Q$\mathrm{.}5)$ Vaudeville Inc. is a small entertainment firm. It has $20$ million shares outstanding, trading at $ $10$ a share and $ $50$ million in outstanding debt. The firm$$s only business is making movies, but it does have $$25$ million as a cash balance. The firm has a regression beta based upon two years of stock returns of $1\mathrm{.}85.$ The unlevered beta, cleansed of and corrected for cash holdings, for firms in the movie business is $1\mathrm{.}20.$ The corporate tax rate is $40\%.$

a$.$ Estimate the bottom$-$up beta for Vaudeville.

b$.$ The firm is considering borrowing $$100$ million and using the proceeds, in conjunction with the cash it has on hand, to enter the entertainment software business. The unlevered beta for firms in this business is $2\mathrm{.}0.$ Estimate the beta for the company after the transaction.

Q$\mathrm{.}6)$ Novacell Inc. is a manufacturer of solar panels that is considering moving from its existing policy of not borrowing money. The firm has $4$ million shares outstanding, trading at $ $25$ a share, no cash holdings and a beta of $1\mathrm{.}20.$ The risk free rate is $5\%,$ the equity risk premium is $4\%$ and the corporate tax rate is $40\%.$

a$.$ Estimate the current cost of capital for the firm.

b$.$ Assume that the firm can borrow $ $25$ million at a pre$-$tax rate of $7\%$ and buy back shares.. Assuming that the firm is growing $3\%$ a year in perpetuity and that investors are rational, estimate the change in value per share after the buyback.

c$.$ Assume that instead of buying back shares, the firm had borrowed $$25$ million and invested the money in expanding its existing business. If the expansion has a net present value of $ $5$ million, estimate the change in value per share after the transaction.

Q$\mathrm{.}7)$ Damocles Inc., a publicly traded firm, has $80$ million shares trading at $ $10$ a share and $ $200$ million in debt $($market value and book value$).$ The firm currently has a beta of $1\mathrm{.}20$ and a pre$-$tax cost of debt of $5\%.$ The risk free rate is $4\%$ and the market risk premium is $4\mathrm{.}5\%.$ The marginal tax rate is $40\%.$

a$.$ Estimate the current cost of capital for the firm.

b$.$ The firm has announced that it will be borrowing $ $200$ million and buying back shares. The rating for the firm will drop to BBB$,$ causing the pre$-$tax cost of debt to rise to $6\%.$ Estimate the new cost of capital for the firm.

c$.$ Now assume that investors are rational and that the firm is growing $4\%$ a year in perpetuity. How many shares can Damocles expect to buy back with $ $200$ million?