Question

Steinberg Corporation and Dietrich Corporation are identical firms expect 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 60 percent for the next year, and the probability of a recession is 40 percent. If the expansion continues, each firm will generate earnings before interest and taxes (EBIT) of $4 million. If a recession occurs, each firm will generate earnings before interest and taxes (EBIT) of $2 million. Steinberg's debt obligation requires the firm to pay $1 million at the end of the year. Dietrich's debt obligation requiresthe firm to pay $1.2 million at the end of the year. Neither firm pays taxes. Assume a discount rate of 10 percent.

A: What is the value today of Steinberg's debt and equity? What about that for Dietrich's?

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

The total value of a firm’s equity is the discounted expected cash flow to the firm’s stockholders. If the expansion continues, each firm will generate earnings before interest and taxes of $4 million. If there is a recession, each firm will generate earnings before interest and taxes of only $2 million.

Steinberg's debt obligation is $1 million, its stockholders will receive $3 million ($4-$1) in case of expansion and if there is a recession its stockholders will receive $1 million ($2-$1).

Assuming a discount rate of 10%, the market value of Steinberg’s equity is

S(equity) = [.60($3 mil) + .40($1 mil)] / 1.1 = 2 Million

Steinberg’s bondholders will receive $1 MILLION whether there is a recession or a continuation of the expansion. So, the market value of Steinberg’s debt is:

S(Bond)= [.6($1 mil) + .4($1 mil)]/1.1=$909090.9

Similarly for Dietrich, Assuming a discount rate of 10%, the market value of Steinberg’s equity is

D(Equity)= [.60($2.8 mil) + .40($ .8 mil)] / 1.1 = $ 1818182

Dietrich’s bondholders will receive $1.2 MILLION whether there is a recession or a continuation of the expansion. So, the market value of debt is:

D(Bond)= [.60($1.2 mil) + .40($ 1.2mil)] / 1.1= $1090909

Ans a) The value of company is the sum of the value of the firm’s debt and equity. So, the value of Steinberg is:
Value=B+S
Value=$909090.9+$2 Million
Value=$ 2909091

Value of Dietrich= B+S=$1090909+$1818182 = $2909091

Ans b)       Assuming that there is no bankruptcy costs; you should disagree with the CEO’s statement. The risk of bankruptcy per se does not affect a firm’s value. It is the actual costs of bankruptcy that decrease the value of a firm