Question

Steinberg Corporation and Dietrich Corporation are identical firms except that Dietrich is more levered. Both companies will remain in business for one more year. The companies' economists agree that the probability of the continuation of the current expansion is 70 percent for the next year and the probability of a recession is 30 percent. If the expansion continues, each firm will generate earnings before interest and taxes (EBIT) of $3 million. If a recession occurs, each firm will generate earnings before interest and taxes (EBIT) of $1.4 million. Steinberg's debt obligation requires the firm to pay $930,000 at the end of the year. Dietrich's debt obligation requires the firm to pay $1.5 million at the end of the year. Neither firm pays taxes. Assume a discount rate of 12 percent.

  

a-1.	What is the value today of Steinberg's debt and equity? (Do not round intermediate calculations and enter your answers in dollars, not millions of dollars, rounded to the nearest whole number, e.g., 1,234,567.)
a-2.	What is the value today of Dietrich's debt and equity? (Do not round intermediate calculations and enter your answers in dollars, not millions of dollars, rounded to the nearest whole number, e.g., 1,234,567.)
b.	Steinberg’s CEO recently stated that Steinberg’s value should be higher than Dietrich’s because the firm has less debt and therefore less bankruptcy risk. Do you agree or disagree with this statement?

       
        

Answer 1

(a)
We know that the total value of a firm's equity is equal to the discounted expected cash flow to the firm's shareholders.

If the expansion of the economy continues both the Steinberg Corporation and Dietrich Corporation will generate an EBIT of $3,000,000. However, the debt obligation of the Steinberg Corporation is  $930,000 at the end of the year. Again, in case of a recession, the EBIT of both the the firms will be $1,400,000, but Steinberg still have to pay $930,000 as an interest to its debtholders at the end of the year.

The discount rate given 12% or 0.12.

Therefore the market value of the Steinberg Corporation's Equity :-

Value of Equity = Expected value / (1+r)

where. r = discount rate = 01.2

The probabilty of expansion is 0.70 & that of recession is 0.30.

Hence, market value of the Steinberg Corporation's Equity is :-

E_Steinberg = [0.70 * ($3,000,000 - $930,000) + 0.30 * ($1,400,000 - $930,000)] / (1+ 0.12)

= ($1,449,000 + $141,000) / 1.12

= $1,590,000 / 1.12

= $1,419,643

Steinberg's debtholders will receive $930,000 at the end of the year irrespective of expansion or recession in the economy. Thus the market value of the Steinberg's debt is given by :-

Debt value = Debt obligation / (1 + discount rate)

Hence, Steinberg's debt value :-

D_Steinberg = (0.70 * $930,000 + 0.30 * $930,000) / 1.12

= $830,357

Thus the market value of Steinberg's equity = $1,419,643.

& the market value of Steinberg's debt = $830,357.

Dietrich's EBIT in case of expansion is $3,000,000 & in recession is $1,400,000. Dietrich's debt obligation in both expansion & recession is $1,500,000 at the end of the year.

Hence, in the event of expansion, the Dietrich's shareholders will receive ($3,000,000 - $1,500,000) = $1,500,000. But in the event of recession the Dietrich's shareholders will receive nothing since the EBIT is $1,400,000 which is less than the debt obligation of $1,500,000.

Therefore, the market value of Dietrich's equity is given by :-

Value of Equity = Expected value / (1+r)

where, r = 0.12

Or, E_Dietrich = [0.70 * ($3,000,000 - $1,500,000) + 0.30 * ($0)] / (1+0.12)

= $1,050,000 / 1.12

= $937,500

Dietrich's debtholders will receive $1,500,000 in case of expansion but in the event of recession they will only receive $1,400,000 (i.e. a loss of $100,000 to the debtholders).

Hence, the market value of the Dietrich's debtholders is given by :-

Debt value = Debt obligation / (1 + discount rate)

Or, D_Dietrich = [0.70 * $1,500,000 + 0.30 * $1,400,000] / (1 + 0.12)

= $1,470,000 /1.12

= $1,312,500

Thus the market value of Dietrich's equity = $937,500

& the market value of Dietrich's debt = $1,312,500.

(b) The value of the Steinberg Corporation is :-

Value of firm = Equity Value + Debt Value

V_Steinberg = ($1,419,643 + $830,357) = $2,250,000

The value of the Dietrich Corporation is :-

V_Dietrich = ($937,500 + $1,312,500) = $2,250,000

Thus we can see that both the firm values are same. We know that the risk of bankruptcy doesn't affect a firm's value, it is the actual bankruptcy costs that reduce a firm's value. In this problem it is assumed that there are no bnakruptcy costs. Hence, we disagree with the Steinberg’s CEO's statement.