Jungle, Inc., has a target debt−equity ratio of 0.84. Its WACC is 11.5 percent, and the tax rate is 34 percent.
Required:
(a)
If Jungle's cost of equity is 14.5 percent, its pretax cost of debt is percent.
(b) If instead you know the aftertax cost of debt is 6.5 percent, the cost of equity is percent.
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(a) To find the pretax cost of debt, we can use the formula for the weighted average cost of capital (WACC), which is given by:
WACC = (E/V) * Re + (D/V) * Rd * (1 - tax rate)
Where:
- E is the market value of equity,
- V is the total market value of the firm's debt and equity,
- Re is the cost of equity,
- D is the market value of debt,
- Rd is the pretax cost of debt, and
- tax rate is the corporate tax rate.
We are given:
- WACC = 11.5% (0.115)
- tax rate = 34% (0.34)
- debt-equity ratio = 0.84
Let's assume the market value of equity is 1 (for simplicity). Since the debt-equity ratio is 0.84, the market value of debt would be 0.84.
Using the formula, we can write the equation as:
0.115 = (1/1.84) * 0.145 + (0.84/1.84) * Rd * (1 - 0.34)
Simplifying the equation:
0.115 = 0.07880435 + 0.45543478 * Rd * (0.66)
0.115 = 0.07880435 + 0.30038183 * Rd
0.03619565 = 0.30038183 * Rd
Rd = 0.03619565 / 0.30038183
Rd ≈ 0.12 (or approximately 12%)
Therefore, the pretax cost of debt is approximately 12%.
(b) If we know the aftertax cost of debt is 6.5% (0.065), we can use a similar approach to find the cost of equity.
Using the same formula for WACC:
0.115 = (1/1.84) * Re + (0.84/1.84) * 0.065 * (1 - 0.34)
Simplifying the equation:
0.115 = 0.05434783 * Re + 0.01706522
0.09793478 = 0.05434783 * Re
Re = 0.09793478 / 0.05434783
Re ≈ 1.8 (or approximately 18%)
Therefore, the cost of equity is approximately 18%.