Question

1. Discuss Modigliani and Miller's Propositions I and II in a perfect world without taxes nor distress costs. List the basic assumptions, results, and intuition of the model. Based on this model, if the original unlevered firm value is $100 million and the CFO is planning to carry out a leveraged recapitalization to a debt equity ratio of 1:1. What’s the levered firm value? If the unlevered equity requires 10% annual return and the debt requires a 6% of annual return, what’s the required return for the levered equity?

Answer 1

Modigliani and Miller's (M&M's )Propositions states that capital structure i.e the level of equity and debt in the company doesn't affect the total value of the company .Whether the company is leveraged or un- leveraged the value of the company doesn't get affected .

Some assumptions of this theory are

• There are no taxes
• Markets are efficient
• There are no transaction costs
• Bankruptcy cost is zero
• Companies borrow at same cost as of the investor
• There is also no tax on corporate dividend

So M&M'S

I Proposition was that capital structure doesn't affect the value of the company . The priority is same for both equity and debt holders.The reasoning behind this is value of the firm is dependent on the present value of future cash flows of the firm so capital structure couldn't affect it .

V_L = V_u

_{Where ,}

V_L = Value of leveraged firm (debt + Equity )

V_U = Value of unleveraged firm (only equity )

II Proposition was that the leverage was directly proportional to cost of equity , and with rise in leverage the default probability will also rise and equityholders should be compensated with higher cost of equity as they assume more risk .

r_E= r_A + D/E ( r_A- r_D )

where r_E = Cost of levered equity

r_A = Cost of unlevered equity

r_D = Cost of debt

D/E = Debt-to-equity ratio

Now using first proposition we can say that Value of unleveraged firm is equal value of leveraged firm

So if Unlevered Firm was equal $100 Million

The New Leveraged Firm will also Equal $100 Million

Now Using Second Proposition we can find the increased required return for the leveraged equity

r_E= r_A + D/E ( r_A- r_D )

So here

D/E =1:1

r_a =10%

r_d = 6%

Now Using this is equation we get

r_E = 10 + 1(10-6)

r_E  = 14%

So after using leverage the cost of equity has risen from 10% to 14%