital structure. Its overall cost of capital is 9%. The firm is considering a new capital structure with 40% debt. The interest rate on the debt would be 4%. Assuming that the corporate tax rate is 34%, what would its cost of equity capital with the new capital structure be? r
E
=
r
A
+
(
r
A
−
r
D
)
D
E
∗
(
1
−
T
c
)
=
0.09
+
(
0.09
−
0.04
)
∗
0.4
0.6
∗(
1
−
0.34
)=
0.112
=
11.2%
10. Consider two firms, U and L, both with $100,000 in assets. Firm U is unlevered, and firm L has $40,000 of debt that pays 5% interest. There are two investors, Mike and Steve, who own 20% of firm L each. Mike believes that leverage works in his favor. Steve says that this is an illusion, and that with the possibility of borrowing on his own account at 5% interest, he can replicate Mike's payout from firm L. Given a level of operating income of $5000, show the specific strategy that Steve has in mind. Mikeis entitled
¿
0.2
(
$
5000
−
$
2000
)=
$
6000.2
∗(
Operatingincome
−
Interest expense
)
Steveliquidateshis position
(
20%
of L’ s equity
)∧
receives
20%
∗(
100,000
−
40,000
)=
$
12,000
Steve borrows $
8,000
at
5%
interest
(
20%
of Firm L' s Debt
)∧
pays $
400
∈
interest .
Stevethen purchases
20%
of FirmU
∧
pays
20%
∗(
100,000
)=
$
20,000
Steveisnow entitled
¿
receive
20%
∗(
$
5000
)=
$
1000
¿
firmU ’ searnings.
Steve' stotal payout is $
1000
−
$
400
=
$
600
,
∨
Mike' s payout .
11. The Nantucket Nugget is unlevered and is valued at $640,000. Nantucket is currently deciding whether including
debt in its capital structure would increase its value. The current cost of equity is 12%. Under consideration is issuing $300,000 in new debt with an 8% interest rate. Nantucket would repurchase $300,000 of stock with the
proceeds of the debt issue. There are currently 32,000 shares outstanding and effective marginal tax bracket is zero. What will Nantucket's new WACC be? New FirmValue
:
$
640,000
+(
.0
)(
$
300,000
)=
$
640,000
Capital Structure
=
D
+
E
=
300,000
+
340,000
r
E
¿
0.12
+(
300
/
340
)∗(
0.12
−
0.08
)=
0.12
+
0.0353
=
0.1553
=
15.53%
WACC
=(
300
/
640
)∗(
0.08
)+(
340
/
640
)∗(
0.1553
)=
0.0375
+
0.0825
=
0.12
=
12%
The value of the firm stays at $
640,000
(
MM I
)
,the cost of levered equity rises
¿
15.53%
∧
the WACC
remainsat
12%
.
12. (
WACC
) The Nantucket Nugget is unlevered and is valued at $640,000. Nantucket is currently deciding whether including debt in its capital structure would increase its value. The current of cost of equity is 12%. Under consideration is issuing $300,000 in new debt with an 8% interest rate. Nantucket would repurchase $300,000 of stock with the proceeds of the debt issue. There are currently 32,000 shares outstanding and its effective marginal tax bracket is 34%. What will Nantucket's new WACC be? New FirmValue
:
$
640,000
+(
.34
)(
$
300,000
)=
$
742,000
Capital Structure
=
D
+
E
=
$
300,000
+
$
442,000
r E
=
0.12
+(
300
/
442
)∗(
0.12
−
0.08
)∗(
1
−
0.34
)=
0.12
+
0.0179
=
0.1379
=
13.79%
WACC
=(
300
/
742
)∗(
0.08
)∗(
1
−
0.34
)+(
442
/
742
)∗(
0.1379
)=
0.0213
+
0.0821
=
0.1034
=
10.34 %
The value of the firm increases
¿
$
742,000
(
¿
Valueof the Tax Shield
)
,increasingthe relative
weight of equity
∧
the cost of levered equityrises
¿
13.79%
∧
the WACC falls
¿
at
10.34%
whichisconsistent withthe increase
∈
firm value .
