Question

Q1) A stock fund has an expected return of 15% and a standard deviation of 25% and a bond fund has an expected return of 10% and a standard deviation of 10%. The correlation between the two funds is 0.25. The risk free rate is 5%. What is the (a) expected return and (b) standard deviation of the portfolio with 70% weight in the stock portfolio and 30% weight in the bond portfolio?

Q2) The variance of Stock A is .004, the variance of the market is .007 and the covariance between the two is .0026. What is the correlation coefficient between the two?

Q3) Road Rollers Paving Company is considering buying a new asphalt laying machine. The machine costs $1,300,000 and can be depreciated to zero on a straight-line basis over its life of 10 years. The machine is expected to have no salvage value. Revenues are expected to be $600,000 per year, and costs are estimated at $220,000 per year. The firm is in the 34% tax bracket. What are the annual operating cash flows for each year? (Note that since the operating cash flows will be the same every year, you just have to calculate the operating cash flow for any one year)

Q4) The variance of Stock A is .004, the variance of the market is .007 and the covariance between the two is .0026. What is beta of the stock?

Answer 1

1.
=70%*15%+30%*10%=13.50%

2.
=SQRT((70%*25%)^2+(30%*10%)^2+2*70%*25%*30%*10%*0.25)=18.4797186125763%

3.
=0.0026/SQRT(0.004*0.007)=0.491353814911995

4.
=(600000-220000-1300000/10)*(1-34%)+1300000/10=295000

5.
=0.0026/0.007=0.371428571428571