Question

Trade-Off Theory. Smoke and Mirrors currently has EBIT of $25,000 and is all-equity- financed. EBIT is expected to stay at this level indefinitely. The firm pays corporate taxes equal to 21% of taxable income. The discount rate for the firm’s projects is 10%.

a. What is the market value of the firm?

b. Now assume the firm issues $50,000 of debt paying interest of 6% per year, using the proceeds to retire equity. The debt is expected to be permanent. What will happen to the total value of the firm (debt plus equity)?

c. Recompute your answer to (b) under the following assumptions: The debt issue raises the probability of bankruptcy. The firm has a 30% chance of going bankrupt after 3 years. If it does go bankrupt, it will incur bankruptcy costs of $200,000. The discount rate is 10%.

d. Should the firm issue the debt under these new assumptions?

Answer 1

ANSWER:

a)

Calculation of the market value of the firm

Given,

EBIT = $25,000

Corporate tax rate = 21%

Discount rate = 10%

Market value of the firm (V) = EBIT x [1-tax rate]/Discount rate (r)

Market value of the firm  = $25,000 x (1-0.21) / 0.10

Market value of the firm =$197,500.

b)

the firm issues $50,000 of debt paying interest of 6% per year

Increament in the value of the firm = Tax rate x Debt value

Increament in the value of the firm = 0.21 x $50,000

Increament in the value of the firm =$10,500

Therefore, the value of the firm increases by the present value of interest tax sheild which is $ 10,500.

c)

Here, if the chance of bankruptcy is 30% after 3 years which cost the company is $ 200,000

so calculate expected cost of bankruptcy:

The Expected Cost of Bankruptcy = Chance of bankruptcy x bankruptcy cost

The Expected Cost of Bankruptcy =0.30 x $200,000

The Expected Cost of Bankruptcy =$60,000

Now calculate the present value of cost of bankruptcy

present value of cost of bankruptcy = cost of bankruptcy / [discount rate(r)]^3

present value of cost of bankruptcy = $60,000 / (1.10)^3

present value of cost of bankruptcy=$45,079.

d)

as the present value of cost of bankruptcy is higher than the present tax sheild so the firm should not issue the debt.