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# Finance: NPV, Payback period, Portfolio analysis etc.

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10-5. RejuveNation needs to estimate how long the payback period would be for their new facility project. They have received two proposals and need to decide which one is best. Project Weights will have an initial investment of \$200,000 and generate positive cash flows of \$100,000 at the end of year 1, \$75,000 at the end of year 2, \$50,000 at the end of year 3, and \$100,000 at the end of year 4. Project Waters will have an initial investment of \$300,000 and will generate positive cash flows of \$200,000 at the end of year 1 and \$150,000 at the end of years 2, 3, and 4. What is the payback period for Project Waters? What is the payback period for Project Weights? Which project should RejuveNation choose?

10-6. Calculate the NPV of each project in problem 10-5 using RejuveNation's cash flows and a 10 perecent discount rate.

10-7. The Bedford Falls Bridge Bilding Company is considering the purchase of a new crane. George Bailey, the new manager, has had some past management experience while he was the chief financial officer of the local savings and loan. The cost of the crane is \$17,291.42, and the expected incremental cash flows are \$5,000 at the end of year 1, \$8,000 at the end of year 2, and \$10,000 at the end of year 3.
a. Calculate the NPV is the required rate of return is 12 percent.
b. Calculate the IRR

10-8. Lin McAdam and Lola Manners, managers of the Winchester Company, do not practice capital rationing. They have three independent projects they are evaluating for inclusion in this year's capital budget. One is for a new machine to make rifle stocks. The second is for a new forklift to use in the warehouse. The third project involves the purchase of automated packaging equipment. The Winchester Company's required rate of return is 13%. The initial investment (a negative cash flow) and the expected positive net cash flows for years 1 through 4 for each project follow:
Expected Net Cash Flow

Year Stock Fork Pack
0 (\$9,000) (\$12,000) (\$18,200)
1 \$2,000 \$5,000 \$0
2 \$5,000 \$4,000 \$5,000
3 \$1,000 \$6,000 \$10,000
4 \$4,000 \$2,000 \$12,000

Calculate the NPV and IRR of each project.
Which proejct(s) should be undertaken? Why?
10-10. Buzz Lightyear has been offered an investment in which he expects to receive payments of \$4,000 at the end of the next 10 years in return for an initial investment of \$10,000 now.
What is the IRR of the proposed investment?
What is the MIRR of the proposed investment? Assume a cost of capital of 15 percent

Assume that a company has an existing portfolio A with an expected return of 9 percent and a standard deviation of 3 percent. The company is considering adding an asset B to its portfolio. Asset B's expected return is 12 percent with a standard deviation of 4 percent. Also assume that the amount invested in A is \$700,000 and the amounts to be invested in B is \$200,000. If the degree of correlation between returns from portfolio A and project B is zero, calculate:
a. The standard deviation of the new combined portfolio and compare it with that of the existing portfolio.

b. The coefficient of variation of the new combined portfolio and compare it with that of the existing portfolio.

Assume the risk-free rate is 5 percent, the expected rate of return on the market is 15 percent, and the beta of your firm is 1.2. Given these conditions, what is the required rate of return on your company's stock per the capital asset pricing model?