Question

1) A bank with a leverage ratio of 20 has a cost of debt of 1.5%pa and a portfolio of assets with an expected yield of 3.5%pa. What are the expected ROA net of debt funding costs and the expected ROE of the bank, using the approach to defining leverage taken in the lecture slides? Show your workings.

2) What will the ROA and ROE actually be if the yield on assets turns out to be 3%? Show your workings. (1 mark)

3) What will the ROA and ROE actually be if the yield on assets turns out to be 1%? Show your workings.

4) Redo the above calculations in parts 1) and 3) for a leverage ratio of (i) 10 (ii) 30? What effect does a higher leverage ratio have on your answers? Show your workings.

5) What is the relationship between a bank’s capital ratio and the risks and returns faced by (i) its depositors and (ii) its shareholders? Explain your answers.

do not copy other answers

Answer 1

Since, it has not been mentioned which questions are to be done. Hence, doing the first question only.

1) A Leverage ratio of 20 signifies that the bank has an Asset to Equity of 20, which means Assets amounting to 1 is funded by Equity and remaining 19 are funded by debt.

Using the leverage ratio, we can know the Assets, Liabilities and Equity.

Assets = 20

Equity = 1 (Using A/E = 20)

Debt = Assets - Equity = 19

Since Assets have an expected yield of 3.5% pa and cost of debt is 1.5%, then-

Yield from Assets = 20 * 3.5% = 0.7

Cost of Debt = 19 * 1.5% = 0.285

Profit = 0.7 - 0.285 = 0.415

Return on Assets = Profit / Assets = 0.415 / 20 = 2.075%

Return on Equity = Profit / Equity = 0.415 / 1 or ROA * Leverage Ratio = 41.5%