Question $1$

a$.$ NRG Energy, Inc. $($NRG$)$ is an energy company with a market debt$-$equity ratio of $2.$ Suppose its current debt cost of capital is $6\%,$ and its equity cost of capital is $12\%.$ Suppose also that if N R G issues equity and uses the proceeds to repay its junior debt and reduce its debt$-$equity ratio to $1,$ it will lower its debt cost of capital to $5\mathrm{.}5\%.$ With perfect capital markets, what effect will this transaction have on NRG$\text{'}$s equity cost of capital and WACC? What would happen if N R G issues even more equity and pays off its debt completely? How would these alternative capital structures affect N R G$\text{'}$s enterprise value?

b$.$ Suppose the risk of a railroad accident for a major railroad is $1\mathrm{.}2\%$ per year, with a beta of zero. If the risk$-$free rate is $6\%,$ what is the actuarially fair premium for a policy that pays $$100$ million in the event of a loss? What is the NPV of purchasing insurance for the railroad if it would experience $$25$ million in financial distress costs and $$15$ million in issuance costs in the event of a loss if it were uninsured? Going through the same process, find the NPV if the risk had a beta of $-2$

c$.$ Explain the Dividend Signaling Theory. Explain how an investor can derive information about the performance of a firm based on the payout policy it adopts.

d$.$ Explain the Concept of Debt Overhung

Question $2$

a$.$ Rexton Oil is an all$-$equity firm with $100$ million shares outstanding. Rexton has $$150$ million in cash and expects future free cash flows of $$65$ million per year. Management plans to use the cash to expand the firm's operations, which will in turn increase future free cash flows by $12\%.$ If the cost of capital of Rexton's investments is $10\%,$ how would a decision to use the cash for a share repurchase rather than the expansion change the share price?

b$.$ Altgreen is an all$-$equity firm with $250$ million shares outstanding. Altgreen has $$300$ million in cash and expects future free cash flows of $$150$ million per year. Management plans to use the cash to expand the firm's operations, which will in turn increase future free cash flows by $10\%.$ If the cost of capital of Altgreen's investments is $7\%,$ how would a decision to use the cash for a share repurchase rather than the expansion change the share price?

c$.$ Explain Clientele Effect

d$.$ Greenleaf Industries is considering adding leverage to its capital structure. Greenleaf's managers believe they can add as much as $$35$ million in debt and exploit the benefits of the tax shield $($for which they estimate $({}^{**}=15\%).$ However, they also recognize that higher debt increases the risk of financial distress. Based on simulations of the firm's future cash flows, the CFO has made the following estimates $($in millions of dollars$)$:$\backslash$table$[[$Debt$,0,10,20,25,30,35],[PV($Interest taxshield$),0\mathrm{.}00,1\mathrm{.}50,3\mathrm{.}00,3\mathrm{.}75,4\mathrm{.}50,5\mathrm{.}25],[PV($Financial distress costs$),0\mathrm{.}00,0\mathrm{.}00,0\mathrm{.}38,1\mathrm{.}62,4\mathrm{.}00,6\mathrm{.}38]]$

What is the optimal debt choice for Greenleaf?