Question

1. You wish to start a small side business, competitors in this industry have the following costs of capital:

Firm 1: re=15% rd=5% d/e=.5

Firm 2: re=18% rd = 5.2% d/e=.68

A. What will be a good estimate of your unlevered cost of capital for your new business?

B. If your firm will have cashflows of 3 million next year and it will grow by 2% per year what is the unlevered value of your firm? (online fill in 1)

C. If your tax rate is 35% and you wish to have a constant interest coverage ratio of 0.2, what will the levered value of your firm be?

Answer 1

The unlevered cost of equity can be found out as:

Firm 1: rE = rU + (rU - rD)* D/E

where rE is levered cost of equity, rU is unlevered cost of equity, rD is cost of debt, D is debt , E is equity

rE = rU + (rU - rD)* D/E

0.15 = rU + (rU-0.05)*0.5

0.15= rU + 0.5rU - 0.5*0.05

rU = 0.175 / 1.5 = 0.11667 = 11.67%

Firm 2:

rE = rU + (rU - rD)* D/E

0.18 = rU + (rU-0.052)*0.68

0.18= rU + 0.5rU - 0.052*0.68

rU = 0.21536 / 1.5 = 0.14357 = 14.36%

B) Unlevered Value of firm

Vu = FCF / (rU-g)

For firm 1: Vu = FCF / (rU-g) = 3 / (0.1167-0.02) = 31.03 million

For firm 2: Vu = FCF / (rU-g) = 3 / (0.14357-0.02) = 24.28 million

C) VL= (1+t*K)*Vu where VL is levered value, Vu is unlevered value, t is tax rate, K is interest coverage ratio

Firm 1:

VL= (1+t*K)*Vu = (1+0.35*0.2)*31.03 = 33.21 million

Firm 2:

VL= (1+t*K)*Vu = (1+0.35*0.2)*24.28= 25.98 million