What proportion of the firm is financed by debt for a firm that expects a 15 percent return on equity,a 12 percent return on assets,and a 10 percent return on debt? The tax rate is 25 percent.

Question

Quizplus · Accepted Answer

Using the formula for Return on Equity:
ROE = Net Income / Equity
We can rearrange it to get Equity / Net Income = 1 / ROE

Therefore, Equity = Net Income / ROE
Given the information in the question, we can calculate the equity as:
Equity = 0.15

Using the formula for Return on Assets:
ROA = Net Income / Total Assets
We can rearrange it to get Net Income = ROA x Total Assets

Therefore, Net Income = 0.12 x Total Assets
From this, we calculate the Net Income as:
Net Income = 0.12

Using the formula for Return on Debt:
ROD = (Interest Expense x (1 - Tax Rate)) / Total Debt
We can rearrange it to get Total Debt = (Interest Expense x (1 - Tax Rate)) / ROD

Therefore, Total Debt = (0.10 x (1-0.25)) / 0.10

From this, we can calculate Total Debt as:
Total Debt = 0.6

Finally, we can calculate the proportion of the firm that is financed by debt as:
Total Debt / (Total Debt + Equity)
= 0.6 / (0.6 + 0.15)
= 0.8
Therefore, 2/3 or 66.6% of the firm is financed by debt.

The best choice is D, as it is the correct answer based on the calculations above.

What Proportion of the Firm Is Financed by Debt for a Firm