In 1990, John Deere is looking to acquire a company specializing in developing artificial intelligence (AI) assisted agricultural machinery. A potential target is AEye Farms, Inc., which has two divisions, namely, Software Development and Robotics Technology. AEye Farms is a private start-up firm with no debt in its capital structure. John Deere is considering acquiring one of AEye Farms divisions. The analyst of John Deere has collected information on historical returns on the market portfolio and the relevant industries:

Market portfolio Covariance with the market

Estimation period: Mean return E[r_M ] Variance Var(r_M ) Software industry Cov(r_SW,r_M ) Robotics industry Cov(r_Rob,r_M )

19601989 0.10 0.020 0.028 0.052

Answer questions a) and b) below. (Lecture notes p.12, and the basic thought experiment concerning the discount rate and valuation)

A) Assume that the risk-free rate is 5%. Using the information provided, calculate the CAPM betas for AEye Farms Software and Robotics divisions, respectively, and determine the required rates of return on each division. Answer (show the steps/calculation toward your results):

B)Despite the analysts estimates, an executive director of John Deere has insisted: Use 15% as the discount rate for the valuation of start-up tech firms. Had the directors rule been applied, for which division of AEye Farms would John Deere end up overpaying?