Calculating NPV and IRR: for the cash flows in the previous problem, suppose the firm uses the NPV decision rule. At a required return 11 percent, should the firm accept this project? What if the required return was 30 percent?
Year    Cash flow
0          -$34000
1             16000
2             18000
3             15000

Calculating IRR: What is the IRR of the following set of cash flows?
Year      Cash flow
0             -$19500
1                   9800
2                10300
3                   8600

Problems with IRR: Light Sweet Petroleum, Inc. is trying to evaluate a generation project with the following cash flows:
Year       Cash flow
0          -$45,000,000
1             78,000,000
2             14,000,000

a. If the company requires a 12 percent return on its investments, should it accept this project? Why?
b. Compute the IRR for this project. How many IRRs are there? Using the IRR decision rule, should the company accept the project? What’s going on here? Arithmetic and geometric returns: A stock has had returns of 3 percent, 38 percent, 21 percent, -15 percent, 29 percent, and -13 percent over the last six years. What are the arithmetic and geometric returns for the stock Arithmetic and geometric returns: What are the arithmetic and geometric returns for the stock?
A stock has had the following yearend prices and dividends:
Year         Price          dividend
1             $60.18                -
2               73.66             $.60
3               94.18               .64
4               89.35               .72
5               78.49               .80
6               95.05             1.20

Portfolio expected return: You own a portfolio that is 60 percent invested in Stock X, 25 percent in Stock 7, and 15 percent in Stock Z. The expected returns on these three stocks are 9 percent, 17 percent, and 13 percent, respectively. What is the expected return on the portfolio?

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Calculating NPV and IRR:
The internal rate of return is found by
0 = -34,000 + 16,000/(1+IRR) + 18,000/(1+IRR)2+15,000/(1+IRR)3
So IRR = 20.97%
If the required rate of return is 11%, the firm should accept the project because 20.97% > 11%.
If the required rate of return is 30%, the firm should reject the project because 20.97% < 30%...
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