3.) Alternatives to NPV a.) Payback is defined as the number of years before cumulative (non-discounted) cash inflows exceed the initial investment. The payback "rule" says that you should ignore NPV and instead take all projects with payback less than a chosen cutoff date. Consider the following projects, which are not mutually exclusive: i.) Calculate payback for each project. Note that Payback may be a fraction of a year. ii.) Calculate NPV for each project if the discount rate is 10%. iii.) Which projects should you undertake if you use the NPV rule? Which would you undertake if you were using the payback rule with a cutoff of 1 year? iv.) Explain the differences between payback and NPV. Based on this example, what do you think of payback rules an alternative to NPV? b.) Internal Rate of Return (IRR): The internal rate of return is the discount rate that makes the NPV of a project zero. See question (2f) above. The IRR "rule" says that you should accept an investment if the actual opportunity cost of capital is less than the internal rate of return and reject it if the actual opportunity cost of capital is greater than the internal rate of return. Consider a project with the following cash flows: The cash flows are negative in the last period because of decommissioning costs. i.) Write an equation that a good calculator or computer might be able to solve to calculate the IRR (but do not solve it). ii.) Two of your associates have gotten into a fist-fight over the IRR of the project in (i). One claims it is 29.519270%, way above the relevant cost of capital, so that the company should take the project. The other claims it is 34.793795%, way below the relevant cost of capital, so the company should reject the project. What happens when you plug these values into your equation from (i)? Is one of the associates right? What does this imply about the IRR rule