capital structure compiled
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Student: _____________________
Date: _____________________
Instructor: Min Kim
Course: FE 323 Fall 2023 B5 - Kim
Assignment: HW #17 Chapter 16 - Capital
Structure I
You are an entrepreneur starting a biotechnology firm. If your research is successful, the technology can be sold for million. If your research is unsuccessful, it will be worth nothing. To fund your research, you need to raise million. Investors are willing to provide you with million in initial capital in exchange for of the unlevered equity in the firm.
$40
$7.0
$7.0
38%
a.
What is the total market value of the firm without leverage?
b
. Suppose you borrow million. According to MM, what fraction of the firm's equity must you sell to raise the additional million you need?
$1.3
$5.7
c. What is the value of your share of the firm's equity in cases (
a
) and (
b
)?
a.
What is the total market value of the firm without leverage?
To determine the total value of equity, use the following formula:
Value of Equity =
Initial Capital 100%
% of investor ownership for initial capital
Therefore,
Value of Equity =
$7.0 million = $18.4 million
100%
38%
The market value without leverage is $
million.
18.4
b
. Suppose you borrow million. According to MM, what fraction of the firm's equity must you sell to raise the additional million you need?
$1.3
$5.7
The value of the unlevered equity, and thus the unlevered firm, is $
million, as found in part (
a
). MM state that , so if you borrow $
million then the value of the levered equity is the value of the unlevered firm less the debt. Then since you still need to raise an additional $
million (
) in equity, the percentage of equity you need to sell is the addititional $
million divided by the value of the total levered equity. This can be summarized using the following formula:
18.4
=
+
=
V
L
E
D
V
U
1.3
5.7
= $7.0 million − $1.3 million
5.7
Percentage to Sell =
Initial Capital − Debt Unlevered MV
− Debt The fraction of the firm's equity you will need to sell is %.
33
c. What is the value of your share of the firm's equity in cases (
a
) and (
b
)?
In case (a)
, your value of the firm's equity would be the total value of the unlevered firm found in part (
a
) minus the initial capital provided by investors, .
$18.4 million − $7.0 million = $11.4 million
The value of your share of the firm's equity in case (
a
) is $
million. 11.4
In case
(b)
, your value of the firm's equity would be the unlevered MV of the firm less the debt less the equity sold to investors, .
$18.4 million − $1.3 million − $5.7 million = $11.4 million
The value of your share of the firm's equity in case (
b
) is $
million. 11.4
Student: _____________________
Date: _____________________
Instructor: Min Kim
Course: FE 323 Fall 2023 B5 - Kim
Assignment: HW #17 Chapter 16 - Capital
Structure I
Your firm is financed 100% with equity and has a cost of equity capital of %. You are considering your first debt issue, which would change your capital structure to % debt and % equity. If your cost of debt is %, what will be your new cost of equity? Assume no change in your firm's WACC due to the change in capital structures.
16
40
60
9
Since you are 100% equity-financed, your current cost of equity is your total cost of capital (your WACC). Since a capital structure change will not affect your pre-tax WACC, we know that it will remain % after the change. With the capital structure weights and your expected cost of debt, we can solve for your new cost of equity:
16
WACC =
+
r
E
E
E + D
r
D
D
E + D
Therefore,
0.16 =
(0.60) + (0.09)(0.40)
r
E
= 0.2067 = 20.67%
r
E
The new cost of equity is %.
20.67
Student: _____________________
Date: _____________________
Instructor: Min Kim
Course: FE 323 Fall 2023 B5 - Kim
Assignment: HW #17 Chapter 16 - Capital
Structure I
Suppose Microsoft has no debt and a WACC of . The average debt-to-value ratio for the software industry is . What would be its cost of equity if it took on the average amount of debt for its industry at a cost of debt of ?
