Suppose Levered Bank is funded with 2% equity and 98% debt. Its current market c

Question

Suppose Levered Bank is funded with 2% equity and 98% debt. Its current market capitalization is

$10 billion, and its market to book ratio is 1. Levered Bank earns a 4.22% expected return on its

assets (the loans it makes), and pays 4% on its debt. New capital requirements will necessitate that

Levered Bank increase its equity to 4% of its capital structure. It will issue new equity and use the

funds to retire existing debt. The interest rate on its debt is expected to remain at 4%.

a. What is Levered Bank’s expected ROE with 2% equity?

b. Assuming perfect capital markets, what will Levered Bank’s expected ROE be after it increases

its equity to 4%?

c. Consider the difference between Levered Bank’s ROE and its cost of debt. How does this

“premium” compare before and after the Bank’s increase in leverage?

d. Suppose the return on Levered Bank’s assets has a volatility of 0.25%. What is the volatility of

Levered Bank’s ROE before and after the increase in equity?

e. Does the reduction in Levered Bank’s ROE after the increase in equity reduce its attractiveness to

shareholders? Explain.

Explanation / Answer

Current Market Capitalisation $ 10,000,000.00 Market to Book ratio 1 So Book capital $ 10,000,000.00 Compraised of: Equity @2% $        200,000.00 Debt capital $    9,800,000.00 Bank Earnings @4.22% $        422,000.00 Less: Interest Paid @ 4% on Debt $        392,000.00 Net Earnings $          30,000.00 Return on Equity(ROE = 30000/200000) 15.00% Question b. Now if Bank want to increase equity to 4% then 9,800,000 will be equal to 96% Hence total capital will be 9,800,000/96% $ 10,208,333.33 So new equity will be $        408,333.33 Earnings @4.22% $        430,791.67 Less: Interest Paid @ 4% on Debt $        392,000.00 Net Earnings $          38,791.67 Return on Equity (38,791.67/408,333.33) 9.50% Answer: 9.50% Question c. Levered bank's ROE has decreased by 5.5% with 2% increase in equity. Question d. With 2% change in equity, change in Return on equity =5.50% So, for 0.25 change in equity, ROE will be 5.5/2*0.25 = 0.69% Question e. Rediction on ROE will reduce attractiveness. Because return on equity has reduced from 15% to 9.50%

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