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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
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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- Please answer question 4 & 5 after reading the scenario thank you. Question at the end Stephanie Carter has been gifted a sum of $50,000 by her grandparents on completing her graduation successfully. She is a fresh finance graduate and is excited to invest some money in the capital market, for which she intends to use the gifted sum of $50,000. However, instead of committing this money to the market immediately, she decides to wait for some time, work in the field and acquire some experience before proceeding with her intended investment. She thus contemplates an extremely conservative investment in a portfolio of stocks and bonds, at the start of year 5 from now. For now, she will leave the $50,000 in a fixed deposit with the bank which promises an interest rate of 6% per annum. She will require a return of at least 9% on her stock investments and 4% on bond investments. Stephanie would have to pay 25% taxes on any interest income. Dividends will be tax-free. Stephanie’s research…arrow_forwardPlease answer question 2 & 3 after reading the scenario thank you. Question at the end Stephanie Carter has been gifted a sum of $50,000 by her grandparents on completing her graduation successfully. She is a fresh finance graduate and is excited to invest some money in the capital market, for which she intends to use the gifted sum of $50,000. However, instead of committing this money to the market immediately, she decides to wait for some time, work in the field and acquire some experience before proceeding with her intended investment. She thus contemplates an extremely conservative investment in a portfolio of stocks and bonds, at the start of year 5 from now. For now, she will leave the $50,000 in a fixed deposit with the bank which promises an interest rate of 6% per annum. She will require a return of at least 9% on her stock investments and 4% on bond investments. Stephanie would have to pay 25% taxes on any interest income. Dividends will be tax-free. Stephanie’s research…arrow_forwardHi good morning the previous questions have been completed by you all. Please answer question 6 & 7 after reading the scenario thank you. Question at the end Stephanie Carter has been gifted a sum of $50,000 by her grandparents on completing her graduation successfully. She is a fresh finance graduate and is excited to invest some money in the capital market, for which she intends to use the gifted sum of $50,000. However, instead of committing this money to the market immediately, she decides to wait for some time, work in the field and acquire some experience before proceeding with her intended investment. She thus contemplates an extremely conservative investment in a portfolio of stocks and bonds, at the start of year 5 from now. For now, she will leave the $50,000 in a fixed deposit with the bank which promises an interest rate of 6% per annum. She will require a return of at least 9% on her stock investments and 4% on bond investments. Stephanie would have to pay 25% taxes…arrow_forward
- MGMT2023 - Financial Management 1-UWI Open Campus Stephanie Carter has been gifted a sum of $50,000 by her grandparents on completing her graduation successfully. She is a fresh finance graduate and is excited to invest some money in the capital market, for which she intends to use the gifted sum of $50,000. However, instead of committing this money to the market immediately, she decides to wait for some time, work in the field and acquire some experience before proceeding with her intended investment. She thus contemplates an extremely conservative investment in a portfolio of stocks and bonds, at the start of year 5 from now. For now, she will leave the $50,000 in a fixed deposit with the bank which promises an interest rate of 6% per annum. She will require a return of at least 9% on her stock investments and 4% on bond investments. Stephanie would have to pay 25% taxes on any interest income. Dividends will be tax-free. Stephanie's research has allowed her to narrow down on the…arrow_forwardOnly qno2 ,÷needddddddd okkkkarrow_forwardQuestion 9arrow_forward
- Question 1 Assuming that you have beeh appointed finance director of BPX Bhd. The company is considering investing in the production of an electronic device used in automobile. There are two mutually exclusive projects available to achieve the plan. Project I Return in one year (RM) 60,000 60,000 Project II State of economy Probability Good 0.3 58,000 62,000 Moderate 0.5 Poor 0.2 50,000 48,000 Project I or II would require an investment of RM50,000. The company has a current market value of RM800,000. The estimated returns of the market in one year are: Good state 20%, Moderate state 15% and Poor state 10% respectively. Assume that the treasury bill rate as 9%. The research director projects that the company's share price will move in line with the market. Required (in no more than 1,000 words, show all relevant workings) (a) Calculate i market variance ii. systematic risk for Project I iii. systematic risk for Project II iv. covariance between Project I and the market v. covariance…arrow_forwardPlease answer question 1 after reading the scenario thank you. I am confused of which rate I should use for market rate(k) Question at the end Stephanie Carter has been gifted a sum of $50,000 by her grandparents on completing her graduation successfully. She is a fresh finance graduate and is excited to invest some money in the capital market, for which she intends to use the gifted sum of $50,000. However, instead of committing this money to the market immediately, she decides to wait for some time, work in the field and acquire some experience before proceeding with her intended investment. She thus contemplates an extremely conservative investment in a portfolio of stocks and bonds, at the start of year 5 from now. For now, she will leave the $50,000 in a fixed deposit with the bank which promises an interest rate of 6% per annum. She will require a return of at least 9% on her stock investments and 4% on bond investments. Stephanie would have to pay 25% taxes on any interest…arrow_forwardQuestion 12 Wealth (thousands of dollars) Total utility 10 50 20 90 30 120 40 140 Gunnar can work as a campus security officer at a guaranteed salary of $20,000 per year or as a real estate agent. If Gunnar works as a real estate agent, there is a 50 percent chance that he will earn $10,000 per year and a 50 percent chance that he will earn $30,000 per year. Based on the table above, Calculate Gunnar's expected utility if he works as a real estate agent? Show step by step calculations. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).arrow_forward
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