NPV and Other Investment Criteria P.V. Viswanath For an Introductory Course in Finance Key Concepts and Skills The NPV Rule Understand the payback rule and its shortcomings Understand accounting rates of return and their problems Understand the internal rate of return and its strengths and weaknesses Understand the net present value rule and why it is the best decision criteria P.V. Viswanath 2 Chapter Outline Net Present Value The Payback Rule The Average Accounting Return The Internal Rate of Return The Profitability Index The Practice of Capital Budgeting P.V. Viswanath 3 Sources of Investment Ideas Three categories of projects: New Products Cost Reduction Replacement of Existing assets Sources of Project Ideas: Existing customers R&D Department Competition Employees P.V. Viswanath 4 Good Decision Criteria We need to ask ourselves the following questions when evaluating decision criteria Does the decision rule adjust for the time value of money? Does the decision rule adjust for risk? Does the decision rule provide information on whether we are creating value for the firm? The Net Present Value rule satisfies these three criteria, and is, therefore, the preferred decision rule. P.V. Viswanath 5 Net Present Value The difference between the market value of a project and its cost How much value is created from undertaking an investment? The first step is to estimate the expected future cash flows. The second step is to estimate the required return for projects of this risk level. The third step is to find the present value of the cash flows and subtract the initial investment. P.V. Viswanath 6 NPV Decision Rule If the NPV is positive, accept the project A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners. Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal. NPV is an additive measure: If there are two projects A and B, then NPV(A and B) = NPV(A) + NPV(B). P.V. Viswanath 7 Project Example Information You are looking at a new project and you have estimated the following cash flows: Year 0: CF = -165,000 Year 1: CF = 63,120; NI = 13,620 Year 2: 70,800; NI = 3,300 Year 3: 91,080; NI = 29,100 Average Book Value = 72,000 Your required return for assets of this risk is 12%. P.V. Viswanath 8 Computing NPV for the Project Using the formulas: NPV = 63,120/(1.12) + 70,800/(1.12)2 + 91,080/(1.12)3 – 165,000 = 12,627.42 Do we accept or reject the project? P.V. Viswanath 9 Estimating Project Cashflows Before the NPV decision rule can be applied, we need project cashflow forecasts for each year. These are built up from estimates of incremental revenues and associated project costs. Cash Flow = Revenues – Fixed Costs – Variable Costs – Taxes – Long-term Investment Outlays – Changes in Working Capital An equivalent formula is: Cashflow = Net Income + Noncash expenses (that were included in the Net Income computation) +(1-tax rate)Interest – Long-term Investment Outlays – Changes in Working Capital P.V. Viswanath 10 Cost of Capital The cost of capital is the opportunity cost of capital for the firm’s investors and is used to discount the project cashflows. The cost of capital is also called the WACC and is computed as the firm’s after-tax weighted cost of debt and equity WACC = (E/V)Re + (D/V)Rd(1-t), where E, D are market values of the firm’s equity and debt; V = D+E is the total value of the firm; and t is the firm’s corporate tax rate The cost of debt Rd is multiplied by (1-t) because interest payments on debt are deductible for tax purposes. Since the tax advantage of debt is taken into account in the denominator, we do not include it in the numerator as well, thus avoiding double counting. P.V. Viswanath 11 Sensitivity Analysis Since the firm will not know the future level of output, or the other cost parameters with certainty, it is important to know how the value of the project changes as these parameters are varied. This is called sensitivity analysis If the final decision on the project is very sensitive to a particular parameter, it would be more valuable to expend resources on obtaining more precise estimates of that parameter. The break-even point is the point of indifference between accepting and rejecting the project. With respect to sales, this is the number of units that have to be sold in order for the project to be in the black. P.V. Viswanath 12 Issues to keep in mind Sunk costs should be ignored. These costs have already been incurred and cannot be undone whatever the decision that is going to be currently taken. Only incremental cashflows should be considered. Hence if a machine is to be replaced by a new machine, only the additional flows implied by the new machine should be considered to make the decision of whether to buy the new machine. Only cashflows must be considered; allocated expenses, such as depreciation are to be ignored because they reflect capital expenditures already made and are a kind of sunk cost. Of course, if there are any tax implications related to depreciation computations, these must be taken into account. P.V. Viswanath 13 Projects with Unequal Lives Suppose we have to choose between the following two machines, L and S to replace an existing machine. Machine L costs $1000 and needs to be replaced once every four years, while machine S costs $600 a unit and must be replaced every two years. The flows C1-C4 represent cost savings over the current machine, for the next four years. The discount rate is 10 percent. Project C0 C1 C2 C3 C4 NPV ---------------------------------------------------------------------------L -1000 500 500 500 500 584.93 S -600 500 500 267.77 P.V. Viswanath 14 Projects with Unequal Lives Treating this problem as a simple present value problem, we would choose machine L, since the present value of L is greater than that of S. However, choosing S gives us additional flexibility because we are not locked into a four-year cycle. Perhaps