All the questions below are linked together with some explanation. I need a step by step explaination from question 4 to 7. Question 1 to 3 are included for your reference so that you can explain 4 -7 better. I do not understand what is S in question 4? It seemed like the answer is incomplete. Why did we subtract 600 by 15? How was it determined firm 4 (question 4) is worth more than firm 2 (question 2)?

Questions:

1 Let EBIT=600. The beta is 2. We expect that the market will earn .14 and the risk free rate is 3%.Find the value of the firm with no debt and no taxes.

Using CAPM, r(su)=.03+2*(.14-.03)=.25. V=600/.25=2400.

2 If the firm in example 4-1 has to pay 30% in taxes, what would the value be?

V(u)=(600*(1-.3))/.25=1680. Comparing a firm with taxes to the same firm with no taxes shows how the decrease in FCF lowers value, but this is not really the point of MM. NOI falls, meaning less money is going to the financial markets.

3 Take the firm in 4-1. Let the firm borrow 500 of .03 perpetual debt using the proceeds to buy back stock. Find S, D, and V. Remember, there are no taxes.

To find S we need the new firm value from Proposition I. V(L)=2400 + 0*500=2400. To find S, subtract debt from firm value, 2400-500=1900. The firm in example one and example three are valued the same. Debt does not matter because there is no tax effect from the debt.

4 Add 500 in debt to the firm in 4-2, the one that has to pay taxes. Find S and V. Please explain the 2nd (S) part in detail.

V(L)=1680 + .3*500=1830. The firm in example two has to pay .3*600=180 (EBIT*tax rate) in taxes per year, forever. The firm in 4 only has to pay .3*(600-15)=175.5 in taxes. The 15 is the interest per year (debt times rd, which is rf because of the assumption). The interest tax deduction causes firm 4 to be worth more than firm 2.

5 Find the new cost of equity and the WACC for the firm in example three.

R(sL)=.25+(500/1900)*(1)*(.25-.03)=.3079.

WACC=(500/2400)*.03 + (1900/2400)*.3079=.00625+.2437=.25. The firms in examples one and three have the same WACC and the same FCF, so they must have the same value.

6 Find the r(sL) for the firm in example 4.

R(sL)=.25+(500/1330)*(1-.3)*(.25-.03)=.3079.

WACC=(500/1830)*.03*(1-.3)+ (1330/1830)*.3079 = .00574 + .22377 = .2295.

The firm in example 4 is worth more than the firm in example two because tax deductibilty of interest makes the wacc lower and firm value higher. This means firms can increase value by increasing the wd.

If r(s) from Proposition II is set equal to the equity return given by CAPM, the Hamada beta can be calculated, B(L)=B(u)[1+(1-t)*(D/S)]. This version of beta is useful for estimating the effect a change in capital structure might have on the cost of equity.

7 The B(u) for the firm in example 1 was 2. Find the new beta when we add debt and taxes like in example 4.

B(L) = 2*[1+.7*(500/1330)]=2.5263. We should be able to plug this into the CAPM to get the same r(sL) we got in example six. .03+2.5263*(.14-.03)=.3079.