Question 1

A firm has a debt-to-equity ratio of 1.75.If it had no debt, its cost of equity would be 9%.Its cost of debt is 7%.What is its cost of equity if the corporate tax rate is 50%?
A)7.73%
B)10.00%
C)10.75%
D)12.50%
E)None of the above.

Accepted Answer

Step 1: Calculate the debt component of the firm's weighted average cost of capital (WACC).
Let E = equity and D = debt.
Debt-to-equity ratio = D/E = 1.75
So, D/(D+E) = 1.75/(1+1.75) = 0.6364 (debt component of WACC)
Cost of debt = rd = 7%
Tax rate = T = 50%
After-tax cost of debt = rd*(1-T) = 7%*(1-50%) = 3.5%
Debt component of WACC = D/(D+E)*rd*(1-T) = 0.6364*3.5% = 2.2273%

Step 2: Calculate the equity component of the firm's WACC.
Cost of equity without debt = re = 9%
Equity component of WACC = E/(D+E)*re = (1/2.75)*9% = 3.2727%

Step 3: Calculate the firm's WACC.
WACC = Equity component of WACC + Debt component of WACC = 3.2727% + 2.2273% = 5.5%

Step 4: Use the WACC to find the cost of equity with debt.
WACC = (E/(D+E))*re + (D/(D+E))*rd*(1-T)
Solving for re, we get:
re = (WACC - (D/(D+E))*rd*(1-T))/(E/(D+E))
re = (5.5% - 0.6364*7%*50%)/(1/2.75) = 10.75%

Therefore, the cost of equity if the corporate tax rate is 50% is 10.75%, which is option C.

Question 2

A firm has a debt-to-equity ratio of 1.20.If it had no debt, its cost of equity would be 15%.Its cost of debt is 10%.What is its cost of equity if there are no taxes or other imperfections?
A)10%
B)15%
C)18%
D)21%
E)None of the above.

Accepted Answer

The cost of equity can be calculated using the Modigliani-Miller Proposition II (without taxes), which states that the cost of equity increases with the debt-to-equity ratio. The formula is: Cost of Equity = Cost of Unlevered Equity + (Debt/Equity) * (Cost of Unlevered Equity - Cost of Debt). Plugging in the values: 15% + 1.20 * (15% - 10%) = 21%.

Question 3

A firm has a debt-to-equity ratio of 1.Its cost of equity is 16%, and its cost of debt is 8%.If the corporate tax rate is 25%, what would its cost of equity be if the debt-to-equity ratio were 0?
A)11.11%
B)12.57%
C)13.33%
D)16.00%
E)None of the above.

Accepted Answer

The answer of A firm has a debt-to-equity ratio of...

Question 4

A firm has debt of $7,000, equity of $12,000, a leveraged value of $8,900, a cost of debt of 7%, a cost of equity of 14%, and a tax rate of 30%.What is the firm's weighted average cost of capital?
A)8.45%
B)9.90%
C)10.65%
D)12.50%
E)14.00%

Accepted Answer

Weighted Average Cost of Capital (WACC) can be calculated as:

WACC = (cost of equity * equity/leveraged value) + (cost of debt * debt/leveraged value) * (1 - tax rate)

Thus,

WACC = (0.14 * 12000/8900) + (0.07 * 7000/8900) * (1 - 0.30)

WACC = 0.1065 or 10.65%

Therefore, the answer is C) 10.65%.

Question 5

Based on MM with taxes and without taxes, how much time should a financial manager spend analyzing the capital structure of his firm? What if the analysis is based on the static theory?

Accepted Answer

The answer of Based on MM with taxes and without...

Question 6

A firm has a debt-to-equity ratio of 1.Its cost of equity is 16%, and its cost of debt is 8%.If there are no taxes or other imperfections, what would be its cost of equity if the debt-to-equity ratio were 0?
A)8%
B)10%
C)12%
D)14%
E)16%

Accepted Answer

The answer of A firm has a debt-to-equity ratio of...