13. (
BREAK-EVEN EPS EBIT
) Solin Inc. has 2,000,000 shares outstanding, $4,000,000 of debt at 5% interest and
is subject to 35% tax rate. An additional $1,000,000 has to be raised, and the following alternatives are available:
Common shares
The company can issue equity at $5 a share
200,000 new shares.
Debt
Debt can be issued at 5% again. (Solin does not use debt to repurchase shares.)
Compute EPS asafunction of EBIT for both alternatives
∧
derivethe break even point .
You need to equalize the EPS values under both “shares” and “debt” capital structures to find the break-even EBIT. EPS
shares
=
(
EBIT
−
Interest
)(
1
−
T
c
)
¿
of sharesoutstanding
=
[
EBIT
−
(
4,000,000
∗
0.05
)
]
∗(
1
−
0.35
)
2,000,000
+
200,000
EPS
debt
=
(
EBIT
−
Interest
)(
1
−
T
c
)
¿
of shares outstanding
=
[
EBIT
−
(
5,000,000
∗
0.05
)
]∗(
1
−
0.35
)
2,000,000
EPS
shares
=
EPS
debt
→
[
EBIT
−
(
4,000,000
∗
0.05
)
]
∗
0.65
2,200,000
=
[
EBIT
−
(
5,000,000
∗
0.05
)
]∗
0.65
2,000,000
(
EBIT
−
200,000
)
∗
0.65
2,200,000
=
(
EBIT
−
250,000
)
∗
0.65
2,000,000
→EBIT
=
$
750,000
EPS
shares
=
EPS
debt
=
$
0.1625
Numerator representsthe aftertax earnings,whiledenominator
¿
of sharesoutstanding .
¿
findthebreakeven point ,equatethe EPS for the twoalternatives
∧
solvefor the EBIT .
If EBIT
<
$
750,000
,commonshares wouldbe favoured ,but if
EBIT
>
$
750,000
debt wouldbe favoured .
14. Homemade Leverage Example:
•
You have 150 shares of an all-equity firm.
•
There are 9,000 shares outstanding.
•
EBIT = $40,000 and P
0
= $42
•
Company is considering a new capital structure with 40% debt at 8% interest rate. Ignore taxes.
a)
Calculate the current and proposed capital structures.
Current Cap. Structure
:
Proposed Cap. Structure
:
Assets
Debt (0)
Assets
Debt (378,000*0.4) = 151,200
378,000
378,000
Equity
Equity
9000*42=378,000
226,800
Firm will use debt in order to repurchase shares.
151,200
42
=
3600
shareswill berepurchased
b)
What’s the CF to you (as a S/H of 150 shares) under both capital structures?
Current (unlevered)
Proposed (levered)
EBIT = $40,000
EBIT = $40,000
Int = 0
Int = (151,200*0.08) = $12,096
Tax = 0
Tax = 0 EPS = ¿
¿
of shares
=
40,000
9000
=
$
4.444444
EPS =
¿
¿
of shares
=
40,000
−
12,096
9000
−
3600
=
$
5.167407
CF to you
150 shares * 4.44 EPS = $666.667
CF to you
150 shares * 5.17 EPS = $775.11
c)
Assume that the firm keeps the current all-equity capital structure, and you’d like to have the proposed one.
Can you use the homemade leverage to replicate the payoff of proposed capital structure?
CF
unl
= $666.667
You have this. CF
lv
= $775.11
You’d like to have this.
Increase leverage
You own stock of unlevered firm
+ Borrow & purchase more
= Levered CF.
You need to replicate the capital structure of the levered firm in your personal portfolio.