9.9%
12.0%
7.0%
To compute the levered cost of equity we can use the equation:
=
+
r
E
r
U
D
E
r
U
−
r
D
where is the unlevered cost of equity, which is WACC when there is no debt, is the cost of debt, and and are the amount of debt and equity, respectively.
r
U
r
D
D
E
Using the formula above to determine the cost of equity:
= 9.9% +
(
) = 10.30%
r
E
12.0%
88.0%
9.9% − 7.0%
The cost of equity is %. 10.30
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Student: _____________________
Date: _____________________
Instructor: Min Kim
Course: FE 323 Fall 2023 B5 - Kim
Assignment: HW #17 Chapter 16 - Capital
Structure I
Hardmon Enterprises is currently an all-equity firm with an expected return of . It is considering borrowing money to buy back some of its existing shares. Assume perfect capital markets.
17.25%
a
. Suppose Hardmon borrows to the point that its debt-equity ratio is 0.50. With this amount of debt, the debt cost of capital is . What will be the expected return of equity after this transaction?
7%
b.
Suppose instead Hardmon borrows to the point that its debt-equity ratio is 1.50. With this amount of debt, Hardmon's debt will be much riskier. As a result, the debt cost of capital will be . What will be the expected return of equity in this case?
9%
c.
A senior manager argues that it is in the best interest of the shareholders to choose the capital structure that leads to the highest expected return for the stock. How would you respond to this argument?
a
. Suppose Hardmon borrows to the point that its debt-equity ratio is 0.50. With this amount of debt, the debt cost of capital is . What will be the expected return of equity after this transaction?
7%
To compute the expected return of equity, use the following formula:
r
E
= r
U
+
D
E
r
U
− r
D
where: r
E Expected return (cost of capital) of levered equity
=
r
U Expected return (cost of capital) of unlevered equity
=
r
D = Expected return on debt
D
Market value of debt
=
E
Market value of levered equity
=
Using the formula above, the equation is:
= 17.25% + 0.50
(
) = 22.38%
r
E
17.25% − 7%
The expected return is %. 22.38
b.
Suppose instead Hardmon borrows to the point that its debt-equity ratio is 1.50. With this amount of debt, Hardmon's debt will be much riskier. As a result, the debt cost of capital will be . What will be the expected return of equity in this case?
9%
Using the formula above, the equation is:
= 17.25% + 1.50
(
) = 29.63%
r
E
17.25% − 9%
The expected return is %. 29.63
c.
A senior manager argues that it is in the best interest of the shareholders to choose the capital structure that leads to the highest expected return for the stock. How would you respond to this argument?
(Select the best choice below.)
False, because returns are higher because risk is higher and the return fairly compensates for the risk.
Rogot Instruments makes fine violins, violas, and cellos. It has million in debt outstanding, equity valued at million, and pays corporate income tax at rate . Its cost of equity is and its cost of debt is .
$1.1
$4.3
25%
15%
9%
a. What is Rogot's pre-tax WACC?
b.
What is Rogot's (effective after-tax) WACC?
a. What is Rogot's pre-tax WACC?
Rogot's pre-tax WACC is %. 13.78
b.
What is Rogot's (effective after-tax) WACC?
Rogot's (effective after-tax) WACC is %. 13.32
Week 11-2
Q1
Rumolt Motors has million shares outstanding with a share price of per share. In addition, Rumolt has issued bonds with a total current market value of million. Suppose Rumolt's equity cost of capital is , and its debt cost of capital is .
85
$9
$150
17%
6%
a.
What is Rumolt's pre-tax WACC?
b. If Rumolt's corporate tax rate is , what is its after-tax WACC?
25%
a.
What is Rumolt's pre-tax WACC?
Rumolt's pre-tax weighted average cost of capital is %.
15.20
b. If Rumolt's corporate tax rate is , what is its after-tax WACC?
25%
Rumolt's after-tax weighted average cost of capital is %.
14.95
Q2
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Pelamed Pharmaceuticals had EBIT
of million in . In addition, Pelamed had interest expenses of million and a corporate tax rate of .
$525
2018
$175.00
25%
a.
What is Pelamed's net income?
2018
b.