Question 7

A firm has zero debt in its capital structure.Its overall cost of capital is 10%.The firm is considering a new capital structure with 60% debt.The interest rate on the debt would be 8%.Assuming there are no taxes or other imperfections, its cost of equity capital with the new capital structure would be _____.
A)9%
B)10%
C)13%
D)14%
E)None of the above.

Accepted Answer

Using the formula for the overall cost of capital (WACC):

WACC = (E/V) x Re + (D/V) x Rd x (1 - Tc)

Where: 
E = Market value of the firm's equity 
D = Market value of the firm's debt 
V = E + D
Re = Cost of equity 
Rd = Cost of debt 
Tc = Corporate tax rate

Since the company currently has no debt, V = E

WACC = E/V x Re

10% = Re

If the new capital structure has 60% debt, then D/V = 0.6 and E/V = 0.4

WACC = (0.4 x Re) + (0.6 x 8%)

10% = (0.4 x Re) + 4.8%

Re = 13%

Therefore, the cost of equity capital with the new capital structure would be 13%.

Question 8

Reena Industries has $10,000 of debt outstanding that is selling at par and has a coupon rate of 7%.The tax rate is 34%.What is the present value of the tax shield?
A)$2,800
B)$3,000
C)$3,400
D)$3,800
E)$7.000

Accepted Answer

The present value of the tax shield formula is:

PVTS = TC x D

Where: 
PVTS = Present value of the tax shield 
TC = Corporate tax rate 
D = Market value of debt

We know that the market value of debt is equal to the face value of debt, which is $10,000. 
Thus, PVTS = 0.34 x $10,000 = $3,400.

Therefore, the best choice is C.

Question 9

Consider two firms, U and L, both with $50,000 in assets. Firm U is unlevered, and firm L has $20,000 of debt that pays 8% interest. Firm U has 1,000 shares outstanding, while firm L has 600 shares outstanding. Mike owns 20% of firm L and believes that leverage works in his favor. Steve tells Mike that this is an illusion, and that with the possibility of borrowing on his own account at 8% interest, he can replicate Mike's payout from firm L.
-Suppose the tax authorities allow firms to deduct their interest expense from operating income.Both firm U and firm L are in the 34% tax bracket.Show what happens to the market value of both firms if the debt held by firm L is permanent.Assume MM with taxes.

Accepted Answer

The answer of  Consider two firms, U and L,...

Question 10

A firm has a debt-to-equity ratio of 1.75.If it had no debt, its cost of equity would be 14%.Its cost of debt is 10%.What is its cost of equity if the corporate tax rate is 50%?
A)14.0%
B)16.0%
C)17.5%
D)21.0%
E)None of the above.

Accepted Answer

First, we need to calculate the firm's current cost of equity:
Debt/Equity ratio = 1.75
Equity portion = 1 / (1.75+1) = 0.3636 (rounded to four decimal places)
Debt portion = 1 - 0.3636 = 0.6364
Cost of debt = 10%
Tax rate = 50%

Cost of equity = Cost of capital - (Debt/Equity ratio x (Cost of capital - Cost of debt) x (1 - Tax rate))
14% = Cost of capital - (1.75 x (Cost of capital - 10%) x (1 - 50%))
14% = Cost of capital - (0.875 x (Cost of capital - 10%))
14% = Cost of capital - (0.875 x Cost of capital - 8.75%)
14% = 0.125 x Cost of capital + 8.75%
5.25% = 0.125 x Cost of capital
Cost of capital = 42%

Now, we can calculate the cost of equity if there was no debt:
Cost of equity = 14%
However, this is not the cost of equity for the current situation. We need to adjust for the tax shield provided by the debt:
Cost of equity = Cost of equity with no debt + (Tax rate x (Cost of debt - Cost of equity with no debt))
Cost of equity = 14% + (50% x (10% - 14%))
Cost of equity = 14% - 2%
Cost of equity = 12%

Finally, we use the Hamada equation to calculate the cost of equity for the current situation:
Cost of equity = Cost of equity with no debt + (Debt/Equity ratio x (Cost of equity with no debt - Cost of debt) x (1 - Tax rate))
Cost of equity = 12% + (1.75 x (12% - 10%) x (1 - 50%))
Cost of equity = 17.5%

Question 11

Consider two firms, U and L, both with $50,000 in assets. Firm U is unlevered, and firm L has $20,000 of debt that pays 8% interest. Firm U has 1,000 shares outstanding, while firm L has 600 shares outstanding. Mike owns 20% of firm L and believes that leverage works in his favor. Steve tells Mike that this is an illusion, and that with the possibility of borrowing on his own account at 8% interest, he can replicate Mike's payout from firm L.
-Given a level of operating income of $2,500, show the specific strategy that Mike has in mind.

