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# Ross, Chapter 8: NPV

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• T is willing to buy a car. ---all we require is a down payment of \$3000. Then you can borrow \$12000 from our finance company at 12%.He'll make monthly payments of 266.93 for 5 years,totaling 16,015.80. If you do that, you get to keep your \$12000.Say, T keeps this money in a money market account that pays 8% compounded quarterly. In 5 yrs, the \$12,000 will grow to \$17831.40. Hence,T will be better off by \$1815.60 than if he pays the additional \$12,000 in cash. Is this offer to good to be true.

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• This example will be used for each of the decision rules so that the students can compare the different rules and see that conflicts can arise. This illustrates the importance of recognizing which decision rules provide the best information for making decisions that will increase owner wealth.
• We learn how to estimate the cash flows in chapter 9. We learn how to estimate the required return in chapter 12.
• Again, the calculator used for the illustration is the TI- BA-II plus. The basic procedure is the same; you start with the year 0 cash flow and then enter the cash flows in order. F01, F02, etc. are used to set the frequency of a cash flow occurrence. Many of the calculators only require you to use that if the frequency is something other than 1.
• The answer to all of these questions is yes
• Click on the Excel icon to go to an embedded Excel worksheet that has the cash flows along with the right and wrong way to compute NPV. Click on the cell with the solution to show the students the difference in the formulas.
• The payback period is year 3 if you assume that the cash flows occur at the end of the year, which we do with all of the other decision rules. If we assume that the cash flows occur evenly throughout the year, then the project pays back in 2.34 years.
• The answer to all of these questions is no.
• The example in the book uses straight line depreciation to a zero salvage; that is why you can take the initial investment and divide by 2. If you use MACRS, you need to compute the BV in each period and take the average in the standard way.
• Students may ask where you came up with the 25%. Point out that this is one of the drawbacks of this rule. There is no good theory for determining what the return should be. We generally just use some rule of thumb.
• The answer to all of these questions is no. In fact, this rule is even worse than the payback rule in that it doesn’t even use cash flows for the analysis. It uses net income and book value.
• The IRR rule is very important. Management, and individuals in general, often has a much better feel for percent returns and the value that is created than they do for dollar increases. A dollar increase doesn’t seem to provide as much information if we don’t know what the initial expenditure was.
• Many of the financial calculators will compute the IRR as soon as it is pressed; others require that you press compute.
• The answer to all of these questions is yes, although it is not always as obvious. The IRR rule accounts for time value because it is finding the rate of return that equates all of the cash flows on a time value basis. The IRR rule accounts for the risk of the cash flows because you compare it to the required return, which is determined by the risk of the project. The IRR rule provides an indication of value because we will always increase value if we can earn a return greater than our required return. We should consider the IRR rule as our primary decision criteria, but as we will see, it has some problems that the NPV does not have. That is why we end up choosing the NPV as our ultimate decision rule.
• You should point out, however, that if you get a very large IRR, you should go back and look at your cash flow estimation again. In competitive markets, extremely high IRRs should be rare.
• So, what should we do – we have two rules that indicate to accept and two that indicate to reject.
• Click on the Excel icon to go to an embedded spreadsheet so that you can illustrate how to compute IRR on the spreadsheet.
• NPV = 132,000 / 1.15 + 100,000 / (1.15) 2 – 150,000 / (1.15) 3 – 90,000 = 1,769.54 Calculator: CF 0 = -90,000; C01 = 132,000; F01 = 1; C02 = 100,000; F02 = 1; C03 = -150,000; F03 = 1; I = 15; CPT NPV = 1,769.54 If you compute the IRR on the calculator, you get 10.11% because it is the first one that you come to. So, if you just blindly use the calculator without recognizing the uneven cash flows, NPV would say to accept and IRR would say to reject.
• You should accept the project if the required return is between 10.11% and 42.66%
• As long as we do not have limited capital, we should choose project A. Students will often argue that you should choose B because then you can invest the additional \$100 in another good project, say C. The point is that if we do not have limited capital, we can invest in A and C and still be better off. If we have limited capital, then we will need to examine which combination of projects with project A provides the highest NPV and which combination of projects with project B provides the highest NPV. You then go with the set that will create the most value. If you have limited capital and a large number of mutually exclusive projects, then you will want to set up a computer program to determine the best combination of projects within the budget constraints. The important point is that we DO NOT use IRR to choose between projects regardless of whether or not we have limited capital.
• If the required return is less than the crossover point of 11.8%, then you should choose A If the required return is greater than the crossover point of 11.8%, and doesn’t exceed B’s IRR of 22.17%, then you should choose B
• 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. The fact that payback is commonly used as a secondary criteria may be because short paybacks allow firms to have funds sooner to invest in other projects without going to the capital markets
• Payback period = 4 years NPV = -2,758.72 IRR = 7.93%
• NPV = -\$6,472; reject the project since it would lower the value of the firm. IRR = 11.81%, so reject the project since it would tie up investable funds in a project that will provide insufficient return. The NPV and IRR decision rules will provide the same decision for all independent projects with conventional/normal cash flow patterns. If a project adds value to the firm (i.e., has a positive NPV), then it must be expected to provide a return above that which is required. Both of those justifications are good for shareholders; sadly, neither is the case for this project. Other questions to pose: Payback of the project? 5 years PI of the project? .9935 (benefits are below the costs) MIRR of the project? All three methods are the same for this conventional project, and it’s basically a moot point, but MIRR = 11.91% (higher than the IRR due to the negative NPV of the project; the reinvestment rate is above the discount rate in this case).
• ### Ross, Chapter 8: NPV

