Finding the Capital Structure Fama's Llamas has a weighted average cost of capital of 9.8 percent. The company's cost of equity is 15 percent, and its cost of debt is 7.5 percent. Tha tax rate is 35 percent. What is Fama's debt-equity ratio?
To find Fama's debt-equity ratio, we need to understand the relationship between debt, equity, and the weighted average cost of capital (WACC).
The WACC is the average rate of return a company must provide to its investors to compensate for the risk they undertake by investing in the company. It is a weighted average of the cost of equity and the cost of debt, with the weights determined by the proportion of each in the company's capital structure.
The formula for WACC is:
WACC = (Equity / Total Capital) * Cost of Equity + (Debt / Total Capital) * Cost of Debt * (1 - Tax Rate)
We can rearrange this equation to solve for the debt-equity ratio:
Equity / Total Capital = 1 - (Debt / Total Capital)
Now, let's substitute the given values into the equation:
WACC = 9.8% (0.098)
Cost of Equity = 15% (0.15)
Cost of Debt = 7.5% (0.075)
Tax Rate = 35% (0.35)
We don't know the specific values for Equity, Debt, or Total Capital, but we can still find the debt-equity ratio. Let's solve the equation for the unknown ratio.
0.098 = (1 - Debt / Total Capital) * 0.15 + (Debt / Total Capital) * 0.075 * (1 - 0.35)
Simplifying the equation:
0.098 = 0.15 -0.15(Debt / Total Capital) + 0.075(Debt / Total Capital) - 0.075(Debt / Total Capital) * 0.35
0.098 = 0.15 - 0.075(Debt / Total Capital) * 0.35
0.098 - 0.15 = -0.02625(Debt /Total Capital)
Now, let's isolate the ratio:
-0.052 = -0.02625(Debt / Total Capital)
Debt / Total Capital = -0.052 / -0.02625
Debt / Total Capital = 1.981
Finally, we have the debt-equity ratio:
Debt-equity ratio = Debt / Equity
= Debt / (Total Capital - Debt)
= 1.981 / (1 - 1.981)
= 1.981 / (-0.981)
= -2.02
Therefore, Fama's debt-equity ratio is approximately -2.02.