The CapmBeta Company is considering a new capital investment proposal. This project's risk structure is very similar to that of the company's existing business. Returns for this company's stock for the past ten years are given in Table 7.4, together with returns for a country's stock-market index (e.g. the All Ordinaries Index in Australia or the S\&P Index in the United States). The government treasury bill rate was around $5.6 \%$ per annum. The total capital outlay of the proposed project is estimated
$$
\begin{array}{lll}
\hline \hline \text { Year } & \text { Company's stock returns }\left(r_{i t}\right) & \text { Stock-market index returns }\left(r_{m t}\right) \\
\hline 1992 & 0.09 & 0.07 \\
1993 & 0.10 & 0.09 \\
1994 & 0.10 & 0.10 \\
1995 & 0.11 & 0.12 \\
1996 & 0.10 & 0.11 \\
1997 & 0.11 & 0.10 \\
1998 & 0.11 & 0.10 \\
1999 & 0.10 & 0.09 \\
2000 & 0.09 & 0.08 \\
2001 & 0.07 & 0.07 \\
\hline \hline
\end{array}
$$
$$
\begin{array}{lc}
\hline \hline \text { Year } & \text { Net cash inflows (\$ million) } \\
\hline 1 & 25 \\
2 & 2,000 \\
3 & 4,000 \\
4 & 6,000 \\
5 & 6,500 \\
\hline \hline
\end{array}
$$
as $$\$ 3,000$$ million and it is to be incurred at the beginning of year 1 . The forecasted after-tax net cash inflows of the project are provided in Table 7.5.
(a) Compute the average stock-market (index) return.
(b) Compute the average company stock return.
(c) Compute the variance and standard deviation of the stock-market return: $\operatorname{var}\left(r_m\right)$, or $\sigma_m^2$, and $\operatorname{SD}\left(r_m\right)$, or $\sigma_m$.
(d) Compute the variance and standard deviation of the company stock return: $\operatorname{var}\left(r_i\right)$, or $\sigma_i^2$, and $\operatorname{SD}\left(r_i\right)$, or $\sigma_i$.
(e) Compute the covariance between company stock return and stock-market index return.
(f) Compute the correlation between company stock return and stock-market index return.
(g) Estimate beta as $\beta_i=\frac{\operatorname{cov}\left(r_1, r_m\right)}{\operatorname{var}\left(r_m\right)}$
(h) Estimate beta as $\beta_i=\frac{\rho_{i, m} \sigma_i}{\sigma_n}$
(i) Calculate the average risk premium, $u$, for the firm.
(j) Estimate the RADR to be used as the discount rate for this project.
(k) Compute the project's NPV using this RADR.
(1) Compute the certainty equivalent coefficients using the relevant information from the question under the condition that if risk adjustments are made correctly, the net present value calculated from any given future cash flows must be identical in the RADR and CE methods.
(m) Calculate the NPV using the RADR and CE methods to show the answer is the same under both methods.