Debt = 151,200 Equity = $226,800
Debt
Equity
=
151,200
226,800
=
2
3
this D/E ratio will be applied in your own portfolio.
Personal equity = 150 *42 = $6300
Personal debt = 6300 *
2
3
=
4200
So, you need to borrow $4,200 and pay 8% interest for this loan just like the firm. You will purchase additional stocks with this loan
4200
42
=
100
shareswillbe purchased.
Now, you own 150 + 100 = 250 shares of the unlevered firm and $4,200 of personal debt.
CF to you
250 * 4.444444 = $1111.11
Interest on debt
4,200 * 0.08 = $336
Net CF to you
1110 – 336 = $775.11 You have successfully replicated the payoff of the investor who invests in the levered firm by staying in the unlevered firm and mimicking the levered firm’s capital structure in your personal portfolio.
d)
Now assume that you own 150 shares in the company that follows the proposed capital structure, that is levered and following a D/E ratio of 2/3. Can you use the homemade leverage to replicate the payoff of current capital structure (unlevered firm’s capital structure)?
CF
unl
= $666.667
You’d like to have this. CF
unl
= $775.11
You have this.
Decrease leverage in your personal portfolio
You own stock of levered firm
+ Sell & Lend
= Un
Levered CF.
You need to replicate the capital structure of the unlevered firm in your personal portfolio.
Debt
Equity
=
151,200
226,800
=
2
3
this D/E ratio will be applied in your own portfolio.
Personal levered investment value = 150 *42 = $6300, only the equity portion of proposed cap. Structure.
Personal lending should be
6300 *
2
5
=
$
2520
of your levered investment value.
So, you need to sell $2520 worth of stocks and lend it to earn 8% interest.
$
2520
42
=
60
sharesneed
¿
be sold .
After that, you’ll be left with 150-60=90 shares, each of which will bring $5.1674 EPS.
You’ll make the following CF from earnings
90 * $5.1674 = $465.06
You’ll also make an interest income of
$2520 * 8% = $201.60
So, you’ll have a total CF of $465.06 + $201.60 = $666.66
You have successfully replicated the payoff of the investor who invests in the unlevered firm by staying in the levered firm and mimicking the unlevered firm’s capital structure in your personal portfolio.
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****PLEASE ANSWER PART D AND E ONLY. thanks
Consolidated Pasta is currently expected to pay annual dividends of $10 a share in perpetuity on the 2.7 million shares that are outstanding. Shareholders required a 10 % rate of return on consolidated stock. A. What is the price of Consolidated stock? B. What is the total market value of its equity?
Consolidated now decides to increase next year’s dividends to $20 a share, without changing its investment or borrowing plans. Thereafter, the company will revert to its policy of distributing $10 per year. C. How much new equity capital will the company need to raise to finance the extra dividend payment (enter answer in millions). D. What will be the total present value of dividends paid each year on the new shares that the company will need to issue (answer in millions)? E. what will be the transfer of value from old shareholder to new shareholder (answer in million)?
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Do solve all 3 parts
ABC Corp. is an all-equity firm, and has 25,000 outstanding shares. The current earnings per share is $1.5. The expected value of the firm one year from now is $1,725,000. The firm currently has a 60% payout policy. The appropriate discount rate for the company is 12%, and the dividend tax rate is zero. We also assume that the market is efficient and frictionless.
What is the company’s stock price before paying the current dividend? What is the ex-dividend price of the company’s stock if the board follows its current policy?
At the dividend declaration meeting several board members claimed that the dividend is too meagre and is probably depressing the company’s stock price. They proposed to switch to a 150% payout policy. Comment on the claim that the low dividend is depressing the stock price. Support your argument with calculation.
If the proposed policy is adopted, the firm will have to sell new shares to finance its dividend. At what price will the new…
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Recommended textbooks for you
- Cornerstones of Financial AccountingAccountingISBN:9781337690881Author:Jay Rich, Jeff JonesPublisher:Cengage Learning
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