Question

Firm U is all-equity financed, while Firm L is both debt- and equity-financed. The following table gives some relevant data on the two firms:

	Firm U	Firm L
Annual expected future cash flow	$5 M	$5 M
Cost of equity (rE)	15%	16%
Market value of debt (D)	0	$15 M
Cost of debt (rD)	N/A	12%
Market value of equity (E)	?	?
Market value of the firm (V)	?	?
Weighted average cost of capital (WACC)	?	?

Questions

1. What are the equity values of U and L? What are the total firm values of U and L?
2. What are the WACCs for U and L?
3. Suppose that an investor owns 10% of the stock of firm L, and assume that they can lend and borrow at the same interest rate as firm L, that is, at 12% (recall the assumption of perfect markets). Further, assume that whatever financial transaction the investor undertakes, they want to put themselves in a leveraged position that is similar to what firm L’s managers have already done on behalf of the investor. Is there an arbitrage opportunity here? Describe (very simply and briefly) how to undertake the arbitrage transaction to take advantage of the opportunity.
4. If others in the market could do the same thing, what would happen to the values of the two firms? What conclusions can, therefore, be drawn?

Answer 1

a & b ]		Firm U	Firm L
	Annual expected future cash flow	$                   5.00	$              5.00
	Cost of equity (rE)	15.00%	16.00%
	Market value of debt (D)	$                       -	$            15.00
	Cost of debt (rD)	N/A	12.00%
	Market value of equity (E)	$                33.33	$            20.00
	Market value of the firm (V)	$                33.33	$            35.00
	Weighted average cost of capital (WACC)	15.00%	14.29%
c]	Value of existing holdings = 10% of equity of L =		$              2.00
	Return = (5-15*12%)*10% =		$              0.32
	Debt/Value		42.86%
	10% of equity of Firm U = 33.33*10% =	$                   3.33
	Debt in investment to maintain 42.86% debt = 3.33*42.86% =	$                   1.43
	Equity = 3.33-1.43 =	$                   1.90
	Total income = 5*10% =	$                   0.50
	Less: Cost of debt = 1.43*12% =	$                   0.17
	Net income for investment	$                   0.33
	Return = 0.33/1.90 =	17.24%
	The MM theory argues that both firms should have the same value. If not, it would
	be profitable for an investor to shift from the higher valued firm to the lower valued
	firm and increase his rate of return.
	In the given case, Firm L has higher value. Hence, an investor could sell his investment
	in that firm, which gives him a return of 16% and shift to Firm U. As firm U has no debt
	the investor would borrow debt to the extent of 42.83% of his investment at the
	rate of 12% [called home made leverage] and buy 10% of equity of Firm U.
	Here, he has to invest $3.3m as 10% of equity. For this he will borrow $1.43m at 12%,
	the balance being his equity.
	For the investment of 3.33, he will get 5*10% = $0.50m as his share of NI of firm U.
	Out of this he will pay the interest on debt equal to 1.43*12% = $0.17m. The balance
	of 0.50-00.17 = $0.33 is the return on his investment [own equity] of $1.90. Hence,
	his return would be 0.33/1.90 = 17.24%. Thus, return increases from 16% [in firm L) to
	17.24% [in firm U]. This is because of homemade leverage.
d]	As more and more investors would shift their investment form L to U, the supply of
	share of L would increase and the demand of shares of U would increase. As a result
	the price of shares of L will decrease and the price of shares of U would increase, till
	the value of the two firms become equal. At this point arbitrage would not be
	possible and the value of the two firms will become equal-the equilibrium state.