Stock Y has a beta of 1.0 and an expected return of 12.4 percent. Stock Z has a beta of 6 and an expected return of 8.2 percent.
What would the risk-free rate have to be for the two stocks to be correctly priced? (Do
not round intermediate calculations and enter your answer as a percent rounded to 2
decimal places, e. g., 32.16.)

Risk free rate = 1.9%

Explanation:

The Capital Asset Pricing Model allows for the calculation of the required return using the market return, beta and risk free rate.

Required return = Risk free rate + Beta * ( Market return - Risk free rate)

First find the market rate. Stock Y is uniquely positioned to help with that:

12.4% = Risk free rate + 1.0 * (Market return - Risk free rate)  

12.4% = rf + Market return - rf  

Market return = 12.4%

Apply this to the formula using Stock Z:

8.2% = rf + 0.6 * (12.4% - rf)  

8.2% = rf + 7.44% - 0.6rf  

rf - 0.6rf = 8.2% - 7.44%  

0.4rf = 0.76%  

rf = 0.76% / 0.4  

Risk free rate = 1.9%