M & M Micro Processors Limited is in the process of purchasing a high$-$tech equipment for its production of microchips for the electronic industry. In its search, it has gathered the following information about two possible Equipment, A and B$.$ Both equipment will be able to provide benefits over a ten$-$year period, and each required an investment of J$ $10000.$

A$.$ Management has constructed the following table of estimates of rate of return and probabilities for pessimistic, most likely and optimistic results:

Equipment A Equipment B

State of nature Rate of Return Probability Rate of Return Probability

Recession $11\%0\mathrm{.}309\%0\mathrm{.}30$

Normal $18\%0\mathrm{.}4518\%0\mathrm{.}45$

Boom $22\%0\mathrm{.}2525\%0\mathrm{.}25$

Required:

i$.$ Compute expected rate of return for each equipment. $(3$ marks$)$ ii$.$ Compute variance and standard deviation of rate of return for each equipment.

$(3$ marks$)$ iii. Determine the coefficient of variation for each equipment. $(3$ marks$)$ iv$.$ Recommend which equipment the firm should purchase and why? $(4$ marks$)$

B$.$ The firm wishes to estimate the beta of a portfolio that consists of two assets X and Y$.$ The investment manager of the firm has gathered the following information on the two assets.

Securities Rate of Return Standard Deviation Beta

X $20\%20\%1\mathrm{.}5$

Y $10\%30\%1\mathrm{.}0$

Risk free asset $5\%$

Calculate:

i$.$ The beta of the portfolio if $75\%$ of the funds are invested in Y and $25\%$ in X

$(2$ marks$)$ ii$.$ The portfolio expected return and the portfolio beta if you invest $35\%$ in X$,45\%$ in Y and $20\%$ in the risk$-$free asset $(2$ marks$)$

iii. Assuming the CAPM applies, if the market$$s expected return is $13$ percent, the riskfree rate is $8\%$ and stock X$$s required rate of return is $16\%,$ what is the stock$$s beta coefficient? $(3$ marks$)$