Given:
General pharmacy’s stock has a beta of 1.8 and an expected return of 14%,
Sicoras corp.’s stock has a beta of 1.5 and an expected return of 16.2%.
Let Rf stand for risk free rate.
Let Rm stand for expected market return.
General Pharmacy: 14% = Rf + 1.8(Rm-Rf)
Sicoras Corp.: 16.2% = Rf + 1.5(Rm-Rf)
0.14 = Rf + 1.8Rm - 1.8Rf
0.14 = Rf - 1.8Rf + 1.8Rm
0.14 = -0.8Rf + 1.8Rm
0.14 + 0.8Rf = 1.8Rm
Rm = 0.14/1.8 + 0.8Rf/1.8
Rm = 0.078 + 0.444Rf
0.162 = Rf + 1.5(Rm-Rf)
0.162 = Rf + 1.5[(0.078+0.444Rf) - Rf]
0.162 = Rf + 0.117 + 0.666Rf - 1.5Rf
0.162 - 0.117 = Rf + 0.666Rf - 1.5Rf
0.045 = 0.166Rf
0.045/0.166 = Rf
0.271 = Rf
Rm = 0.078 + 0.444Rf
Rm = 0.078 + 0.444(0.271)
Rm = 0.078 + 0.120
Rm = 0.198
Rf = 27.1% ; Rm = 19.8%
The risk free rate is 27.1% and the expected market return is 19.8%.
To check, simply substitute the value of Rf and Rm in the above equation.