The market expected return is 14% with a standard deviation of 18%.The risk-free rate is 6%.Security XYZ has just paid a dividend of $1 and has a current price of $13.95.What is the beta of Security XYZ if its dividend is expected to grow at 6% per year indefinitely?
A)0.85
B)0.90
C)0.95
D)1.05

Question

Quizplus · Accepted Answer

First, we need to calculate the expected return of Security XYZ using the dividend discount model:

Expected Return = (Next Year's Dividend / Current Price) + Growth Rate
Next Year's Dividend = Current Dividend * (1 + Growth Rate) = $1 * 1.06 = $1.06
Expected Return = ($1.06 / $13.95) + 0.06 = 0.1369 or 13.69%

Next, we need to calculate the beta of Security XYZ using the CAPM equation:

Expected Return = Risk-Free Rate + Beta * (Market Expected Return - Risk-Free Rate)
0.1369 = 0.06 + Beta * (0.14 - 0.06)
Beta = (0.1369 - 0.06) / (0.14 - 0.06) = 0.95

Therefore, the answer is (C) 0.95.

The Market Expected Return Is 14% with a Standard Deviation