Suppose an investment bank has $$900$ billion in assets under management and a

leverage ratio $($Assets $/$ Equity$)$ of $20$ to $1.$ If the bank earns $($annually$)$ a $7\%$

return on its assets and pays $4\%$ interest on its debt and the tax rate is $20\%,$ what

is the $($annual$)$ return$-$on$-$equity?

Consider a one$-$factor Arbitrage Pricing Theory model. There are two well$-$diversified

portfolios: A and B$.$ Portfolio A$\text{'}$s expected return is $24$ percent and its beta is

$0\mathrm{.}6$; Portfolio B$\text{'}$s expected return is $12$ percent and its beta is $0\mathrm{.}2.$ What is the

risk$-$free rate in the model?

Suppose all assumptions of the Capital Asset Pricing Model are true. Consider

two firms A and B$,$ which invest in the same type of risky projects. The asset side

of both firms is worth $$100$ million. Firm $A$ is purely equity financed, and firm

B is financed with $$60$ million risk$-$free debt and $$40$ million equity. Suppose the

risky project's expected return is $8\%$ and the risk$-$free interest rate is $2\%.$

a$)$ What is the expected return on firm A$\text{'}$s equity?

b$)$ What is the expected return on firm B$\text{'}$s equity?

c$)$ What is ratio of firm A$\text{'}$s equity beta to firm B$\text{'}$s equity beta?

Consider a new project, which costs $$1,000$ now and yields the expected cash flow

$$1,100$ next period. Assume that the new project does not change the beta of

either firm.

d$)$ Should firm A$\text{'}$s shareholders vote against the new project and WHY?