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QuestionFind the debt-equity ratio given a cost of equity of 14.9%, cost of debt of 7.3%, and return on assets of 12.6%.

Studdy Solution

STEP 1

Assumptions1. The cost of equity is14.9 percent. The pretax cost of debt is7.3 percent3. The return on assets is12.6 percent4. We are ignoring taxes5. We need to find the debt-equity ratio

STEP 2

We can use the formula for the return on assets (ROA) which is given byROA=Equity RatiotimesCost of Equity+Debt RatiotimesCost of DebtROA = Equity\, Ratio \\times Cost\, of\, Equity + Debt\, Ratio \\times Cost\, of\, Debt

STEP 3

We know that the Equity Ratio + Debt Ratio =1 (since the total assets are financed either by equity or debt). Therefore, we can write the Debt Ratio as (1 - Equity Ratio).

STEP 4

Substitute Debt Ratio in the ROA formulaROA=Equity RatiotimesCost of Equity+(1−Equity Ratio)timesCost of DebtROA = Equity\, Ratio \\times Cost\, of\, Equity + (1 - Equity\, Ratio) \\times Cost\, of\, Debt

STEP 5

Rearrange the equation to solve for the Equity RatioEquity Ratio=ROA−Cost of DebtCost of Equity−Cost of DebtEquity\, Ratio = \frac{ROA - Cost\, of\, Debt}{Cost\, of\, Equity - Cost\, of\, Debt}

STEP 6

Plug in the given values for ROA, cost of equity, and cost of debt to calculate the Equity RatioEquity Ratio=12.6%−.3%14.9%−.3%Equity\, Ratio = \frac{12.6\% -.3\%}{14.9\% -.3\%}

STEP 7

Calculate the Equity RatioEquity Ratio=5.3%7.6%=0.6973684210526316Equity\, Ratio = \frac{5.3\%}{7.6\%} =0.6973684210526316

STEP 8

Now, calculate the Debt Ratio by subtracting the Equity Ratio from1Debt Ratio=1−Equity Ratio=1−0.6973684210526316Debt\, Ratio =1 - Equity\, Ratio =1 -0.6973684210526316

STEP 9

Calculate the Debt RatioDebt Ratio=−.6973684210526316=.3026315789473684Debt\, Ratio = -.6973684210526316 =.3026315789473684

STEP 10

The debt-equity ratio is given by the formulaDebt−Equity Ratio=Debt RatioEquity RatioDebt-Equity\, Ratio = \frac{Debt\, Ratio}{Equity\, Ratio}

STEP 11

Plug in the values for the Debt Ratio and Equity Ratio to calculate the Debt-Equity RatioDebt−Equity Ratio=0.30263157894736840.6973684210526316Debt-Equity\, Ratio = \frac{0.3026315789473684}{0.6973684210526316}

STEP 12

Calculate the Debt-Equity RatioDebt−Equity Ratio=0.30263157894736840.6973684210526316=0.434Debt-Equity\, Ratio = \frac{0.3026315789473684}{0.6973684210526316} =0.434So, the debt-equity ratio is approximately0.43, which corresponds to option C.

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