What is the total of Pelamed's net income plus interest payments? 2018
c. If Pelamed had no interest expenses, what would have been its net income? How does it compare to your answer in part (
a
)? 2018
d.
What is the amount of Pelamed's interest tax shield in ?
2018
a.
What is Pelamed's net income?
2018
The net income is $
million.
2018
263
b.
What is the total of Pelamed's net income plus interest payments? 2018
The total of Pelamed's net income plus interest payments is $
million.
2018
438
c. If Pelamed had no interest expenses, what would have been its net income? How does it compare to your answer in part (
a
)? 2018
The net income would be $
million. 2018
394
Difference = $394 million
−
$263 million = $131 million
d.
What is the amount of Pelamed's interest tax shield in ?
2018
Pelamed's interest tax shield in is $
million. 2018
44
Q3
Milton Industries expects free cash flows of million each year. Milton's corporate tax rate is , and its unlevered cost of capital is . Milton also has outstanding debt of million, and it expects to maintain this level of debt permanently.
$22
25%
17%
$37.53
a.
What is the value of Milton Industries without leverage?
b.
What is the value of Milton Industries with leverage?
a.
What is the value of Milton Industries without leverage?
The value of Milton Industries without leverage is $
million. 129.41
b.
What is the value of Milton Industries with leverage?
The value of Milton Industries with leverage is $
million. 138.79
Q4
Now that your firm has matured, you are considering adding debt to your capital structure for the first time. Your all-equity firm has a market value of $
million and you are considering issuing $
million in debt with an interest rate of % and using it to repurchase shares. You pay a corporate tax rate of %. Assume taxes are the only imperfection and the debt is expected to be permanent.
27
6
10
25
a. What will be the total value of the firm after the change in capital structure?
b.
What will be the value of the remaining equity after the change in capital structure?
Value of the firm = $27 million + $1.5 million = $28.5 million
The total value of the firm after the change in capital structure is $
million.
28.5
b.
As the residual claimant, the equity will capture all of the gain from the PV of the interest tax shield. Therefore, the remaining equity is equal to the total value minus the amount owed to the debt holders:
Remaining equity = $28.5 million
−
$6 million = $22.5 million
The value of the remaining equity is $
million.
22.5
Q5
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Marpor Industries has no debt and expects to generate free cash flows of million each year. Marpor believes that if it permanently increases its level of debt to million, the risk of financial distress may cause it to lose some customers and receive less favourable terms from its suppliers. As a result, Marpor's expected free cash flows with debt will be only per year. Suppose Marpor's tax rate is , the risk-free rate is , the expected return of the market is , and the beta of Marpor's free cash flows is (with or without leverage).
$18
$30.00
$17 million
25%
5.5%
13%
1.4
a. Estimate Marpor's value without leverage.
b. Estimate Marpor's value with the new leverage.
a. Estimate Marpor's value without leverage.
Marpor's value without leverage is $
million.
112.50
b. Estimate Marpor's value with the new leverage.
Marpor's value with the new leverage is $
million.
113.75
Q6
Hawar International is a shipping firm with a current share price of and million shares outstanding. Suppose that Hawar announces plans to lower its corporate taxes by borrowing million and repurchasing shares, that Hawar pays a corporate tax rate of , and that shareholders expect the change in debt to be permanent.
$5.70
12.0
$12.3
25%
a.
If the only imperfection is corporate taxes, what will be the share price after this announcement?
b.
Suppose the only imperfections are corporate taxes and financial distress costs. If the share price rises to after this announcement, what is the PV of financial distress costs Hawar will incur as the result of this new debt?
$5.75
The share price after this announcement will be per share.
$5.96
b.
Suppose the only imperfections are corporate taxes and financial distress costs. If the share price rises to after this announcement, what is the PV
of financial distress costs Hawar will incur as the result of this new debt?
