Question 16 Mojito Mint Company has a debt-to-equity ratio of 2/3. The required return on the firm’s unlevered equity is 16%, and the pre-tax cost of the firm’s debt is 10%. Sales revenue for Mojito is expected to remain stable indefinitely at last year’s level of $19,740,000. Variable costs amount to 60% of sales. Mojito is taxed at the corporate tax rate of 40%. The firm distributes all of its earnings as dividends at the end of each year. a. If Mojito were financed entirely by equity, how much would it be worth? b. What is the required return on the firm’s levered equity (r S)? c. Use the Weighted Average Cost of Capital method to calculate the value of Mojito Mint. What is the value of the firm’s equity? What is the value of the firm’s debt? d. Use the Flow-to-Equity method to calculate the value of Mojito Mint’s equity.
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%.
Mojito Mint Company Sales Revenue Variable Costs EBIT Taxes at 40% Unlevered After-Tax Earnings
$19,740,000 11,844,000 7,896,000 3,158,400 4,737,600
VU = $4,737,600 / 0.16 = $29,610,000
Therefore, Mojito Mint Company would be worth $29,610,000 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
= 0.16
rB = 0.10 TC = 0.40 B/S = 2/3
The required return on Mojito’s levered equity is:
rS = r0 + (B/S)(r0 – rB)(1 – TC) = 0.16 + (2/3)(0.16 – 0.10)(1 – 0.40) = 0.184
The required return on Mojito’s levered equity (rS) is 18.4%.
c)
In a world with corporate taxes, a firm’s weighted average cost of capital (r wacc)
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 equityto-value ratio. However, the firm’s debt-to-equity ratio of 2/3 is given, which can be written algebraically as:
B / S = 2/3
Solving for B:
B = (2/3)(S)
A firm’s debt-to-value ratio is: B / (B+S)
Since B = (2/3)(S):
Mojito’s debt-to-value ratio
= (2/3)(S) / { (2/3)(S) + S}
= (2/3)(S) / (5/3)(S) = (2/3)/(5/3) = 2/5
Mojito’s debt-to-value ratio is 2/5.
A firm’s equity-to-value ratio is: S / (B+S)
Since B = (2/3)(S):
Mojito’s equity-to-value ratio
= S / {(2/3)(S) + S} = S / (5/3)(S) = (1 / (5/3)) = 3/5
Mojito’s equity-to-value ratio is 3/5.
The inputs to the WACC calculation are:
B / (B+S)
= 2/5
S / (B+S)
= 3/5
rB
= 0.10
rS
= 0.184
TC
= 0.40
rwacc
= {B / (B+S)}(1 – TC) rB + {S / (B+S)}rS = (2/5)(1 – 0.40)(0.10) + (3/5)(0.184) = 0.1344
Mojito’s weighted average cost of capital is 13.44%. Use the weighted average cost of capital to discount the firm’s unlevered after-tax earnings.
VL = $4,737,600 / 0.1344 = $35,250,000
Therefore, the value of Mojito Mint Company is $35,250,000.
Since the firm’s equity-to-value ratio is 3/5, the value of Mojito’s equity is $21,150,000 {= (3/5)($35,250,000)}. Since the firm’s debt-to-value ratio is 2/5, the value of Mojito’s debt is $14,100,000 {= (2/5)( $35,250,000)}.
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 (r S).
Since the pre-tax cost of the firm’s debt is 10%, and the firm has $14,100,000 of debt outstanding, Mojito must pay $1,410,000 (= 0.10 * $14,100,000) in interest at the end of each year.
Mojito Mint Company Sales Revenue
19,740,000
Variable Costs EBIT Interest Pre-Tax Earnings Taxes at 40% After-Tax Earnings
11,844,000 7,896,000 1,410,000 6,486,000 2,594,400 3,891,600
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 = $3,891,600 / 0.184 = $21,150,000
The value of Mojito’s equity is $21,150,000.
