A stock generates a perpetual cash flow of $6 per share, per year. The market index has an expected return of 10% and the risk free rate is 4%. If the stock's listed beta is 1.0 and I believe the true beta is 1.2, how much is the stock overpriced?
A) $13.58
B) $15.88
C) $33.20
D) $44.12

Question

Quizplus · Accepted Answer

The correct price of the stock can be calculated using the Capital Asset Pricing Model (CAPM), which gives us the expected return based on the risk-free rate, the market return, and the beta of the stock. The formula for the expected return using CAPM is: Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate). Given the true beta is 1.2, the expected return would be 4% + 1.2 * (10% - 4%) = 11.2%. The price of the stock, assuming it pays a perpetual cash flow, can be calculated using the formula Price = Dividend / (Discount Rate - Growth Rate). Assuming no growth (Growth Rate = 0), the price would be $6 / (11.2% - 0) = $53.57. If the stock is priced assuming a beta of 1.0, the expected return would be 4% + 1.0 * (10% - 4%) = 10%, and the price would be $6 / (10% - 0) = $60. The stock is overpriced by $60 - $53.57 = $6.43, but since this option is not available, it seems there was a mistake in the calculation or interpretation of the provided options. The correct approach, however, involves recalculating based on the given information and methodology, which might have led to a misinterpretation of the final step or the options provided.

A Stock Generates a Perpetual Cash Flow of $6 Per