A common stock is expected to generate an end-of-period dividend of $5 and an end-of-period price of $62.If this security has a beta coefficient of 1.3,the risk-free interest rate is 10%,and the expected return on the market portfolio is 19%,then what is the value of this security today?
A) $55.50
B) $59.98
C) $55.05
D) $56.30

Question

Quizplus · Accepted Answer

The value of the security today can be calculated using the dividend discount model (DDM) for a one-period model, which is $ P_0 = \frac{D_1 + P_1}{1 + k} $, where $P_0$ is the price of the stock today, $D_1$ is the dividend at the end of the period, $P_1$ is the price of the stock at the end of the period, and $k$ is the required rate of return. The required rate of return can be calculated using the Capital Asset Pricing Model (CAPM), which is $ k = r_f + \beta (r_m - r_f) $, where $r_f$ is the risk-free rate, $\beta$ is the beta coefficient, and $r_m$ is the expected return on the market portfolio. Substituting the given values:- $r_f = 10\%$- $\beta = 1.3$- $r_m = 19\%$The required rate of return ($k$) is $10\% + 1.3(19\% - 10\%) = 10\% + 1.3(9\%) = 10\% + 11.7\% = 21.7\%$.Now, substituting into the DDM:$ P_0 = \frac{5 + 62}{1 + 0.217} = \frac{67}{1.217} \approx 55.05 $.Therefore, the value of the security today is approximately $55.05.

A Common Stock Is Expected to Generate an End-Of-Period Dividend