Question

1) A bank with a leverage ratio of 15 has a cost of debt of 2%pa and a portfolio of assets with an expected yield of 4%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) What is the unweighted bank’s capital (or E/A) ratio (i) for a leverage ratio of 20 and (ii) for a leverage ratio of 30? Show your workings. (1 mark)

5) Redo the above calculations in parts 1) and 3) for a leverage ratio of 25. What affect does the higher leverage ratio have on your answers? Show your workings.

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

Answer 1

1)	Leverage ratio = 15
	This means bank is using $100 own capital and $1400 Borrowed capital
	This makes them to do business of 15 times by having capital of 1
	Overall Assets involved = 1500
	Return on Assets = 4%
	Return = 1500 * 4% = 60
	Debt cost = 1400 * 2% = 28
	Net Return = Total Return - Debt cost = 60 - 28 = 32
	ROA = 32/1500 = 2.13%
	ROE = Net return / Equity Capital
	Net Return = 32
	Equity capital = 100
	ROE = 32/100 = 32%
	:- One more intereting thing to know is
	ROA * Leverage ratio = ROE
	2.133* 15 = 32%
2)	Yield = 3% * 1500 = 45
	Debt cost = 28
	Net Return = 17
	ROA = 17/1500 = 1.133%
	ROE = 17/100 = 17%
3)	Return = 1% * 1500 = 15
	Debt cost = 28
	Net return = 15 -28 = -13
	ROA = -13/1500 = -.86% i.e Loss of .86%
	ROE = -13/100 = -13% Loss
4)	Bank capital if leverage ratio is 20 Times
	Leverage = Assets/ Equity
	Let Say total Assets = 100
	20   =    100/x
	X = 5
	So bank capital is 5% of total capital
	IF leverage ratio is 30 then
	30   =   100/x
	x   = 3.33
	So bank capital is 3.33% of tatal capital

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Thanks & Regards,
Devendra agarwal