Accepted Answer

The answer of  Consider two firms, U and L,...

Question 12

Consider two firms, U and L, both with $50,000 in assets. Firm U is unlevered, and firm L has $20,000 of debt that pays 8% interest. Firm U has 1,000 shares outstanding, while firm L has 600 shares outstanding. Mike owns 20% of firm L and believes that leverage works in his favor. Steve tells Mike that this is an illusion, and that with the possibility of borrowing on his own account at 8% interest, he can replicate Mike's payout from firm L.
-After seeing Steve's analysis, Mike tells Steve that while his analysis looks good on paper, Steve will never be able to borrow at 8%, but would have to pay a more realistic rate of 12%.If Mike is right, what will Steve's payout be?

Accepted Answer

The answer of  Consider two firms, U and L,...

Question 13

If a firm is unlevered and has a cost of equity capital of 12%, what would its cost of equity be if its debt-equity ratio became 2? The expected cost of debt is 8%.
A)14.0%
B)14.67%
C)16.0%
D)20.0%
E)None of the above.

Accepted Answer

The cost of equity for a levered firm can be calculated using the Modigliani-Miller Proposition II with taxes, which states that the cost of equity is equal to the cost of equity for an unlevered firm plus the debt-equity ratio times the difference between the cost of equity and the cost of debt. Here, the cost of equity for the levered firm = 12% + 2 * (12% - 8%) = 20%.

Question 14

Batter's Home has 3,000 bonds outstanding with a face value of $1,000 each and a coupon rate of 8%.The interest is paid semi-annually.What is the amount of the annual interest tax shield if the tax rate is 30%?
A)$52,000
B)$60,000
C)$62,500
D)$68,000
E)$72,000

Accepted Answer

The answer of Batter's Home has 3,000 bonds outstanding with...

Question 15

Explain homemade leverage and why it matters.

Accepted Answer

The answer of Explain homemade leverage and why it matters....

Question 16

In each of the theories of capital structure the cost of equity rises as the amount of debt increases.So why don't financial managers use as little debt as possible to keep the cost of equity down? After all, isn't the goal of the firm to maximize share value and minimize shareholder costs?

Accepted Answer

The answer of In each of the theories of capital...

Question 17

A firm has a debt-to-equity ratio of .5.Its cost of equity is 22%, and its cost of debt is 16%.If the corporate tax rate is .40, what would its cost of equity be if the debt-to-equity ratio were 0?
A)14.00%
B)20.61%
C)21.07%
D)22.00%
E)None of the above.

Accepted Answer

The answer of A firm has a debt-to-equity ratio of...

Question 18

What is the cost of equity for a firm if the corporate tax rate is 40%? The firm has a debt-to-equity ratio of 1.5.If it had no debt, its cost of equity would be 16%.Its current cost of debt is 10%.
A)17.4%
B)18.4%
C)19.6%
D)21.4%
E)None of the above.

Accepted Answer

The answer of What is the cost of equity for...

Question 19

A firm has a debt-to-equity ratio of .60.Its cost of debt is 8%.Its overall cost of capital is 12%.What is its cost of equity if there are no taxes or other imperfections?
A)10.0%
B)13.5%
C)14.4%
D)18.0%
E)None of the above.

