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MODIGLIANI-MILLER PROPOSITIONS

M-M Proposition 1: In competitive, transaction costless, information efficient markets, with no taxes, the market value of the firm (i.e., market value of all of its securities) is independent of the firm’s capital structure. That is, [pic] = [pic] (see definition below) [Brealey, Myers and Allen, Chapter 17]

The proof of this proposition is based on the following arbitrage property of perfect markets.

Arbitrage Property: Two identical assets must have the same market price. Two assets are identical if either can be converted into the other.

Logic of M-M Proof: Let firm U be an unlevered firm and let firm L be an identical firm if levered (or be the same firm if levered); U and L differ only in that
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That is,

P [pic] ( P [pic]( P [pic],

which implies that:

[pic] ( [pic] + [pic] =[pic] (1)

Now we will show that we can convert L into U. Compare two strategies: [1(] Buy P percent of firm U; [2(] Buy P percent of the shares of firm L, and buy percent P of the debt of firm L. Exhibit 2 shows that the incomes of the two strategies are identical.

Exhibit 2. Convert L into U [using [2(])
|Strategy |Net Investment of the strategy |Income |
|[1(] Buy percent P of firm U equity |P [pic] |P Profit |
|[2(] Buy percent P of firm L debt and |P [pic] + P [pic]= P [pic] |P [Profit ( Interest] + P Interest |
|percent P of firm L equity | |= P Profit |

Since we can use strategy [2(] to create the stock under strategy [1(], strategy [2(] must be at least as good as strategy [1(], and therefore we must be willing to pay at least as much for strategy [2(] as for strategy [2(]. That is,

P [pic] ( P [pic]

which implies

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