Finance- Chapter 9 HW

This problem is useful for testing the ability of financial calculators and computer software. Consider the cash flows in the table. How many different IRRs are there? (Hint: Search between 20 percent and 70 percent.) When should we take this project?

Although there are 4 sign changes among the cash flows there are only 2 IRRs. We should take this project when the NPV is greater than O. Therefore, we should take this project when the required return is between 42.86% and 66.67%.

Suppose a project has conventional cash flows and a positive NPV. What do you know about its payback? Its discounted payback? Its profitability index? Its IRR? Explain.

If a project has a positive NPV for a certain discount rate, then it will also have a positive NPV for a zero discount rate. Therefore, the payback period must be less than the project life. Since discounted payback is calculated at the same discount rate as is NPV, if NPV is positive, the discounted payback period must be less than the project's life. If NPV is positive, then the present value of future cash inflows is greater than the initial investment cost, thus, PI must be greater than 1. Lastly, if NPV is positive for a certain discount rate R, then it will be zero for some larger discount rat. Therefore, the IRR must be greater than the required return.

A project has an initial cost of I, has a required return of R, and pays C annually for N years. a. Find C in terms of I and N such that the project has a payback period just equal to its life. b. Find C in terms of I, N, and R such that this is a profitable project according to the NPV decision rule. c. Find C in terms of I, N, and R such that the project has a benefit-cost ratio of 2.

a) C = I/N b) C > I/(present value of an ordinary annuity favtor at R%, n) c) C= (2 x I)/ (PVOAF at R%, n)