The expected return on Justus, Inc. stock is 15.63% while the expected return on the market is 12.4%. The beta of Justus's stock is 1.48. What is the risk-free rate of return?
Solution :
As per Capital Asset Pricing Model, Expected return of a stock is calculated using the following formula :
RS = RF + [ β * ( RM - RF ) ]
Where
RS = Expected return on stock ; RF = Risk free rate of return ; β = Beta of the stock ;
RM = Expected return on the market
As per the information given in the question we have
RS = 15.63 % = 0.1563 ; RM = 12.4 % = 0.124 ; β = 1.48
RF = To find ; Let RF be ‘X’
Applying the above values in the formula we have
0.1563 = X + [ 1.48 * ( 0.124 – X) ]
0.1563 = X + 0.183520 – 1.48X
0.1563 = 0.183520 – 0.48X
0.48X = 0.183520 – 0.1563
0.48X = 0.027220
X = 0.027220 / 0.48
X = 0.056708
X = 5.6708 %
Thus the Risk free rate = 5.6708 %
= 5.67 % ( when rounded off to two decimal places )
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