I need a step by step explanation for this question.

Question:

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

Answer:

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.

For reference:

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.