8 Wizards o Electron Wizards Ine EWs a new idea for producin

8. (Wizards o) Electron Wizards, Ine (EWs a new idea for producing IV sels, and it is planning to enter the developmen stage Once he product is developed (which will be at the end o year), the company expecls lo sell its new process foi a price p, with expected value p= $24M Howevet, this sale price wit depend on ihe market for TV sets at the time By examing the stock iistories of various TV companies, is determined at the final sales price p is correlated with 1he market return as EKp_PJ&M-7M;))-$20M? To deve?op the process. EWI must invesi in a research and development projectl The cost of this project will be known shorlly afierIhe project is begun (when a echnical uncertainly will be resolved) The curent esimate is that the cost will be either 1 $20M 01 c-$16M, and each of these is cqually likely (This uncertainly is uncolreluted with the final price and is so uncorrelated wilh he market) Assume hat the risk-free rate is t/-9% and lhe expected return 011 the niai ket is rat 33% (a) What is he expected rate o re ol this project? (b) What is the beta of this projeci? [Hirt In ihis case, noic that (c) Is ihis an acceplable projeci based on a CAPM ciiieiion? ln pariicular, whai is the excess rate of retun o) above lhe relurn predicted by the CAPM?

Solution

(a)

Since the cost is equally likely to be $16M & $20M, the expected cost of project is 0.5*($20M) + 0.5*($16M) = $18M.

i.e, E(c) = $18M.

E(p) = $24M.

Therefore, expected compouned rate of return of the project = (24/18)¹ -1 = 0.33 or 33.33%

(b)

(c)

Return based on CAPM :  or 35.64%

Therefore, excess return = 33.33% - 35.64% = - 2.31% (i.e, 231bp below CAPM return)

Since the excess return is negative, the project is not acceptable.