Answer:
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
