I need a step by step explanation for this question.

Question:

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.

Answer:

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.

For reference:

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.

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.