Suppose that you are the sole owner of an all-equity firm, the assets of which a
ID: 2772252 • Letter: S
Question
Suppose that you are the sole owner of an all-equity firm, the assets of which are worth $500,000. The ROA is 15% per year paid as a dividend to you. If you have the firm issue $100,000 of debt at 6%, the interest expense will be paid by the firm out of the earnings that had constituted ROA. The debt is secured by the firm, not by you. The firm pays a special dividend to you of $100,000 on the day the debt is issued. The tax rate is 34%. What will your return on equity be in the year after you go into debt?
Explanation / Answer
Return on Equity = 14.21%
Working
Existing captal
Total Assets = $500,000
Since this is an all equity firm Total Assets = Total Liabilities = Equity
ROA = 15% or 0.15
ROA = Net Income / Total Assets
0.15 = Net Income / Total Assets = Net Income / 500,000
Net Income = $ 500,000 * 0.15 = $ 75,000
Net Income = $ 75000
Pre Tax Profit = $ 75000 * (1-Tax) = $ 75000 / (1-0.34) = $ 75,000 / 0.66
= $ 1,13,636.36
This is equal to EBIT as the Firm does not have any Debt
ROE = PAT / Equity * 100 = 15% since this is an all equity
After Change
Debt Issued = $ 100,000
Rate of Interest = 6%
Annual interest payment = 100,000 * 6% = $ 6,000
On the date of Debt a special dividend of $100,000 is paid to the owner. That is the debt amount is basically used to pay the special dividend.
Total Assets = Total Liabilities = Equity + Debt = $ 500,000 + $ 100,000
= $ 600,000
Assuming that the Earnings constituting ROA does not change
EBIT = $ 1,13,636.36
Less : Interest = $ 6,000.00
EBT = $ 1,07,636.36
Tax (34%) = $ 36,596.36
Net Income = $ 71,040.00
ROA = (Net Income / Total Assets)*100 = (71040/600000)*100 = 11.84%
Return on Equity = (Net Income / Share Holders Equity)*100 = (71040/500000)*100
= 14.208 or 14.21%
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