Suppose LD Bank is funded with 2% equity and 98% debt. Its current market capita

Question

Suppose LD Bank is funded with 2% equity and 98% debt. Its current market capitalization is $10 billion, and its market to book ratio is 1. LD 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 LD 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 LD Bank’s expected ROE with 2% equity?

b.         Assuming perfect capital markets, what will LD Bank’s expected ROE be after it increases its equity to 4%?

c.         Consider the difference between LD Bank’s ROE and its cost of debt. How does this “premium” compare before and after the Bank’s increase in leverage?

d.         Does the reduction in Levered Bank’s ROE after the increase in equity reduce its attractiveness to shareholders? Explain.

Explanation / Answer

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

Asset = 10/2% = $ 500 Billion

Equity = $ 10 Billion

Debt = 500-10 = $ 490 Billion

Net Income = ROA*Asset - Cost of Debt*Debt

Net Income = 4.22%*500 - 4%*490

Net Income = $ 1.5 Billion

LD Bank’s expected ROE = Net Income /Equity

LD Bank’s expected ROE = 1.5/10

LD Bank’s expected ROE = 15%

b.         Assuming perfect capital markets, what will LD Bank’s expected ROE be after it increases its equity to 4%?

Equity = 4%*500 = $ 20 Billion

Debt = 96%*500 = 480 Billion

Net Income = 4.22%*500 - 4%*480

Net Income = $ 1.90 Billion

LD Bank’s expected ROE = Net Income /Equity

LD Bank’s expected ROE = 1.9/20

LD Bank’s expected ROE = 9.50%

c.         Consider the difference between LD Bank’s ROE and its cost of debt. How does this “premium” compare before and after the Bank’s increase in leverage?

Premium before the Bank’s increase in leverage = 15%-4%

Premium before the Bank’s increase in leverage = 11%

Premium after the Bank’s increase in leverage = 9.5% - 4%

Premium after the Bank’s increase in leverage = 5.5%

Premium drops from 11% to 5.5% i.e half

d.         Does the reduction in Levered Bank’s ROE after the increase in equity reduce its attractiveness to shareholders? Explain.

No , premium and risk both fall by half

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