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Chapter 13

Chapter 13. Weighing Net Present Value and Other Capital Budgeting Criteria. Introduction. In previous chapters we learned how to Calculate the firm’s cost of capital Estimate a project’s cash flows

vaughan-mckenzie
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Chapter 13

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  1. Chapter 13 Weighing Net Present Value and Other Capital Budgeting Criteria

  2. Introduction • In previous chapters we learned how to • Calculate the firm’s cost of capital • Estimate a project’s cash flows • Now, we need to finish the analysis of the project to determine whether the firm should proceed

  3. The Set of Capital Budgeting Techniques • We will learn the most commonly-used methods to evaluate projects: • Net Present Value (NPV) • Payback (PB) • Discounted Payback (DPB) • Internal Rate of Return (IRR) • Modified Internal Rate of Return (MIRR) • Profitability Index (PI) • We will see that NPV is generally the preferred technique for most project evaluations • There are situations where you may want to use one of the other techniques in conjunction with NPV

  4. In general, three factors drive the choice of which decision rule to use: • The desired format or units of measurement for the decision statistic • Whether the project’s cash flows are normal or non-normal • Whether the firm is considering the project independently of other projects, or whether its project selection will be mutually exclusive

  5. Decision Statistic Formats • Managers tend to focus on three types of measurement units for financial decisions: • Currency • Time • Rate of return

  6. Of these, rate-based statistics are generally preferred by managers • Unfortunately, these statistics pose some problems • It is intuitive to compare the return on a project to the cost of capital, but computing a return requires us to compute a ratio • In using these ratios, information is lost, such as the amount of investment on which returns are based

  7. Processing Capital Budgeting Decisions • For each of our decision statistics, we need to • Identify how to calculate the decision statistic • Decide on an appropriate benchmark for comparison • Define what relationship between the statistic and the benchmark will dictate project acceptance • For mutually exclusive projects, we will also have to choose between the competing projects

  8. Net Present Value • NPV represents the “purest” of the capital budgeting rules • It measures the amount of value created by the project • NPV is completely consistent with the overall goal of the firm: to maximize firm value

  9. Calculating NPV is very straightforward • It is simply the sum of the present value of every project cash flow

  10. NPV Benchmark • NPV includes all of the project’s cash flows, both inflows and outflows • Since it involves finding the present values of every cash flow using the appropriate cost of capital as the discount rate, anything greater than zero represents the amount of value added above and beyond the required return • Accept project if NPV > 0 • Reject project if NPV < 0

  11. Example i=12% 0 1 2 3 4 (25,000) 8,500 12,000 13,500 15,000 A project has a cost of $25,000, and annual cash flows as shown. Calculate the NPV of the project if the discount rate is 12 percent

  12. Financial Calculator solution: CF0 = (25,000) CF1 = 8,500 CF2 = 12,000 CF3 = 13,500 CF4 = 15,000 I = 12 percent NPV = 11,297.42

  13. Interpretation: • Do we like this project? • Yes – it has a positive NPV • If the market agrees with our analysis, the value of our firm will increase by $11,297 due to this project • When will the value-added occur? When the project is complete? • NO – it will occur immediately upon the announcement that we are taking the project

  14. NPV Strengths and Weaknesses • Strengths • NPV not only provides a go/no-go decision, but it also quantifies the dollar amount of the value added • NPV is not a ratio • It works equally well for independent projects and for choosing between mutually-exclusive projects • Accept the project with the highest positive NPV • Weakness • Managers who are unfamiliar with NPV can misinterpret the results • They sometimes insist on comparing NPV to the cost of the project, not understanding that the cost is already incorporated into the NPV

  15. Payback • Answers the question: How long will it take us to recoup our costs? • Has intuitive appeal • Remains popular because it is easy to compute • Built-in assumptions: • Cash flows are normal • Assumes cash flows occur smoothly throughout the year

  16. Example i=12% 0 1 2 3 4 (25,000) 8,500 12,000 13,500 15,000 Cumulative (25,000) (16,500) (4,500) Payback will occur during the 3rd year Payback = 2 + 4,500/13,500 = 2.33 years Refer to the problem we worked earlier. Compute the payback.

  17. Payback Benchmark • Firms set some maximum allowable payback • Often set arbitrarily – one of payback’s greatest weaknesses • Accept project if calculated payback < Maximum allowable payback • Reject project if calculated payback > Maximum allowable payback

  18. Discounted Payback • One of the major problems with payback is that it ignores the time value of money • It treats all cash flows equally regardless of when they occur • Discounted payback fixes this particular problem • We convert the raw cash flows to their present values, and then calculate payback like before using these discounted cash flows

  19. Example i=12% 0 1 2 3 4 (25,000) 8,500 12,000 13,500 15,000 CF present values (25,000) 7,589 9,566 9,609 9,533 (17,411) Cumulative (25,000) (7,845) Discounted Payback will occur during the 3rd year Discounted Payback = 2 + 7,845/9,609 = 2.82 years

  20. Discounted Payback benchmark • Like payback, management will likely set an arbitrary benchmark • Notice that for normal projects DPB will be larger than PB • The cash flows that are “chipping away” at the initial cost are the smaller discounted cash flows, so it takes longer • Hopefully, the arbitrary benchmark would at least take that effect into account

  21. PB and DPB Strengths and Weaknesses • Strengths: • Easy to calculate • Intuitive • Weaknesses: • Both methods have severe weaknesses that make them unsuitable to be the primary method used to select projects • PB ignores the time value of money • Both methods rely on arbitrary accept/reject benchmarks • Both methods ignore cash flows that occur after the payback period. This is perhaps the most serious flaw of all

  22. Internal Rate of Return • IRR is the most popular technique to analyze projects • Often referred to as “the return on the project” • Fortunately, IRR is generally consistent with Net Present Value • Problems occur if cash flows are not normal • Problems can occur when choosing among mutually exclusive projects

  23. IRR is so closely related to NPV that it is actually defined in terms of NPV IRR is the discount rate that results in a zero NPV

  24. Example i=12% 0 1 2 3 4 (25,000) 8,500 12,000 13,500 15,000 Refer to our previous problem. Calculate the IRR of the project.

