Suppose Levered Bank is funded with 2.0% equity and 98.0% debt. Its current mark
ID: 2614469 • Letter: S
Question
Suppose Levered Bank is funded with 2.0% equity and 98.0% debt. Its current market capitalization is $10.00 billion, and its market-to-book ratio is 1.0. Levered Bank earns a 4.22% expected return on its assets (the loans it makes), and pays 4.0% on its debt. New capital requirements will necessitate that Levered Bank increase its equity to 4.0% 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 4.0%. b. Aosuming perfect capital markes whil evered Banks expected Ro b. Assuming perfect capital markets, what will Levered Bank's expected ROE be after it increases its equity to 4.0%? 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
(a) Initial Capital Structure: 98% Debt and 2 % Equity = $ 10 billion (market capitalization)
Therefore, Total Asset Value = 10 / 0.02 = $ 500 billion and Debt Value = $ 490 billion
As the market to book ratio is 1, the market value is equal to the book value. This implies that the asset value calculated above is both the book value and the market value.
Return on Assets = 4.22 % of Total Assets = ROA = 0.0422 x 500 = $ 21.1 million
Return on Debt = Debt Expense = 0.04 x 490 = $ 19.6 million
Return to Equity Holders = ROA - Debt Expense = 21.1 - 19.6 = $ 1.5 million
ROE = 1.5 / 10 = 0.15 or 15 %
(b) Equity = 4 % of Total Assets = 0.04 x 500 = $ 20 billion, Debt = $ 480 billion
Debt Expense = 0.04 x 480 = $ 19.2 million and ROA = 0.0422 x 500 = $ 21.1 million
Return to Equity = 21.1 - 19.2 = $ 1.9 million
ROE = 1.9 / 20 = 0.095 or 9.5 %
(c) Before equity raise, premium = 15 - 4 = 11 % and Post equity raise, premium = 9.5 - 4 = 5.5 %
As is observable the ROE premium over the cost of debt decreases as more equity is raised because the shareholder's equity expansion dilutes the impact of increased return to equity (not return on equity/numerator in the ROE equation).
(d) ROE = ROA x (Total Assets / Shareholder's Equity)
Pre-Equity Rise:
Volatility in ROE = Volatility in ROA x (1/0.02) = 0.0025 x 50 = 0.125 or 1.25 %
Post=Equity Rise:
Volatility in ROE = Volatility in ROA x (1/0.04) = 0.0025 x 25 = 0.0625 or 6.25 %
NOTE: Please raise a separate query for the solution to the last sub-part.
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