Question

Prove MM proposition 1 without tax with an Example

Answer 1

The MM proposition 1 say that the value of the firm is independent of the percentage of debt or equity in its capital structure.The main idea of the MM theory is that the capital structure of a company does not affect its overall value.

Proof:

Consider a company with no debt(Company G).Company G has a required rate of return of 12.5% and 100 shares outstanding.Suppose that one of three things could happen next year.With probability 1/2,everything will be normal.With probability 1/8,there will be a recession.With probability 3/8 there will be a boom.Possible outcomes for company G

	Recession	Normal	Boom
Operating Income($)	100	250	300
EPS($)	1	2.5	3

Expected EPS=1/8*1+1/2*2.5+3/8*3

=$2.5

Per share value of company with this expeccted EPS=Expected EPS/Required rate of return

=2.5/12.5%=$20

Total value of company G(VG)=100*20=$2000

Suppose Company H is identical to company G in every way.Company H decides that it wants to try to increase value by issuing $1000 of debt and using the proceeds to repurchase shares.Suppose Company H can issue debt at the risk free rate of 10%(like company G its earning are stable).With $1000,company H is able to purchase 50 shares,so there are 50 shares are outstanding.

Possible outcome for company H:

	Recession	Normal	Boom
Operating Income($)	100	250	300
Interest($)	100	100	100
Equity earnings($)	0	150	200
EPS($)	0	3	4

We want to show that the value of comapny H remains exactly the same as before the repurchase,namely exactly the same as that of company G.First suppose that the value of company H under the new capital structure increases.That is VH>$2000

I will show that this is impossible by constructing two strategies with equal future cash flows but different initial outlays;

Strategy 1:Buy one shares in company H

Cost:(VH-Value of debt)/no. of shares>$1000/$50=$20

Cash flows: Recession Normal Boom

Dividends on H 0 3 4

Strategy 2;Buy two shares in company G and borrows $20 at the risk free rate to be paid back in perpetuity.

Cost of strategy2:$40 -$20=$20

Cash flows:

Recession Normal Boom

Dividends on G    2 5 6

Pay back loan -2 -2 -2

Total 0 3 4

These two strategies cannot exist in equilibrium,because all investors would choose the cheaper strategy and no investor would choose the more expensive strategy.Therefore no investor would buy shares in company H and its value would fall until it equaled $2000.Changing capital structures cannot increase value.