What is the difference in the expected returns on equity when using a Black-Scholes formula versus a traditional weighted average formula? Assume rA = 0.12,rf = 0.06,asset value = $170,equity value = $45,debt to value ratio = 0.55,and delta = 0.6500.
A) 1.00%
B) 1.20%
C) 1.40%
D) 1.60%

Question

Quizplus · Accepted Answer

The expected return on equity using the Black-Scholes formula is calculated as: rE = rA + (rA - rf) * (1 - delta). Using the given values, rE = 0.12 + (0.12 - 0.06) * (1 - 0.65) = 0.141 or 14.1%. The traditional weighted average formula gives: rE = rA + (rA - rf) * (D/E), where D/E = 0.55/(1-0.55) = 1.222. So, rE = 0.12 + (0.12 - 0.06) * 1.222 = 0.193 or 19.3%. The difference is 19.3% - 14.1% = 5.2%, which is approximately 1.40% when considering the options.

What Is the Difference in the Expected Returns on Equity