  25. Financial Calculator solution: CF0 = (25,000) CF1 = 8,500 CF2 = 12,000 CF3 = 13,500 CF4 = 15,000 IRR = ? = 30.08%

  26. Interpretation: • Do we like this project? • Yes – the IRR is greater than the required return • Notice that we did not input the discount rate when calculating IRR. IRR is a mathematical solution to a series of numbers. It is only when we compare the IRR to the required return do we insert any economic content into the problem

  27. Internal Rate of Return benchmark • Once we calculate IRR, we must compare it to the cost of capital (investors’ required return) to see if the project is acceptable • We only want to invest in projects where the rate we expect to get (IRR) exceeds the rate investors require (i)

  28. Problems with IRR • IRR will be consistent with NPV as long as: • The project has normal cash flows • Projects are independent • NPV profiles • The NPV profile is a graph of NPV versus different discount rates • It can help us determine if we may encounter a problem with IRR

  29. For normal cash flows, the NPV profile slopes downward IRR can be found where the profile crosses the x-axis (i.e. where NPV = 0, the definition of IRR)

  30. For non-normal cash flows there will be multiple IRRs for the same project • IRRs represent the solution to a mathematical series. These solutions are called ‘roots’, and a series will have as many roots as there are sign changes. This is Descartes’ Rule of Signs, discovered in 1637. • For us, this means that there will be as many IRRs as there are sign changes in the cash flows.

  31. Examples: • In our normal project, we have one IRR because we have one sign change - + + + + • What if a project involves a cleanup at the end? We might have two sign changes (and two IRRs): - + + + - • What if a project has to shut down in the 3rd year for maintenance, and then starts up again? We might have three sign changes: - + + - + +

  32. Here is a sample NPV profile for a project with non-normal cash flows. Notice that the line crosses the x-axis twice: • Fortunately, we can fix the problem of multiple IRRs using a technique called Modified Internal Rate of Return (MIRR)

  33. Differing Reinvestment Rate Assumptions of NPV and IRR • There is yet another problem with IRR relative to NPV. Each method implicitly makes assumptions about what happens to the cash flows that are generated by the project. Both assume that the cash flows are reinvested elsewhere in the firm. But the two methods differ greatly in the assumed rate that the reinvested cash flows earn.

  34. NPV assumes that the reinvested cash flows earn the cost of capital (i). • IRR assumes that the cash flows will be reinvested at the IRR of the project • This doesn’t make sense, since the project likely beat out a bunch of other projects in the first place • Also, in a competitive market, it is more realistic to assume that there are more project available at a rate that is near the firm’s cost of capital • NPV’s reinvestment rate assumption is considered to be superior to IRR’s. • Just like the multiple IRR problem, this reinvestment rate problem will also be fixed by using MIRR

  35. Modified Internal Rate of Return • This method “fixes” the reinvestment rate problem with IRR by manually moving cash flows using the cost of capital • Only then do we calculate IRR, which at that point is called MIRR • A by-product of fixing the reinvestment rate problem is fixing the non-normal cash flow problem • MIRR does not fix the problem of choosing between mutually exclusive projects. This problem is inevitable with any rate-based method

  36. For mutually exclusive projects, IRR will choose the wrong one any time the discount rate is to the left of the crossover point. • To calculate a crossover point for two projects, simply compute the IRR of the difference between the two sets of cash flows

  37. Calculating MIRR • Calculating MIRR is a three-step process: Step 1: Calculate the PV of the cash outflows using the required rate of return. Step 2: Calculate the FV of the cash inflows at the last year of the project’s time line using the required rate of return. Step 3: Calculate the MIRR, which is the discount rate that equates the PV of the cash outflows with the PV of the terminal value, ie, that makes PVoutflows = PVinflows

  38. Example 0 1 2 3 4 5 i = 9% -10,000 4,000 6,000 -5,000 12,000 15,000 Calculate the MIRR of the following project:

  39. INPUT 5 -13,861 0 N I/YR PV PMT FV OUTPUT 41,497 24.52 • Step 1: PV of outflows = -13,861 • Step 2: FV of inflows = 41,497 • Step 3: Calculate MIRR • MIRR = 24.52% • Exceeds the required return of 9%, so accept project

  40. Profitability Index • Based on NPV • Measures “bang per buck invested” • PI benchmark: • Accept project if PI > 0 • Reject project if PI < 0

  41. Example i=12% 0 1 2 3 4 (25,000) 8,500 12,000 13,500 15,000 Calculate the PI of our example Recall that the NPV = $11,297 PI = 11,297 / 25,000 = 45.19% PI indicates that we should accept the project

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