Steinberg Corporation and Dietrich Corporation are identical companies 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 company will generate earnings before interest and taxes (EBIT) of $4 million. If a recession occurs, each company will generate earnings before interest and taxes (EBIT) of $1.4 million. Steinberg's debt obligation requires the company to pay $940,000 at the end of the year. Dietrich's debt obligation requires the company to pay $1.5 million at the end of the year. Neither company pays taxes. Assume a discount rate of 15 percent.

Explanation:

he 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 million, but the firm is also obligated to pay interest of $940,000. If a recession occurs, Steinberg will have an EBIT of $1,400,000 but still have to pay $1,500,000 in interest to bondholders. Therefore, assuming a discount rate of 15%, the market value of Steinberg’s equity will be:

ESteinberg = [(.70)($4,000,000 - $940,000) + (.30)($1,400,000 - $940,000)]/1.15

ESteinberg = $1,982,609

Steinberg’s bondholders will receive $940,000 whether there is a recession or expansion in the economy. So, the market value of Steinberg’s debt is: DSteinberg = {(.70)[$940,000] + (.3)[$940,000]}/1.15 = $817,391

Since Dietrich owes its bondholders $1.5 million at the end of the year, its shareholders will receive $ million [i.e., $4 million - $1.5 million] in the event of expansion. If there is a recession, its shareholders receive nothing because the EBIT of $1.4 million is less than the interest payment of $1.5 million. Therefore, the market value of Dietrich’s equity will be: EDeitrich = {(.70)[$1.5 million} + (.3)[0]}/1.15 = $913,043 Dietrich’s bondholders will receive $1.5 million if the expansion continues, but only $1.4million if there is a recession [i.e., they take a $100,000 loss].

DDeitrich = { (.70)[$1.5 million] + (.3)[$1.4million]}/1.15 = $1,278,261

The value of Steinberg is: VSteinberg = D + E = $2,800,000

The value of Deitrich is: VDeitrich = D + E = $834,783 + $695,652 = $2,191,304

Agreed

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