ABC Inc. is a personal computer $($PC$)$ maker that was a pioneer and early leader in the PC industry. As the technology has matured and PCs have been standardized, the barriers to new entrants have become virtually non$-$existent. Competition is very intense, driving the industry into a phase of maturity, characterized by $$low profitability$$ and $$slow growth$.$ The price of ABC$$s common stock has been steadily falling and currently sits at $$20$ per share on the stock market. ABC has $10$ million shares outstanding and its debt has a market value of $$100$ million at an annual interest rate of $8\%.$ ABC has a corporate tax rate of $40\%.$ Carol, the founder and CEO of ABC has assigned you, her assistant, to study alternatives to boost ABC$$s share price.

Ensure you include the following in your answer:

Based on the information provided by the accounting department, you have projected ABC$$s perpetual earnings before interest and taxes $($EBIT$)$ to be $$48$ million per year. ABC pays out all earnings available to shareholders as dividends. Calculate ABC$$s $($levered$)$ cost of equity implied in its current market value of equity and its projected EBIT.

Calculate ABC$$s current debt$-$to$-$asset ratio and weighted average cost of capital $($WACC$).$ Calculate ABC$$s unlevered cost of equity and show that it is lower than the current levered cost of equity you calculated in part a$).$ Calculate ABC$$s value of unlevered equity and show that it is different from its current market value of equity $($of a levered firm$).$

One alternative to boost ABC$$s share price is to take out a new perpetual loan at an $8\%$ annual interest rate and to repurchase $4$ million common shares. Give two brief explanations why a share repurchase might increase the share price. What is the other purpose that a share repurchase may serve? Calculate the dollar amount of the new loan used to repurchase ABC$$s common shares and the share price after the share repurchase according to Miller & Modigliani $($M&M$)$ Propositions. Lastly, show that a share repurchase does increase ABC$$s share price.