Mojito Mint Company has a debt-equity ratio of .40. The required return on the c
ID: 2807089 • Letter: M
Question
Mojito Mint Company has a debt-equity ratio of .40. The required return on the company's unlevered equity is 13 percent, and the pretax cost of the firm's debt is 7.3 percent. Sales revenue for the company is expected to remain stable indefinitely at last year's level of $17,800,000. Variable costs amount to 70 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, e.g., 1,234,567. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) a. Value of the company b. What is the required return on the firm's levered equity? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Required return c-1. Use the weighted average cost of capital method to calculate the value of the company. (Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Value of the company c-2. What is the value of the company's equity? (Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Value of equity c-3. What is the value of the company's debt? (Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Value of debt d. Use the flow to equity method to calculate the value of the company's equity. (Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Value of equityExplanation / Answer
a. If Mojito were financed entirely by equity, the value of the firm would be equal to the present value of its unlevered after-tax earnings, discounted at its unlevered cost of capital of 16%.
Sales Revenue
$17,800,000
Variable costs
12,460,000
EBIT
5,340,000
Taxes at 34%
1,815,600
Unlevered after-tax earnings
3,524,400
VU = $3,524,400/0.13
VU = $27,110,769
Therefore, Mojito Mint Company would be worth $27,110,769 as an unlevered firm.
b. 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 = 0.073
TC = 0.34
B/S = 0.40
The required return on Mojito’s levered equity is:
rS = r0 + (B/S)(r0 – rB)(1 – TC)
= 0.13 + (0.40)(0.13 – 0.073)(1 – 0.34)
= 0.145
The required return on Mojito’s levered equity (rS) is 14.5%.
c-1. In a world with corporate taxes, a firm’s weighted average cost of capital (rwacc) equals:
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 ratio
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 0.4 is given, which can be written algebraically as:
B / S = 0.4
Solving for B:
B = (0.4)(S)
A firm’s debt-to-value ratio is: B / (B+S)
Since B = (0.40)(S):
Mojito’s debt-to-value ratio = (0.4)(S) / { (0.4)(S) + S}
= (0.4)(S) / (1.4)(S)
= (0.4)/1.4)
= 0.2857
Mojito’s debt-to-value ratio is 0.2857.
A firm’s equity-to-value ratio is: S / (B+S)
Since B = (0.4)(S):
Mojito’s equity-to-value ratio = S / {(0.4)(S) + S}
= S / (1.4)(S)
= (1 / (1.4))
= 0.7143
Mojito’s equity-to-value ratio is 0.7143.
The inputs to the WACC calculation are:
B / (B+S) = 0.2857
S / (B+S) = 0.7143
rB = 0.073
rS = 0.145
TC = 0.34
rwacc = {B / (B+S)}(1 – TC) rB + {S / (B+S)}rS
= (0.2857)(1 – 0.34)(0.073) + (0.7143)(0.145)
= 0.1173
Mojito’s weighted average cost of capital is 11.73%.
Use the weighted average cost of capital to discount the firm’s unlevered after-tax earnings.
VL = $3,524,400/ 0.1173
= $30,046,036
Therefore, the value of Mojito Mint Company is $30,046,036.
c-2: Since the firm’s equity-to-value ratio is 0.7143, the value of Mojito’s equity is $21,461,883.
{= (0.7143)($30,046,036)}.
c-3: Since the firm’s debt-to-value ratio is 0.2857, the value of Mojito’s debt is $8,584,152
{= (0.2857)( $30,046,036)}.
d. 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 7.3%, and the firm has $8,584,152 of debt outstanding, Mojito must pay $626,643 (= 0.073 * $8,584,152) in interest at the end of each year.
Sales Revenue
$17,800,000
Variable costs
12,460,000
EBIT
5,340,000
Interest
$626,643
Pre-tax earnings
$4,713,357
Taxes at 34%
1,602,541
Unlevered after-tax earnings
3,110,816
Since the firm pays all of its after-tax earnings out as dividends at the end of each year, equity holders will receive $3,110,816 of cash flow per year in perpetuity.
S = Cash Flows Available to Equity Holders / rS
= $3,110,816/ 0.145
= $21,453,900
The value of Mojito’s equity is $21,453,900
Sales Revenue
$17,800,000
Variable costs
12,460,000
EBIT
5,340,000
Taxes at 34%
1,815,600
Unlevered after-tax earnings
3,524,400
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