The NPV Rule for Judging Investments and Projects 159 7. 2 The IRR Rule for Judging Investments 161 7. 3 NPV or IRR, Which to Use? 162 7. 4 The “Yes–No” Criterion: When Do IRR and NPV Give the Same Answer? 163 7. 5 Do NPV and IRR Produce the Same Project Rankings? 164 7. 6 Capital Budgeting Principle: Ignore Sunk Costs and Consider Only Marginal Cash Flows 168 7. 7 Capital Budgeting Principle: Don’t Forget the Effects of Taxes—Sally and Dave’s Condo Investment 169 7. 8 Capital Budgeting and Salvage Values 176 7. Capital Budgeting Principle: Don’t Forget the Cost of Foregone Opportunities 180 7. 10 In-House Copying or Outsourcing? A Mini-case Illustrating Foregone Opportunity Costs 181 7. 11 Accelerated Depreciation 184 Conclusion 185 Exercises 186 0195301501_158-192_ch7. qxd 11/3/05 12:47 PM Page 158 CHAPTER 7 Introduction to Capital Budgeting 159 OVERVIEW Capital budgeting is finance terminology for the process of deciding whether or not to undertake an investment project. There are two standard concepts used in capital budgeting: net present value (NPV) and internal rate of return (IRR).
Both of these concepts were introduced in Chapter 5; in this chapter we discuss their application to capital budgeting. Here are some of the topics covered: • Should you undertake a specific project? We call this the “yes–no” decision, and we show how both NPV and IRR answer this question. • Ranking projects: If you have several alternative investments, only one of which you can choose, which should you undertake? • Should you use IRR or NPV? Sometimes the IRR and NPV decision criteria give different answers to the yes–no and the ranking decisions.
We discuss why this happens and which criterion should be used for capital budgeting (if there’s disagreement). • Sunk costs. How should you account for costs incurred in the past? • The cost of foregone opportunities. • Salvage values and terminal values. • Incorporating taxes into the valuation decision. This issue is dealt with briefly in Section 7. 7. We return to it at greater length in Chapters 8–10. Finance Concepts Discussed • IRR • NPV • Project ranking using NPV and IRR • Terminal value • Taxation and calculation of cash flows • Cost of foregone opportunities • Sunk costs Excel Functions Used • NPV IRR • Data Tables 7. 1 The NPV Rule for Judging Investments and Projects In preceding chapters we introduced the basic NPV and IRR concepts and their application to capital budgeting. We start off this chapter by summarizing each of these rules—the NPV rule in this section and the IRR rule in the following section. 0195301501_158-192_ch7. qxd 11/3/05 12:47 PM Page 159 Here’s a summary of the decision criteria for investments implied by the net present value: The NPV rule for deciding whether or not a specific project is worthwhile: Suppose you are considering a project that has cash flows CF0, CF1, CF2, . . , CFN. Suppose that the appropriate discount rate for this project is r. Then the NPV of the project is NPV = CF0 + CF1 (1 + r ) + CF2 (1 + r )2 + · · ·+ CFN (1 + r )N = CF0 + N t=1 CFt (1 + r )t Rule: A project is worthwhile by the NPV rule if its NPV 0. The NPV rule for deciding between two mutually exclusive projects: Suppose you are trying to decide between two projects A and B, each of which can achieve the same objective. For example, your company needs a new widget machine, and the choice is between widget machine A and machine B.
You will buy either A or B (or perhaps neither machine, but you will certainly not buy both machines). In finance jargon, these projects are “mutually exclusive. ” Suppose project A has cash flows CFA0 , CFA1 , CFA2 , . . . , CFA N and that project B has cash flows CFB0 , CFB1 , CFB2 , . . . , CFB N . Rule: Project A is preferred to project B if NPV(A) = CFA0 + N t=1 CFAt (1 + r )t > CFB0 + N t=1 CFBt (1 + r )t = NPV(B) The logic of both NPV rules presented above is that the present value of a project’s cash flows—PV = N t=1[CFt /(1 + r )t ]—is the economic value today of the project.
Thus, if we have correctly chosen the discount rate r for the project, the PV is what we ought to be able to sell the project for in the market. 1 The net present value is the wealth increment produced by the project, so that NPV 0 means that a project adds to our wealth: NPV = CF0 ^ Initial cash flowrequired to implement the project. This is usually a negative number. + N t=1 CFt (1 + r )t ^ Market value of future cash flows. An Initial Example To set the stage, let’s assume that you’re trying to decide whether to undertake one of two projects.
Project A involves buying expensive machinery that produces a better product at a lower cost. The machines for project A cost $1,000 and, if purchased, you anticipate that the project will produce cash flows of $500 per year for the next five years. Project B’s machines are cheaper, costing $800, but they produce smaller annual cash flows of $420 per year for the next five years. We’ll assume that the correct discount rate is 12%. 160 PART TWO CAPITAL BUDGETING AND VALUATION 1This assumes that the discount rate is “correctly chosen,” by which we mean that it is appropriate to the riskiness of the project’s cash flows.
