All the questions below are linked together with some explanation. I need a step by step explaination. 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.

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.