Question

Zebra Group holds total assets of $25 billion and equity capital of $2 billion and has just posted an ROA of 0.95 percent. What is the financial firm's ROE? Alternative scenarios: Suppose Zebra Group finds its ROA climbing by 25 percent, with assets and equity capital unchanged. What will happen to its ROE? Why?

Answer 1

The Zebra Group's initial ROE is calculated at 11.875%. If ROA increases by 25% with unchanged assets and equity, the new ROE becomes 14.84375%. This demonstrates that an increase in ROA while keeping assets and equity stable, results in an increased ROE.

Step-by-step explanation:

The financial firm's Return on Equity (ROE) can be calculated using the ROA value and the given amounts of total assets and equity capital. We use the formula ROE= (ROA × Total Assets) / Equity Capital to get the ROE.

Given the ROA of 0.95%, total assets of $25 billion, and equity capital of $2 billion:

ROE = (0.0095 × $25 billion) / $2 billion = $237.5 million / $2 billion = 11.875%.

In the alternative scenario, if Zebra Group's ROA increases by 25%, the new ROA would be 0.95% × 1.25 = 1.1875%. If the assets and equity remain unchanged, the new ROE will be calculated similarly, resulting in:

ROE = (0.011875 × $25 billion) / $2 billion = $296.875 million / $2 billion = 14.84375%.

This indicates that with an increase in ROA, holding assets, and equity constant, ROE will also increase. It is because the same amount of equity is now generating more income, due to the improved efficiency reflected by the higher ROA.