Question

last years return on on equity was 30%. This year the ROE has decreased by 20% even though the firms earnings equaled last years earnings. the firm has no preferred stock. what caused the decrease?

a. equity decreased by 10%
b. equity increased by 50%
c. equity increased by 10%
d. equity increased by 50%

Answer 1

NI = .3(Old equity)

NI = .2(Old equity + New equity)

.3(Old equity) = .2(Old equity + New equity)

New equity = .5 Old equity

The answer is b. equity increased by 50%

Answer 2

To determine the cause of the decrease in Return on Equity (ROE), we need to consider the components of the ROE formula, which is Net Income divided by Equity.

The formula for ROE is: ROE = Net Income / Equity

Given that the firm's earnings remained the same, but the ROE decreased by 20%, it indicates that there was a change in the equity component of the formula.

Let's analyze the answer choices:

a. Equity decreased by 10% b. Equity increased by 50% c. Equity increased by 10% d. Equity increased by 50%

Since the firm's earnings were the same, a decrease in equity would result in a decrease in ROE, while an increase in equity would lead to an increase in ROE.

The correct answer is: a. Equity decreased by 10%

A decrease in equity would cause the ROE to decrease by the same percentage. In this case, a 10% decrease in equity caused the 20% decrease in ROE, despite the earnings remaining constant.