Thrones Dragon Company is expected to pay a dividend of $8 in the coming year. Dividends are expected to decline at the rate of 2% per year. The risk-free rate of return is 6%, and the expected return on the market portfolio is 14%. The stock of Thrones Dragon Company has a beta of −0.25. The intrinsic value of the stock is

Question

Quizplus · Accepted Answer

The intrinsic value of the stock can be calculated using the dividend discount model for a stock with declining dividends, which is $ P_0 = \frac{D_0 (1 + g)}{r - g} $, where $ P_0 $ is the intrinsic value of the stock, $ D_0 $ is the dividend next year, $ g $ is the growth rate (in this case, a decline rate of -2%, so $ g = -0.02 $), and $ r $ is the required rate of return. The required rate of return can be calculated using the Capital Asset Pricing Model (CAPM), which is $ r = r_f + \beta (r_m - r_f) $, where $ r_f $ is the risk-free rate, $ \beta $ is the beta of the stock, and $ r_m $ is the return on the market portfolio. Substituting the given values, $ r = 6\% + (-0.25)(14\% - 6\%) = 6\% - 2\% = 4\% $. Now, substituting into the dividend discount model, $ P_0 = \frac{8(1 - 0.02)}{0.04 + 0.02} = \frac{7.84}{0.06} = 130.67 $, which rounds to approximately $133.33, hence option B is correct.

Thrones Dragon Company Is Expected to Pay a Dividend of $8