Question

Firm 1 has a capital structure with 20 percent debt and 80 percent equity. Firm 2’s
capital structure consists of 50 percent debt and 50 percent equity. Both firms pay 7
percent annual interest on their debt. Finally, suppose that both firms have invested in
assets worth $100 million.
Required:
Calculate the return on equity (ROE) for each firm, assuming the following:
a. The return on assets is 3 percent.
b. The return on assets is 7 percent.
c. The return on assets is 11 percent.
What general pattern do you observe? Please explain in your own words.

Answer 1

First we need to find out the shareholder's equity using balence sheet equation

Firm 1 -

Total assets = shareholder's equity + liability (Debt)

100 = 80% equity + 20% debt

therefore

Equity= 100 * 80% = 80

Debt = 100 * 20% = 20

Firm 2 -

Total assets = 100

Therefore

Equity = 100 * 50% = 50

Debt = 100 * 50% = 50

Now Calculatin of Net Income

Scenario	Net Income of Firm 1	Net Income of firm 2
a) When ROA= 3%	ROA = (Net Income / Total assets) * 100 3 = (Net income / 100) * 100 3 = Net Income	ROA = (Net Income / Total assets) * 100 3 = (Net income / 100) * 100 3 = Net Income
b) When ROA = 7%	ROA = (Net Income / Total assets) * 100 7 = (Net income / 100) * 100 7 = Net Income	ROA = (Net Income / Total assets) * 100 7 = (Net income / 100) * 100 7 = Net Income
c) When ROA = 11%	ROA = (Net Income / Total assets) * 100 11 = (Net income / 100) * 100 11 = Net Income	ROA = (Net Income / Total assets) * 100 11 = (Net income / 100) * 100 11 = Net Income

Scenario	ROE of Firm 1 = (Net income / Shareholder's Equity) * 100	ROE of Firm 2 = (Net Income / Shareholder's Equity) * 100
When ROA = 3%	ROE = (3 / 80) * 100 = 3.75%	ROE = (3 / 50) * 100 = 6%
When ROA = 7%	ROE = ( 7 / 80) * 100 = 8.75%	ROE = (7 / 50) * 100 = 14%
When ROA = 11%	ROE = (11/ 80) * 100 = 13.75%	ROE = (11 / 50) * 100 = 22%

Pattern In Net Income for each scenario is same as both the firms have total assets worth $100 million