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1 P.V. VISWANATH FOR A FIRST COURSE IN FINANCE 2 Decision Criteria NPV The Payback Rule Accounting Rate of Return IRR Mutually Exclusive Projects The case of multiple IRRs Capital Rationing and Profitability Index 3 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? We will look at these questions for each one of our decision criteria. P.V. Viswanath 4 Suppose 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; Net Income (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%. How would you go about deciding whether to accept this project or not? Let’s look at how the different decision criteria would go about it. Let’s start with Net Present Value P.V. Viswanath 5 The NPV of a project is essentially the difference between the market value of a project and its cost It answers the question: how much value is created from undertaking an project? 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 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. One advantage of NPV is that it is an additive measure: P.V. Viswanath If there are two projects A and B, then NPV(A and B) = NPV(A) + NPV(B). 7 Turning back to our project, we discount the cash flows at the required rate of return and find: 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? Since the NPV > 0, accepting the project would increase firm value by 12,627.42 and we accept the project. P.V. Viswanath 8 The NPV rule accounts for the time value of money. The NPV rule accounts for the risk of the cash flows. The NPV rule provides an indication about the increase in value. The NPV rule satisfies all our criteria for a good decision rule. P.V. Viswanath 9 The payback rule asks the question: 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 10 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 The project pays back fully in year 3 Do we accept or reject the project? In this case, we reject the project because the payback is greater than two years. P.V. Viswanath 11 Advantages Easy to understand Adjusts for uncertainty of later cash flows Biased towards liquidity P.V. Viswanath Disadvantages 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 12 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 13 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 14 There are many different definitions for average accounting return The one we use 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 15 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? In this case, we reject the project because its AAR is less than the cutoff of 25%. P.V. Viswanath 16 Advantages Easy to calculate Needed information will usually be available P.V. Viswanath Disadvantages 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 17 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 18 Definition: IRR is the discount rate that makes the NPV = 0 Decision Rule: Accept the project if the IRR is greater than the required return P.V. Viswanath If we compute the NPVs of the project at different discount rates, and plot them, we see that the IRR of this project is 16.13%. 70,000 IRR = 16.13% because NPV=0 at that discount rate. It is the point where the NPV profile cuts the Xaxis. 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 -20,000 Discount Rate P.V. Viswanath 19 0.22 20 If we do not have a financial calculator, then this becomes a trial and error process. However, financial calculators and spreadsheet programs usually have functions that compute the IRR. Excel, for example, has an IRR function. Do we accept or reject the project? Since the IRR of 16.13% is greater than the required rate of return of 12%, we accept the project. P.V. Viswanath 21 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. Can be used to gauge sensitivity of project value to errors in estimation of the discount rate. P.V. Viswanath Summary Net Present Value Accept Payback Period Reject Average Accounting Return Reject Internal Rate of Return Accept P.V. Viswanath 22 23 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 What do we do if there is a conflict? NPV directly measures the increase in value to the firm. Hence whenever there is a conflict between NPV and another decision rule, you should always use NPV. P.V. Viswanath 24 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 25 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? Let us look at the NPV profile. P.V. Viswanath 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 26 27 If you compute the NPV, you would find it is positive at a required return of 15%, so you should Accept If you compute the IRR using a calculator, you would probably get an IRR of 10.11% which would tell you to Reject What do you do, now? You need to recognize that there are nonconventional cash flows and look at the NPV profile. In this case, we see that there are two IRRs! The right decision using IRR is not so easy! P.V. Viswanath 28 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 But look at the following project P.V. Viswanath 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? 29 30 One way to deal with this problem is to consider project B as accepted, tentatively, and then to ask if it’s worthwhile switching to project A. Period Project Project Switch from Looking at the associated A B B to A incremental cashflows, we see that it’s better to 0 -500 -400 -100 switch. That is, A is better 1 325 325 0 than B, which is what the 2 325 200 125 NPV rule tell us. By IRR 19.43% 22.17% 11.8% looking at NPV profiles, we can see why the IRR NPV 64.05 60.74 3.30 rule behaves as it does. $160.00 IRR for A = 19.43% NPV $140.00 $120.00 IRR for B = 22.17% $100.00 Crossover Point = 11.8% $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 IRR assumes reinvestment of positive cash flows during the project at the same calculated IRR. When positive cash flows cannot be reinvested back into the project, IRR overstates returns. That’s why at low discount rates, the higher IRR project looks bad from an NPV standpoint. P.V. Viswanath 31 32 Measures the benefit per unit cost, based on the time value of money It is computed as the NPV of the project divided by initial investment. 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 33 Advantages 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 Disadvantages May lead to incorrect decisions in comparisons of mutually exclusive investments 34 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; this may be because short paybacks allow firms to have funds sooner to invest in other projects without going to the capital markets Even though payback and AAR should not be used to make the final decision, we should consider the project very carefully if they suggest rejection. There may be more risk than we have considered or we may want to pay additional attention to our cash flow estimations. Sensitivity and scenario analysis can be used to help us evaluate our cash flows. From a logical point of view, NPV is best and should be used if possible. P.V. Viswanath