$5.75
The PV of financial distress costs will be million. $2.52
Q7
Kurz Manufacturing is currently an all-equity firm with million shares outstanding and a stock price of per share. Although investors currently expect Kurz to remain an all-equity firm, Kurz plans to announce that it will borrow million and use the funds to repurchase shares. Kurz will pay interest only on this debt, and it has no further plans to increase or decrease the amount of debt. Kurz is subject to a corporate tax rate.
45
$16.00
$71
25%
a. What is the market value of Kurz's existing assets before the announcement?
b.
What is the market value of Kurz's assets (including any tax shields) just after the debt is issued, but before the shares are repurchased?
c.
What is Kurz's share price just before the share repurchase? How many shares will Kurz repurchase?
d.
What are Kurz's market value balance sheet and share price after the share repurchase?
Week 13-1
Q1
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The share price after repurchase is $
. 16.39
Rally, Inc., is an all-equity firm with assets worth billion and billion shares outstanding. Rally plans to borrow billion and use funds to repurchase shares. Rally's corporate tax rate is , and Rally plans to keep its outstanding debt equal to billion permanently.
$65
25
$16
21%
$16
a. Without the increase in leverage, what would be Rally's share price?
b.
Suppose Rally offers per share to repurchase its shares. Would shareholders sell for this price?
$2.42
c.
Suppose Rally offers per share, and shareholders tender their shares at this price. What will be Rally's share price after the repurchase?
$3.03
d. What is the lowest price Rally can offer and have shareholders tender their shares? What will be its stock price after the share repurchase in that case?
Q2
The stock price after repurchase is $
.
2.73
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FE 323 Week 13-1 Nov 28, 2023 Section: Last name: First name: Hockey Standard expects free cash flow of $9 million each year indefinitely. The company is currently all equity firm but plans to issue permanent debt of $30 million at par with an interest rate of 10%. The company’s unlevered cost of capital is 15%. The corporate tax is 40%. 1. What is the unlevered value of the firm? 2. What would be the levered value of the firm if the tax rate was zero? 3. What would be the levered cost of capital if the tax rate was zero? 4. What would be the debt-to-equity ratio if the tax rate was zero? 5. What is the cost of debt before tax? 6. What would be the levered cost of equity if the tax rate was zero? 7. What is the levered value of the firm? 8. What is the levered cost of capital? 9. What is the cost of debt after tax? 10. What is the debt-to-value ratio? 11. Show how the unlevered cost of capital and the levered cost of capital (in Q8) are related.
Rev 07/2023 © John F. Fox FE323 Recap Corp - Capital Structure Case The company, Recap Corp, has been financing its operations with equity only. That is, it is currently an unlevered company. The expected return on their equity is currently 8%, the share price is $20 per share, and there are 25 million shares outstanding. The market risk premium is 7.5%. The risk-free rate is 3%. For the moment assume that the tax rate is zero. a)
What is the company's cost of capital? b)
What is Recap's equity beta? The CFO of Recap has decided to change the capital structure. She is planning to finance 25% of their capital structure with debt. Assume that the cost of debt is 2% above the risk-free rate. The company would issue debt and use all the proceeds to repurchase some of their shares after levering. Assume that the tax rate is still zero. c)
What is the dollar amount of debt the company must issue? d)
What is the expected return on equity now? (See equations below) e)
How many shares can it repurchase?
Rev 07/2023 © John F. Fox Now assume that Recap wants the expected return on equity to be equal to 2% points above the expected return on the market portfolio. f)
How much total debt should Recap issue in the recapitalization in order to achieve this new goal? Assume that the cost of debt will still be 2% above the risk-free rate at the new level of debt. Finally, now assume they are in the real world with a corporate tax rate of 21%. They have decided to issue $125 Million of permanent debt as calculated in part c) above. g)
How much does the value of the company increase by? h)
What is the new stock price per share immediately after the leveraged recapitalization is announced, but before the debt is issued and any shares are repurchased? i)
How many shares can they repurchase in this case? r
L
= r
U
+ D/E(r
U
– r
D
) r
wacc
= W
E
*r
E
+ W
D
*r
D
*(1-T)
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