I need a step by step explanation for this question.

Question:

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

Answer:

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.

For reference:

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.