Question

ABCCo Inc. is currently an all-equity firm. Because of strong investment opportunities, it needs to raise $5,500,000 in additional funds. By investing in these opportunities, it expects future earnings to be a constant $1,000,000 per year. The firm’s unlevered cost of equity is 13%, and its before tax cost of debt is 7.5%.

If there are no corporate taxes,

A) What is the value of ABCCo if it issues new equity to raise the funds?

B) What is the value of ABCCo if it issues debt to raise the funds?

C) If ABCCo issues debt, what will the new cost of equity be?

D) If ABCCo issues debt, what will the new weighted average cost of capital be?

If corporate taxes are 35%,

E) What is the value of ABCCo if it issues new equity to raise the funds?

F) What is the value of ABCCo if it issues debt to raise the funds?

G) If ABCCo issues debt, what will the new cost of equity be?

H) If ABCCo issues debt, what will the new weighted average cost of capital be?

Answer 1

If there are no corporate taxes

A) Cost of equity = 13% or 0.13

Earnings = 1,000,000

Value of firm = Earnings/cost of equity = 1000000/0.13 = 7,692,308

B) Cost of debt = 7.5%

Interest = 5,500,000 x 7.5% = 412,500

Earnings after interest = 587,500

Cost of equity of levered firm = cost of equity of unleveref firm + ( cost of equity of unleveref frim-cost of debt) x debt/equity

= 0.13 + (0.13-0.075) x 5,500,000/2,192,308

= 0.13 + 0.13798 = 0.26798

Value of equity = 587,500/0.26798 = 2,192,308

Value of firm = Value of equity + Debt = 2,192,308 + 5,500,000 = 7,692,308

Alternatively,

The value of a levered firm is same as an unlevered firm if there are no tax benefits

Earnings before Interest = 1,000,000

Overall cost of capital =0.13

Value of firm = 1,000,000/0.13 = 7,692,308

Value of equity = 7,692,308-5,500,000 = 2,192,208

C) New cost of equity = 26.799% as calculated above (or) Earnings after interest/ New Equity value =587,500/2,192,208 =0.26799

D) New Weighted average cost of capital = Equity value/Total value x cost of equity + Debt/Total Value x cost of debt

= 2,192308/7,692,308 x 0.26799 + 5,500,000/7,692,308 x 0.075

= 0.07638 + 0.0536= 0.13

If Corporate taxes are 35%

E) Cost of equity = 0.13

Earnings after tax = 1,000,000-350,000=650,000

Value of Firm = Earnings after tax / Cost of equity= 650,000/0.13 = 5,000,000

F) Value of levered firm = Value of unlevered firm + Debt x tax rate

= 5,000,000 + 5,500,000 x 35% = 6,925,000

G) New Cost of Equity = Earnings after tax/Value of Equity

= 381875/(6,925,000-5,500,000) = 26.7982%

Earnings =1000000

Interest = 412500

Earnings after int = 587,500

Tax =205625

Earnings after tax =381,875   

H) New weighted average cost of capital = 0.267982 x 1425000/6925000 + 0.075 x (1-0.35) x 5500000/6925000

= 0.05514 + 0.03872 = 0.09386 or 9.386%