Question

The Miller-Modigliani Arguments

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: (No Taxes)

                                                                                               

	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

      a. Find all "?" signs.

      b. 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.

      c. 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)

Market value of equity = Net Income of Cash Flows discounted by Cost of Equity

Market Value of the firm = Market Value of Equity + Market Value of Debt

WACC = Cost of Equity * Market Value of Equity /( Market Value of the firm) + cost of Debt * Market Value of Debt/( Market Value of the firm)

	Firm U	Firm L
Cash Flows	$5	$5
Cost of equity	15%	16%
Market value of debt	0	$15
Cost of debt	N/A	12%
Market value of equity	5 / 0.15 = >$ 33.33	5/ 0.16 =>$  31.25
Market value of firm	33.33 + 0 => $ 33.33	31.25 + 15 => $46.25
Weighted Average Cost of Capital(WACC)	15% * 33.33 / 33.33 + 0= > 15%	16% * 31.25/46.25 + 12% * 15/46.25 = 10.81 + 3.89 =>14.70%

B)

Your stake in firm L =10%

Sell your stake in Firm L = 10% of 31.25 = > $ 3.125

Borrowing on your personal account an amount equal to your share if firm L's debt at  6% = 10% of 15 = $ 1.5

Buying 10 % shares of Unlevered firm U = 10% * 33.33 = > 3.33

You have 3.125 + 1.5 = 4.625 (by selling Firms L share and borrowed funds) with you and your investment in firm L is 3.33 you have surplus cash of 4.625 - 3.33 => 1.295

invest this in firm U

Return from investment = 3.33 * 15% = 0.495

You pay interest on your borrowed funds at 16% => 1.5 * 16% = 0.24

Thus your net return = Return from investment in firm U - Cost of borrowed funds

= 0.495 - 0.24 => 0.255

There exist an arbitrage opportunity

C)

And as per MM the value of levered and unlevered firms are equal (arbitrage ensurers it).Thus the increasing demand for unlevered firms share will increase their market price and declining demand of levered firms share will decrease its market price.U Ultimately the market values of two firms will reach equilibrium and henceforth arbitrage will not be beneficial.