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 $4\mathrm{.}22\%$ expected retum 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 $0\mathrm{.}25\%.$ 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 equity reduce its attractiveness

to shareholders? Explain.