Problems

1. Compute all IRRs for the following sequence of cash flows:

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   Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7
   –$10,000	$8,000	$1,500	$1,500	$1,500	$1,500	–$1,500

2. Consider a project with the following cash flows. Determine the project’s IRR. If the annual cost of capital is 20 percent, would you undertake this project?

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   Year 1	Year 2	Year 3
   –$4,000	$2,000	$4,000

3. Find all IRRs for the following project:

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   Year 1	Year 2	Year 3
   $100	–$300	$250

4. Find all IRRs for a project having the given cash flows on the listed dates.

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   1/10/2003	7/10/2003	5/25/2004	7/18/2004	3/20/2005	4/1/2005	1/10/2006
   –$1,000	$900	$800	$700	$500	$500	$350

5. Consider the following two projects. Assume a company’s cost of capital is 15 percent. Find the IRR and NPV of each project. Which projects add value to the company? If the company can choose only a single project, which project should it choose?

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   	Year 1	Year 2	Year 3	Year 4
   Project 1	–$40	$130	$19	$26
   Project 2	–$80	$36	$36	$36

6. 25-year-old Meg Prior is going to invest $10,000 in her retirement fund at the beginning of each of the next 40 years. Assume that during each of the next 30 years Meg will earn 15 percent on her investments and during the last 10 years before she retires, her investments will earn 5 percent. Determine the IRR associated with her investments and her final retirement position. How do you know there will be a unique IRR? How would you interpret the unique IRR?

7. Give an intuitive explanation of why Project 6 (on the worksheet Which Project in the file IRR.xlsx) has an IRR of 50 percent.

8. Consider a project having the following cash flows.

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   Year 1	Year 2	Year 3
   –$70,000	$12,000	$15,000

   Try to find the IRR of this project without simply guessing. What problem arises? What is the IRR of this project? Does the project have a unique IRR?

9. For the cash flows in Problem 1 assume we can borrow at 12 percent per year and invest profits at 15 percent per year. Compute the project’s MIRR.