The following data reflect the current financial condition of BlueSky Motors Limited:

Sales $$100,000,000$

Fixed costs $$10,000,000$

Variable costs $(70\%$ of sales$)$ $$70,000,000$

Tax rate $40\%$

Market value of debt $$20,000,000$

Market value of equity $$67,500,000$

At the current level of debt, the cost of debt is $10\%,$ and the cost of equity is $16\%.$ BlueSky is wondering whether the present capital structure is optimal. It is estimated that if BlueSky increases the debt level to $$35,000,000,$ the interest rate on new debt $($$$15,000,000)$ would be $12\%$ and the cost of equity would rise to $18\%.$ If BlueSky increases debt level to $$50,000,000,$ interest rate on new debt $($$$30,000,000)$ would be $14\%$ and the cost of equity would increase to $20\%.$ The cost and market value of original debt will not change. BlueSky will use the additional debt to repurchase the stock. BlueSky is a zero growth firm, with all its earnings paid out as dividends.

a$.$ Should BlueSky increase its debt level? What level of total debt BlueSky should choose: $$20$ million, $$35$ million or $$50$ million?

b$.$ The market price of BlueSky$$s stock was originally $$67\mathrm{.}50$ per share. Calculate the new equilibrium share price at the total debt levels of $$35$ million, and $$50$ million.

c$.$ How many shares will be retired at the total debt level of $$35,000,000?$ $$50,000,000?$