better alternatives may be available in year 3. Furthermore, the present comparison is not appropriate because even if no better alternatives are available because we have not considered the tax savings in years 3 and 4 if we go with machine S – we can always buy a second S-type machine at the end of year two! P.V. Viswanath 15 Projects with Unequal Lives Consider the modified alternatives: Project C0 C1 C2 C3 C4 NPV ------------------------------------------------------------------------------------------L -1000 500 500 500 500 584.93 S -600 500 500 267.77 Second S -600 500 500 220.66 Combination S -600 500 -100 500 500 488.43 We see that the combination of two S-type machines are not as disadvantageous compared to one L-type machine, though the L-type machine still wins out. P.V. Viswanath 16 Projects with Unequal Lives Alternatively, we can convert the flows for the machines into equivalent equal annual flows. Thus, we find X, such that the present value of L and L1 are equal. Project C0 C1 C2 C3 C4 NPV ---------------------------------------------------------------------------L -1000 500 500 500 500 584.93 L1 0 X X X X 584.93 This is obtained as the solution to the equation PV(Annuity of $X for 4 years at 10%) = $584.93 and works out to $184.53 P.V. Viswanath 17 Projects with Unequal Lives Similarly, we convert the flows for machine S into equivalent equal annual flows. Thus, we find X, such that the present value of S and S1 are equal. Project C0 C1 C2 C3 C4 NPV ---------------------------------------------------------------------------S -600 500 500 267.77 S1 0 Y Y 267.77 This is obtained as the solution to the equation PV(Annuity of $Y for 2 years at 10%) = $267.77 and works out to $154.29 P.V. Viswanath 18 Projects with Unequal Lives The values X and Y can simply be compared and the project with the lower equivalent annual flow is chosen. We are effectively making the choice between the following two projects Project C0 C1 C2 C3 C4 ---------------------------------------------------------------------------L1 0 X X X X S1 0 Y Y Y Y The advantage of this approach is that we don’t need to explicitly construct two projects with the same project lives. P.V. Viswanath 19 Internal Rate of Return This is the most important alternative to NPV It is often used in practice and is intuitively appealing It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere P.V. Viswanath 20 IRR – Definition and Decision Rule Definition: IRR is the return that makes the NPV = 0 Decision Rule: Accept the project if the IRR is greater than the required return P.V. Viswanath 21 Computing IRR For The Project If you do not have a financial calculator, then this becomes a trial and error process In the case of our problem, we can find that the IRR = 16.13%. Note that the IRR of 16.13% > the 12% required return Do we accept or reject the project? P.V. Viswanath 22 NPV Profile To understand what the IRR is, let us look at the NPV profile. The NPV profile is the function that shows the NPV of the project for different discount rates. Then, the IRR is simply the discount rate where the NPV profile intersects the X-axis. That is, the discount rate for which the NPV is zero. P.V. Viswanath 23 NPV Profile For The Project 70,000 IRR = 16.13% 60,000 50,000 NPV 40,000 30,000 20,000 10,000 0 -10,000 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 -20,000 Discount Rate P.V. Viswanath 24 Decision Criteria Test - IRR Does the IRR rule account for the time value of money? Does the IRR rule account for the risk of the cash flows? Does the IRR rule provide an indication about the increase in value? Should we consider the IRR rule for our primary decision criteria? P.V. Viswanath 25 Advantages of IRR Knowing a return is intuitively appealing It is a simple way to communicate the value of a project to someone who doesn’t know all the estimation details If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task P.V. Viswanath 26 NPV Vs. IRR NPV and IRR will generally give us the same decision Exceptions Non-conventional cash flows – cash flow signs change more than once Mutually exclusive projects Initial investments are substantially different Timing of cash flows is substantially different P.V. Viswanath 27 IRR and Nonconventional Cash Flows When the cash flows change sign more than once, there is more than one IRR When you solve for IRR you are solving for the root of an equation and when you cross the x-axis more than once, there will be more than one return that solves the equation If you have more than one IRR, which one do you use to make your decision? P.V. Viswanath 28 Another Example – Nonconventional Cash Flows Suppose an investment will cost $90,000 initially and will generate the following cash flows: Year 1: 132,000 Year 2: 100,000 Year 3: -150,000 The required return is 15%. Should we accept or reject the project? P.V. Viswanath 29 NPV Profile IRR = 10.11% and 42.66% $4,000.00 $2,000.00 NPV $0.00 ($2,000.00) 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 ($4,000.00) ($6,000.00) ($8,000.00) ($10,000.00) Discount Rate P.V. Viswanath 30 Summary of Decision Rules The NPV is positive at a required return of 15%, so you should Accept If you compute the IRR, you could get an IRR of 10.11% which would tell you to Reject You need to recognize that there are nonconventional cash flows and look at the NPV profile. P.V. Viswanath 31 IRR and Mutually Exclusive Projects Mutually exclusive projects If you choose one, you can’t choose the other Example: You can choose to attend graduate school next year at either Harvard or Stanford, but not both Intuitively you would use the following decision rules: NPV – choose the project with the higher NPV IRR – choose the project with the higher IRR P.V. Viswanath 32 Example With Mutually Exclusive Projects Period Project A Project B 0 -500 -400 1 325 325 2 325 200 IRR 19.43% 22.17% NPV 