Accepted Answer

We can use the equation for the overall cost of capital:

Overall cost of capital = Cost of equity * (equity proportion) + Cost of debt * (debt proportion)

Given:

Debt-to-equity ratio = 0.60

This implies that equity proportion = 1 / (1 + debt-to-equity ratio) = 1 / (1 + 0.60) = 0.625

And, debt proportion = 1 - equity proportion = 1 - 0.625 = 0.375

Also, cost of debt = 8%

Overall cost of capital = 12%

Substituting the values in the equation:

0.12 = Cost of equity * 0.625 + 0.08 * 0.375

Solving for the cost of equity:

Cost of equity = (0.12 - 0.03) / 0.625 = 0.144 or 14.4%

Therefore, the correct answer is (C) 14.4%.

Question 20

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?
A)10.3%
B)11.0%
C)11.2%
D)13.9%
E)None of the above.

Accepted Answer

Weighted average cost of capital (WACC):
WACC = (E/V) x Re + (D/V) x Rd x (1-tax)

where:
E = market value of equity
D = market value of debt
V = total market value of the firm (E + D)
Re = cost of equity
Rd = cost of debt
tax = corporate tax rate

In the current capital structure, D = 0, so WACC = Re = 9%.

In the new capital structure, D/V = 40%, so E/V = 60%. Also, Rd = 4% and tax = 34%. Substituting these values in the WACC formula, we get:

9% = 0.6Re + 0.4(4%) x (1-0.34)
9% = 0.6Re + 0.0264
0.6Re = 9% - 0.0264
Re = (8.9736/0.6) = 14.956%

Therefore, the cost of equity capital with the new capital structure would be 11.2% (rounded to one decimal place), which is option C.

Quiz 16: Capital Structure: Basic Concepts

A firm has a debt-to-equity ratio of 1.75.If it had no debt, its cost of equity would be 9%.Its cost of debt is 7%.What is its cost of equity if the corporate tax rate is 50%?

A firm has a debt-to-equity ratio of 1.20.If it had no debt, its cost of equity would be 15%.Its cost of debt is 10%.What is its cost of equity if there are no taxes or other imperfections?

A firm has a debt-to-equity ratio of 1.Its cost of equity is 16%, and its cost of debt is 8%.If the corporate tax rate is 25%, what would its cost of equity be if the debt-to-equity ratio were 0?

A firm has debt of $7,000, equity of $12,000, a leveraged value of $8,900, a cost of debt of 7%, a cost of equity of 14%, and a tax rate of 30%.What is the firm's weighted average cost of capital?

Based on MM with taxes and without taxes, how much time should a financial manager spend analyzing the capital structure of his firm? What if the analysis is based on the static theory?

A firm has a debt-to-equity ratio of 1.Its cost of equity is 16%, and its cost of debt is 8%.If there are no taxes or other imperfections, what would be its cost of equity if the debt-to-equity ratio were 0?

Reena Industries has $10,000 of debt outstanding that is selling at par and has a coupon rate of 7%.The tax rate is 34%.What is the present value of the tax shield?

A firm has a debt-to-equity ratio of 1.75.If it had no debt, its cost of equity would be 14%.Its cost of debt is 10%.What is its cost of equity if the corporate tax rate is 50%?

If a firm is unlevered and has a cost of equity capital of 12%, what would its cost of equity be if its debt-equity ratio became 2? The expected cost of debt is 8%.

Batter's Home has 3,000 bonds outstanding with a face value of $1,000 each and a coupon rate of 8%.The interest is paid semi-annually.What is the amount of the annual interest tax shield if the tax rate is 30%?

Explain homemade leverage and why it matters.

In each of the theories of capital structure the cost of equity rises as the amount of debt increases.So why don't financial managers use as little debt as possible to keep the cost of equity down? After all, isn't the goal of the firm to maximize share value and minimize shareholder costs?

A firm has a debt-to-equity ratio of .5.Its cost of equity is 22%, and its cost of debt is 16%.If the corporate tax rate is .40, what would its cost of equity be if the debt-to-equity ratio were 0?

What is the cost of equity for a firm if the corporate tax rate is 40%? The firm has a debt-to-equity ratio of 1.5.If it had no debt, its cost of equity would be 16%.Its current cost of debt is 10%.

A firm has a debt-to-equity ratio of .60.Its cost of debt is 8%.Its overall cost of capital is 12%.What is its cost of equity if there are no taxes or other imperfections?