Typical phases in the development of a new technology prior to deployment include research and development $($R&D$)$ demonstration, and commercialisation. In the latter

phase, a successful prototype is prepared for deployment via incremental improvement

of its performance and cost effectiveness based on learning effects.

Within this context, an R&D firm considering the development of an innovative IT product is commencing the development stage and anticipates that upon completion, it will

be able to sell the new product at price P with expected value P $=25$ million. However, the firm is aware that the price will depend on the market price of similar products

at the time of deployment.

Through empirical research, the firm identifies that the covariance between the final sales

P and the market return is $20\backslash$sigma

$2$

M$,$ where $\backslash$sigma M is the standard deviation of the market rate

of return. Also, the cost C of the R&D project is subject to technological uncertainty

that will be resolved after the initiation of the project. Current estimations imply that

the cost will be either $20$ million or $16$ million with equal probability. Assuming a $9\%$

risk$-$free rate $($rf $)$ and a $33\%$ expected return on the market $($rM$)$ determine:

i The expected rate of return of the project.

ii The $\backslash$beta of the project.

iii What is the excess rate of return compared to that predicted by the CAPM?