What is the proportion of equity financing for a firm that expects a 15% return on equity, a 10% return on assets, and an 8% return on debt? Ignore taxes.
A)25%
B)29%
C)75%
D)71%

Question

Quizplus · Accepted Answer

We can use the formula for Return on Equity (ROE) to solve for the proportion of equity financing:

ROE = (Net Income / Equity) * 100

Taking the given values:
15% = (Net Income / Equity) * 100
Net Income / Equity = 0.15

We also know:
Return on Assets (ROA) = (Net Income / Total Assets) * 100
10% = (Net Income / Total Assets) * 100
Net Income / Total Assets = 0.10

Return on Debt (ROD) = (Interest Expense / Debt) * 100
8% = (Interest Expense / Debt) * 100
Interest Expense / Debt = 0.08

Multiplying both sides of the first equation by Equity, we get:
Net Income = 0.15 * Equity

Substituting this value and Net Income / Total Assets = 0.10 in the expression for Net Income / Equity, we get:
0.15 * Equity / Equity = 0.10 * Total Assets / Equity
0.15 = 0.10 * Total Assets / Equity
Total Assets / Equity = 1.5

Using the formula for the proportion of equity financing:
Equity / Total Financing = 1 / (1 + Debt/Equity)
Equity / (Equity + Debt) = 1 / (1 + (Interest Expense / Net Income))
Equity / (Equity + Debt) = 1 / (1 + 0.08/0.15)
Equity / (Equity + Debt) = 0.71

Therefore, the proportion of equity financing is approximately 0.29 or 29%.

What Is the Proportion of Equity Financing for a Firm