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 marks)

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. (2 marks)

Answer 1

Given

Leverage Ratio = [Net Assets/ Debt ] = 20

ROA = Return on Assets = Return/Net Assets = 3.5% p.a.

Debt Cost = 1.5% p.a.

Answer 1:

ROA, net of debt funding costs = ROA - Debt Cost as a % of Net Assets

= 3.5% - [ Debt Cost/Net Assets]

= 3.5% - [ 1.5%/ 20] { Using leverage ratio}

= 3.5% - 0.075%

= 3.425 % p.a.

ROE = (3.425* 19)/20

= 3.254%

Answer 2:

If yield on assets is 3 %

= 3.0% - 0.075%

= 2.925%

ROE = (2.925* 19)/20

=2.779%

Answer 3:

If yield on assets is 1 %

= 1.0% - 0.075%

= 0.925%

ROE = (0.925* 19)/20

=0.879%