Question

Using a specific numerical example explain the statement that "given the return on assets, the lower the bank capital, the higher the return for the owners of the bank."

Answer 1

Return on assets is the net profit after tax per dollar of asset. It shows how efficiently the bank is being managed. It is written as ROA = (net profit after taxes) / (assets)

However, the owners of bank are concerned with their return on equity which means how their investment is responding. It is written as return on equity or ROE = (net profit after taxes) / (equity capital).

ROE and ROA are related by equity multiplier which refers to the assets per dollar of equity capital. This means EM = Assets/equity capital. Also ROE = ROA*EM.

Given the amount of assets, if bank capital or equity capital is high, EM will be lower and for low bank capital, EM will be high.

Numerically, suppose assets = $50 million then for a high bank capital of $10 million, EM will be 5 and for a low bank capital of $5 million, EM will be 50/5 = 10

Thus for a given ROA, ROE will be two times more when bank capital is $5 million than when it is $10 million.