Mojito Mint Company has a debt–equity ratio of .20. The required return on the c
ID: 2766182 • Letter: M
Question
Mojito Mint Company has a debt–equity ratio of .20. The required return on the company’s unlevered equity is 13 percent, and the pretax cost of the firm’s debt is 8.7 percent. Sales revenue for the company is expected to remain stable indefinitely at last year’s level of $19,200,000. Variable costs amount to 60 percent of sales. The tax rate is 34 percent, and the company distributes all its earnings as dividends at the end of each year.
If the company were financed entirely by equity, how much would it be worth? (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
What is the required return on the firm’s levered equity? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Use the weighted average cost of capital method to calculate the value of the company. (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
What is the value of the company’s equity? (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
What is the value of the company’s debt? (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Use the flow to equity method to calculate the value of the company’s equity. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
If the company were financed entirely by equity, how much would it be worth? (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
What is the required return on the firm’s levered equity? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Use the weighted average cost of capital method to calculate the value of the company. (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
What is the value of the company’s equity? (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
What is the value of the company’s debt? (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Use the flow to equity method to calculate the value of the company’s equity. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Explanation / Answer
If the company were financed entirely by equity, how much would it be worth?
VU = $5,068,800 / 0.13
= $38,990,769
Therefore, Mojito Mint Company would be worth 38,990,769 as an unlevered firm.
What is the required return on the firm’s levered equity
According to Modigliani-Miller Proposition II with corporate taxes:
rS = r0 + (B/S)(r0 – rB)(1 – TC)
where r0 = the required return on the equity of an unlevered firm
rS = the required return on the equity of a levered firm
rB = the pre-tax cost of debt
TC = the corporate tax rate
B/S = the firm’s debt-to-equity ratio
In this problem:
r0 = 0.13
rB = 0.10
TC = 0.34
B/S = 1/6
The required return on Mojito’s levered equity is:
rS = r0 + (B/S)(r0 – rB)(1 – TC)
= 0.13+ (1/6)(0.13 – 0.10)(1 – 0.34)
= 0.133
The required return on Mojito’s levered equity (rS) is 13.33%.
Use the weighted average cost of capital method to calculate the value of the company
rwacc = {B / (B+S)}(1 – TC) rB + {S / (B+S)}rS
where B / (B+S) = the firm’s debt-to-value ratio
S / (B+S) = the firm’s equity-to-value rati
rB = the pre-tax cost of debt
rS = the cost of equity
TC = the corporate tax rate
The problem does not provide either Mojito’s debt-to-value ratio or Mojito’s equity-to-value ratio. However, the firm’s debt-to-equity ratio of 2/3 is given, which can be written algebraically as:
B / S =1/6
Solving for B:
B = (1/6))(S)
A firm’s debt-to-value ratio is: B / (B+S)
Since B = (1/6)(S):
Mojito’s debt-to-value ratio = (1/6)(S) / { (1/6)(S) + S}
= (1/6)(S) / (5/6)(S)
= (1/6)/(5/6)
= 1/5
Mojito’s debt-to-value ratio is 1/5.
A firm’s equity-to-value ratio is: S / (B+S)
Since B = (1/6)(S):
Mojito’s equity-to-value ratio = S / {(1/6)(S) + S}
= S / (5/6)(S)
= (1 / (5/6))
= 6/5
Mojito’s equity-to-value ratio is 6/5.
The inputs to the WACC calculation are:
B / (B+S) = 1/5
S / (B+S) = 6/5
rB = 0.10
rS = 0.133
TC = 0.34
rwacc = {B / (B+S)}(1 – TC) rB + {S / (B+S)}rS
= (1/5)(1 – 0.34)(0.10) + (6/5)(0.133)
= 0.1728
Mojito’s weighted average cost of capital is 17.28%.
Use the weighted average cost of capital to discount the firm’s unlevered after-tax earnings.
VL = $5,068,800 / 0.1728
= $29,333,333
Therefore, the value of Mojito Mint Company is $29,333,333
Since the firm’s equity-to-value ratio is 3/5, the value of Mojito’s equity is $35,200,000
{= (6/5)($29,333,333)}.
Since the firm’s debt-to-value ratio is 2/5, the value of Mojito’s debt is $5,866,666
{= (1/5)( $29,333,333)}.
What is the value of the company’s equity?
Since the firm’s equity-to-value ratio is 3/5, the value of Mojito’s equity is $35,200,000
{= (6/5)($29,333,333)}.
What is the value of the company’s debt?
Since the firm’s debt-to-value ratio is 1/5, the value of Mojito’s debt is $5,866,666
{= (1/5)( $29,333,333)}.
Use the flow to equity method to calculate the value of the company’s equity
In order to value a firm’s equity using the Flow-to-Equity approach, discount the cash flows available to equity holders at the cost of the firm’s levered equity (rS).
Since the pre-tax cost of the firm’s debt is 10%, and the firm has $5,866,666 of debt outstanding, Mojito must pay $5,866,666 (= 0.10 * $5,866,666) in interest at the end of each year.
Since the firm pays all of its after-tax earnings out as dividends at the end of each year, equity holders will receive $3,891,600 of cash flow per year in perpetuity.
S = Cash Flows Available to Equity Holders / rS
= $4,681,600 / 0.133
= $35,120,780
The value of Mojito’s equity is $35,120,780
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