Question

You are currently an investor in Bethes mining that earns an EBIT of $ 10,000 each year. The firm’s total assets are currently worth $ 80,000. 30% of the firm’s assets are currently funded by debt at a cost of 8%. There are totally 1000 shares outstanding of which you own 10 shares. In the recent board meeting, the executives have come up with the decision to push the firm’s leverage to 45% by replacing suitable amount of equity with debt. Suppose there are no taxes, the firm’s WACC is 10%, and you can lend/borrow at 8%, prove that increasing leverage is a value neutral proposition for you.

Answer 1

EBIT	10000		10000
WACC	10%		10%
Equity (100000*70%)	70000	Equity (100000*55%)=	55000	1000/70000*55000=785.71 shares
Debt(100000*30%)	30000	Debt(100000*45%)=	45000
Total assets	100000	Total assets	100000
Value of firm at 10%(EBIT/10%)	100000		100000
Less: Value of debt	30000		45000
Value of 1000 shares of Equity	70000		55000	785.7143
Value of 10 shares(70000/1000*10)	700	55000/785.7143*10=	700

Thus proved that increasing leverage is a value neutral proposition for the holder of 10 shares