Electron Wizards, Inc. (EWI) has a new idea for producing TV sets, and it is planning to enter the development stage. Once the product is developed (which will be at the end of 1 year), the company expects to sell its new process for a price $p$, with expected value $\bar{p}=\$ 24 \mathrm{M}$. However, this sale price will depend on the market for TV sets at the time. By examining the stock histories of various TV companies, it is determined that the final sales price $p$ is correlated with the market return as $\mathrm{E}\left[(p-\bar{p})\left(r_{M}-\bar{r}_{M}\right)\right]=\$ 20 \mathrm{M} \sigma_{M}^{2}$.

To develop the process, EWI must invest in a research and development project. The cost $c$ of this project will be known shortly after the project is begun (when a technical uncertainty will be resolved). The current estimate is that the cost will be either $c=\$ 20 \mathrm{M}$ or $c=\$ 16 \mathrm{M}$, and each of these is equally likely. (This uncertainty is uncorrelated with the final price and is also uncorrelated with the market.) Assume that the risk-free rate is $r_{f}=9 %$ and the expected return on the market is $\bar{r}_{M}=33 %$.

(a) What is the expected rate of return of this project?

(b) What is the beta of this project? [Hint: In this case, note that

\[E\left[\left(\frac{p-\bar{p}}{c}\right)\left(r_{M}-\bar{r}_{M}\right)\right]=E\left(\frac{1}{c}\right) E\left[(p-\bar{p})\left(r_{M}-\bar{r}_{M}\right)\right]\]

(c) Is this an acceptable project based on a CAPM criterion? In particular, what is the excess rate of return ( + or - ) above the return predicted by the CAPM?