Steinberg Corporation and Dietrich Corporation are identical firms except that D

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 $4.6 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 $1,000,000 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. What are the current market values of Steinberg's equity and debt? What are the current market values of Dietrich's equity and debt? 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?

Explanation / Answer

The total value of a firm’s equity is the discounted expected cash flow to the firm’s shareholders. If the expansion [in the economy] continues, each firm will generate EBIT of $4.6 million, but the firm is also obligated to pay interest of$1.4million. If a recession occurs, Steinberg will have an EBIT of $1.0million but still have to pay $1.5 in interest to bond holders. Therefore, assuming a discount rate of 12%, the market value of Steinberg’s equity will be:

ESteinberg = [(0.70)($4,600,000 - $1000,000) + (0.3)($1,400,000 - $1000,000)]/1.12

ESteinberg =2520000+120000/1.12= $2357143

Steinberg’s bondholders will receive $750,000 whether there is a recession orexpansion in the economy. So, the market value of Steinberg’s debt is:

DSteinberg = {(0.70)[$1000,000] + (0.3)[$1000,000]}/1.12 = $892858

Since Dietrich owes its bondholders $1.5million at the end of the year, its shareholders will receive $3.1 million [i.e., $4.6million - $1.5 million] in the event of expansion. If there is a recession, its shareholders receive nothing because the EBIT of $1400,000 is more than the interest payment of $1 million. Therefore, the market value of Dietrich’s equity will be:

EDeitrich = {(0.70)[$1 million} + (0.3)[0]}/1.12= $625000

Dietrich’s bondholders will receive $1.5 million if the expansion continues, and$1.4 if there is a recession [i.e., they take a $100,000 loss].

DDeitrich = { (.70)[$1.5 million] + (.3)[$1.400,000]}/1.12 = 1050000+420000/1.12=$1312500

Requirement 2:

The value of Steinberg

VSteinberg = D + E = $892858 + $2357143 = $1937500

The value of Deitrich is:

VDeitrich = D + E = $1312500 + $625000 = $1,937500

The two firm’s have the same value. The risk of bankruptcy per se does not affect a firm’s value. It is the actual costs of bankruptcy that decreases firm value.

Note: this problem assumes that there are no bankruptcy costs.

Requirement 2:

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