For the moment, we fudge the question of how to choose discount rates; this topic is discussed in Chapter 9. 0195301501_158-192_ch7. qxd 11/3/05 12:47 PM Page 160 CHAPTER 7 Introduction to Capital Budgeting 161 7. 2 The IRR Rule for Judging Investments An alternative to using the NPV criterion for capital budgeting is to use the internal rate of return (IRR). Recall from Chapter 5 that the IRR is defined as the discount rate for which the NPV equals zero. It is the compound rate of return that you get from a series of cash flows.
Here are the two decision rules for using the IRR in capital budgeting. The IRR rule for deciding whether or not a specific investment is worthwhile: Suppose we are considering a project that has cash flows CF0, CF1, CF2, . . . , CFN . IRR is an interest rate such that CF0 + CF1 (1 + IRR) + CF2 (1 + IRR)2 + ·· ·+ CFN (1 + IRR)N = CF0 + N t=1 CFt (1 + k)t = 0 Rule: If the appropriate discount rate for a project is r, you should accept the project if its IRR > r and reject it if its IRR < r. EXCEL NOTE EXCEL’S NPV FUNCTION VERSUS THE FINANCE DEFINITION OF NPV
We reiterate our Excel note from Chapter 5 (p. 94): Excel’s NPV function computes the present value of future cash flows; this does not correspond to the finance notion of NPV, which includes the initial cash flow. To calculate the finance NPV concept in the spreadsheet, we have to include the initial cash flow. Hence, in cell B12, the NPV is calculated as NPV($B$2,B6:B10)B5 and in cell C12 the calculation is NPV($B$2,C6:C10)C5. Suppose we apply the NPV criterion to projects A and B: 1 2 3 4 5 6 7 8 9 10 11 12 A B C D Discount rate 12% Year Project A Project B -1000 -800 1 500 420 2 500 420 3 500 420 4 500 420 5 500 420 NPV 802. 39 714. 01 r, you get more than you require. The IRR rule for deciding between two competing projects: Suppose you are trying to decide between two mutually exclusive projects A and B (meaning: both projects are ways of achieving the same objective, and you will choose at most one of the projects). Suppose project A has cash flows CFA0 , CFA1 , CFA2 , . . . , CFA N and that project B has cash flows CFB0 , CFB1 , CFB2 , . . . , CFB N . Rule: Project A is preferred to project B if IRR(A) > IRR(B).
Again the logic is clear: Since the IRR gives a project’s compound rate of return, if we choose between two projects using the IRR rule, we prefer the higher compound rate of return. Applying the IRR rule to our projects A and B, we get: 162 PART TWO CAPITAL BUDGETING AND VALUATION 1 2 3 4 5 6 7 8 9 10 11 12 A B C D Discount rate 12% Year Project A Project B 0 -1000 -800 1 500 420 2 500 420 3 500 420 4 500 420 5 500 420 IRR 41% 44% 12%, which is our relevant discount rate. If we have to choose between the two projects by using the IRR rule, project B is preferred to project A because it has a higher IRR. . 3 NPV or IRR, Which to Use? We can sum up the NPV and IRR rules as follows: “Yes or No”: “Project Ranking”: Choosing Whether or Not to Comparing Two Mutually Criterion Undertake a Single Project Exclusive Projects NPV criterion The project should be undertaken if Project A is preferred to project B its NPV > 0. if NPV(A) > NPV(B). IRR criterion The project should be undertaken if Project A is preferred to project B its IRR > r, where r is the appropriate if IRR(A) > IRR(B). discount rate. 0195301501_158-192_ch7. qxd 11/3/05 12:47 PM Page 162 CHAPTER 7 Introduction to Capital Budgeting 163
Both the NPV rules and the IRR rules look logical. In many cases your investment decision—to undertake a project or not, or which of two competing projects to choose—will be the same whether you use NPV or IRR. There are some cases, however (such as that of projects A and B illustrated above), where NPV and IRR give different answers. In our present value analysis, project A won out because its NPV is greater than project B’s. In our IRR analysis of the same projects, project B was chosen because it had the higher IRR. In such cases, you should always use the NPV to decide between projects.
The logic is that if individuals are interested in maximizing their wealth, they should use NPV, which measures the incremental wealth from undertaking a project. 7. 4 The “Yes–No” Criterion: When Do IRR and NPV Give the Same Answer? Consider the following project. The initial cash flow of $1,000 represents the cost of the project today, and the remaining cash flows for years 1–6 are projected future cash flows. The discount rate is 15%. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 A B C Discount rate 15% Year Cash flow 0 -1,000 1 100 2 200 3 300 4 400 5 500 6 600 PV of future cash flows 1,172. 13