Net Present Value and Other Investment Criteria
project a good investment? Second, if we have more than one good project, but we can take only one of them, which one should we take? The main point of this chapter is that only the NPV criterion can always provide the correct answer to both questions. For this reason, NPV is one of the two or three most important concepts in finance, and we will refer to it many times in the chapters ahead. When we do, keep two things in mind: (1) NPV is always just the difference between the market value of an asset or project and its cost, and (2) the financial manager acts in the shareholders’ best interests by identifying and taking positive NPV projects. Finally, we noted that NPVs can’t normally be observed in the market; instead, they must be estimated. Because there is always the possibility of a poor estimate, financial managers use multiple criteria for examining projects. The other criteria provide additional information about whether or not a project truly has a positive NPV.
C h a p t e r R e v i e w a n d S e l f - Te s t P r o b l e m s 9.1 Investment Criteria This problem will give you some practice calculating NPVs and paybacks. A proposed overseas expansion has the following cash flows: Year Cash Flow
0 1 2 3 4
$200 50 60 70 200
Calculate the payback, the discounted payback, and the NPV at a required return of 10 percent. Mutually Exclusive Investments Consider the following two mutually exclusive investments. Calculate the IRR for each and the crossover rate. Under what circumstances will the IRR and NPV criteria rank the two projects differently? Year Investment A Investment B
0 1 2 3
$75 20 40 70
$75 60 50 15
Average Accounting Return You are looking at a three-year project with a projected net income of $2,000 in Year 1, $4,000 in Year 2, and $6,000 in Year 3. The cost is $12,000, which will be depreciated straight-line to zero over the three-year life of the project. What is the average accounting return (AAR)?
A n s w e r s t o C h a p t e r R e v i e w a n d S e l f - Te s t P r o b l e m s 9.1 In the following table, we have listed the cash flow, cumulative cash flow, discounted cash flow (at 10 percent), and cumulative discounted cash flow for the proposed project.
Cash Flow Year Undiscounted Discounted
Accumulated Cash Flow Undiscounted Discounted
1 2 3 4
$ 50 60 70 200
$ 45.45 49.59 52.59 136.60
$ 50 110 180 380
$ 45.45 95.04 147.63 284.23
Recall that the initial investment was $200. When we compare this to accumulated undiscounted cash flows, we see that payback occurs between Years 3 and 4. The cash flows for the first three years are $180 total, so, going into the fourth year, we are short by $20. The total cash flow in Year 4 is $200, so the payback is 3 ($20/200) 3.10 years. Looking at the accumulated discounted cash flows, we see that the discounted payback occurs between Years 3 and 4. The sum of the discounted cash flows is $284.23, so the NPV is $84.23. Notice that this is the present value of the cash flows that occur after the discounted payback. To calculate the IRR, we might try some guesses, as in the following table: Discount Rate NPV(A) NPV(B)
0% 10 20 30 40
$55.00 28.83 9.95 4.09 14.80
$50.00 32.14 18.40 7.57 1.17
Several things are immediately apparent from our guesses. First, the IRR on A must be between 20 percent and 30 percent (why?). With some more effort, we find that it’s 26.79 percent. For B, the IRR must be a little less than 40 percent (again, why?); it works out to be 38.54 percent. Also, notice that at rates between 0 percent and 10 percent, the NPVs are very close, indicating that the crossover is in that vicinity. To find the crossover exactly, we can compute the IRR on the difference in the cash flows. If we take the cash flows from A minus the cash flows from B, the resulting cash...