64.05 60.74 P.V. Viswanath The required return for both projects is 10%. Which project should you accept and why? 33 NPV Profiles IRR for A = 19.43% $160.00 $140.00 IRR for B = 22.17% $120.00 Crossover Point = 11.8% NPV $100.00 $80.00 A B $60.00 $40.00 $20.00 $0.00 ($20.00) 0 0.05 0.1 0.15 0.2 0.25 0.3 ($40.00) Discount Rate P.V. Viswanath 34 Conflicts Between NPV and IRR NPV directly measures the increase in value to the firm Whenever there is a conflict between NPV and another decision rule, you should always use NPV IRR is unreliable in the following situations Non-conventional cash flows Mutually exclusive projects P.V. Viswanath 35 Additional Decision Rules In addition to the NPV and IRR rules, there are some other decision rules that are popularly used. These are conceptually flawed, but have the advantage of being easy to compute and use. They may, therefore, be used if a quick decision is necessary and not a lot is riding on the decision. Two examples of these alternative decision rules are the payback rule and the accounting rate of return. P.V. Viswanath 36 Payback Period How long does it take to get the initial cost back in a nominal sense? Computation Estimate the cash flows Subtract the future cash flows from the initial cost until the initial investment has been recovered Decision Rule – Accept if the payback period is less than some preset limit P.V. Viswanath 37 Computing Payback For The Project Assume we will accept the project if it pays back within two years. Year 1: 165,000 – 63,120 = 101,880 still to recover Year 2: 101,880 – 70,800 = 31,080 still to recover Year 3: 31,080 – 91,080 = -60,000 project pays back in year 3 Do we accept or reject the project? P.V. Viswanath 38 Decision Criteria Test - Payback Does the payback rule account for the time value of money? Does the payback rule account for the risk of the cash flows? Does the payback rule provide an indication about the increase in value? Should we consider the payback rule for our primary decision criteria? P.V. Viswanath 39 Advantages and Disadvantages of Payback Disadvantages Advantages Easy to understand Adjusts for uncertainty of later cash flows Biased towards liquidity P.V. Viswanath Ignores the time value of money Requires an arbitrary cutoff point Ignores cash flows beyond the cutoff date Biased against long-term projects, such as research and development, and new projects 40 Justifying the Payback Period Rule We usually assume that the same discount rate is applied to all cash flows. Let di be the discount factor for a cash flow at time i, implied by a constant discount rate, r, where . Then di+1/di = 1+r, a constant. However, if the riskiness of successive cash flows is greater, then the ratio of discount factors would take into account the passage of time as well as this increased riskiness. In such a case, the discount factor may drop off to zero more quickly than if the discount rate were constant. Given the simplicity of the payback method, it may be appropriate in such a situation. P.V. Viswanath 41 Justifying the Payback Period Rule Discount factor Discount factor function implied by the payback period rule Discount factor function implied by a constant discount rate True discount factor function 0 Timing of cash flow P.V. Viswanath 42 Average Accounting Return There are many different definitions for average accounting return The one used in the book is: Average net income / average book value Note that the average book value depends on how the asset is depreciated. Need to have a target cutoff rate Decision Rule: Accept the project if the AAR is greater than a preset rate. P.V. Viswanath 43 Computing AAR For The Project Assume we require an average accounting return of 25% Average Net Income: (13,620 + 3,300 + 29,100) / 3 = 15,340 AAR = 15,340 / 72,000 = .213 = 21.3% Do we accept or reject the project? P.V. Viswanath 44 Decision Criteria Test - AAR Does the AAR rule account for the time value of money? Does the AAR rule account for the risk of the cash flows? Does the AAR rule provide an indication about the increase in value? Should we consider the AAR rule for our primary decision criteria? P.V. Viswanath 45 Advantages and Disadvantages of AAR Advantages Disadvantages Easy to calculate Needed information will usually be available P.V. Viswanath Not a true rate of return; time value of money is ignored Uses an arbitrary benchmark cutoff rate Based on accounting net income and book values, not cash flows and market values 46 Summary of Decisions For The Project Summary Net Present Value Accept Payback Period Reject Average Accounting Return Reject Internal Rate of Return Accept P.V. Viswanath 47 Profitability Index Measures the benefit per unit cost, based on the time value of money A profitability index of 1.1 implies that for every $1 of investment, we create an additional $0.10 in value This measure can be very useful in situations where we have limited capital P.V. Viswanath 48 Advantages and Disadvantages of Profitability Index Advantages Disadvantages Closely related to NPV, generally leading to identical decisions Easy to understand and communicate May be useful when available investment funds are limited P.V. Viswanath May lead to incorrect decisions in comparisons of mutually exclusive investments 49 Capital Budgeting In Practice We should consider several investment criteria when making decisions NPV and IRR are the most commonly used primary investment criteria Payback is a commonly used secondary investment criteria P.V. Viswanath 50 Quick Quiz Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9% and required payback is 4 years. What is the payback period? What is the NPV? What is the IRR? Should we accept the project? What decision rule should be the primary decision method? When is the IRR rule unreliable? P.V. Viswanath 51

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