MM Proposition $2($S$16-3)$ "Increasing financial leverage increases both the cost of debt $(($:$r_{\text{d}\text{e}\text{b}\text{b}}\}$ and the cost of equity $(r_{\text{e}\text{q}\text{u}\text{i}\text{t}\text{y}}).$ So the overall cost of capital cannot stay constant." This problem is designed to show that the speaker is confused. Buggins Inc. is financed equally by debt and equity, each with a market value of $$1$ million. The cost of debt is $5\%,$ and the cost of equity is $10\%.$ The company now makes a further $$250,000$ issue of debt and uses the proceeds to repurchase equity. This causes the cost of debt to rise to $5\mathrm{.}5\%$ and the cost of equity to rise to $10\mathrm{.}83\%.$ Assume the firm pays no taxes.

a$.$ How much debt does the company now have?

b$.$ How much equity does it now have?

c$.$ What is the overall cost of capital?

d$.$ What is the percentage increase in earnings per share after the refinancing?

e$.$ What is the new price$-$earnings multiple? $($Hint: Has anything happened to the stock price?$)$