Question

The Company expects its dividends to be $85,000 every other year forever, with the first payment occurring two years from today. The firm can borrow at an EAR of 11%, currently has no debt, and has an effective annual cost of equity of 18%. The corporate tax rate is 35%. Assume tax credits for losses and no financial distress costs.

(a) Calculate the value of the firm. Explain the answer.

(b) What will firm value be if it borrows $60,000 in permanent debt with annual coupon payments and uses the proceeds to repurchase its shares?

Answer 1

a) Company pays dividends every other year. This implies that company pays dividends every two years with first payment in year 2 or at end of year 2.

So let the dividend in year 2 = D2 = $85000

Effective annual cost of equity = 18%

Effective two year cost of equity = (1+ Effective annual cost of equity)² - 1 = (1+18%)² - 1 = (1.18)² - 1 = 1.3924 - 1 = 0.3924 = 39.24%

Considering time period two years as one period, we get

Constant periodic cash flow =Constant Dividend paid every other year = 85000

Constant periodic cost of of equity = Effective two year cost of equity = 39.24%

Since the company is all equity firm, so value of firm = Value of equity of firm

We know that value of equity is equal to present value of future cash flows. In this question dividends form cash flows.So

Value of equity = Present value of dividends = Present value of constant period cash flow

Since these periodic cash flow form an perpetuity as they occur every period or every two years,

So we know that Present value of perpetuity = Cash flow / discount rate

We get Value of firm = Value of equity = Present value of perpetual every two year dividends = Constant Dividend paid every other year / Effective two year cost of equity = Constant periodic cash flow / Constant periodic cost of of equity = 85000 / 39.24% = 216615.6983

So value of firm = $216615.6983

b) After firm borrows it becomes a levered firm with Debt = $60000

Annual Interest tax shield = Effective annual interest rate x debt x tax rate = 11% x 60000 x 35% = $2310

Value of unlevered firm = Value of all equity firm = 216615.6983                    (as calculated in part a )

Now we know that Value of levered firm = Value of unlevered firm + Present value of interest tax shield - Cost of financial distress

Since debt is permanent ;and interest rate and tax rate remain constant, so interest tax shield forms a perpetuity

Present value of interest tax shield = Interest tax shield / Effective annual interest rate or cost of debt = 2310 / 11% = 21000

So Value of levered firm = Value of unlevered firm + Present value of interest tax shield - Cost of financial distress = 216615.6983 + 21000 - 0 = $237615.6983

Hence Value of firm = $237615.6983