1. 1. Chapter 8 Net Present Value and Other Investment Criteria
2. 2. Key Concepts and Skills <ul><li>Understand the payback rule and its shortcomings </li></ul><ul><li>Understand accounting rates of return and their problems </li></ul><ul><li>Understand the internal rate of return and its strengths and weaknesses </li></ul><ul><li>Understand the net present value rule and why it is the best decision criteria </li></ul>
3. 3. Chapter Outline <ul><li>Net Present Value </li></ul><ul><li>The Payback Rule </li></ul><ul><li>The Average Accounting Return </li></ul><ul><li>The Internal Rate of Return </li></ul><ul><li>The Profitability Index </li></ul><ul><li>The Practice of Capital Budgeting </li></ul>
4. 4. Good Decision Criteria <ul><li>We need to ask ourselves the following questions when evaluating decision criteria </li></ul><ul><ul><li>Does the decision rule adjust for the time value of money? </li></ul></ul><ul><ul><li>Does the decision rule adjust for risk? </li></ul></ul><ul><ul><li>Does the decision rule provide information on whether we are creating value for the firm? </li></ul></ul>
5. 5. Project Example Information <ul><li>You are looking at a new project and you have estimated the following cash flows: </li></ul><ul><ul><li>Year 0: CF = -165,000 </li></ul></ul><ul><ul><li>Year 1: CF = 63,120; NI = 13,620 </li></ul></ul><ul><ul><li>Year 2: CF = 70,800; NI = 3,300 </li></ul></ul><ul><ul><li>Year 3: CF = 91,080; NI = 29,100 </li></ul></ul><ul><ul><li>Average Book Value = 72,000 </li></ul></ul><ul><li>Your required return for assets of this risk is 12%. </li></ul>
6. 6. Net Present Value <ul><li>The difference between the market value of a project and its cost </li></ul><ul><li>How much value is created from undertaking an investment? </li></ul><ul><ul><li>The first step is to estimate the expected future cash flows. </li></ul></ul><ul><ul><li>The second step is to estimate the required return for projects of this risk level. </li></ul></ul><ul><ul><li>The third step is to find the present value of the cash flows and subtract the initial investment. </li></ul></ul>
7. 7. NPV Decision Rule <ul><li>If the NPV is positive, accept the project </li></ul><ul><li>A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners. </li></ul><ul><li>Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal. </li></ul>
8. 8. Computing NPV for the Project <ul><li>Using the formulas: </li></ul><ul><ul><li>NPV = 63,120/(1.12) + 70,800/(1.12) 2 + 91,080/(1.12) 3 – 165,000 = \$12,627.41 </li></ul></ul><ul><li>Using the calculator: </li></ul><ul><ul><li>CF 0 = -165,000; C01 = 63,120; F01 = 1; C02 = 70,800; F02 = 1; C03 = 91,080; F03 = 1; NPV; I = 12; CPT NPV = 12,627.41 </li></ul></ul><ul><li>Do we accept or reject the project? </li></ul>
9. 9. Decision Criteria Test - NPV <ul><li>Does the NPV rule account for the time value of money? </li></ul><ul><li>Does the NPV rule account for the risk of the cash flows? </li></ul><ul><li>Does the NPV rule provide an indication about the increase in value? </li></ul><ul><li>Should we consider the NPV rule for our primary decision criteria? </li></ul>
10. 10. Calculating NPVs with a Spreadsheet <ul><li>Spreadsheets are an excellent way to compute NPVs, especially when you have to compute the cash flows as well. </li></ul><ul><li>Using the NPV function </li></ul><ul><ul><li>The first component is the required return entered as a decimal </li></ul></ul><ul><ul><li>The second component is the range of cash flows beginning with year 1 </li></ul></ul><ul><ul><li>Subtract the initial investment after computing the NPV </li></ul></ul>
11. 11. Payback Period <ul><li>How long does it take to get the initial cost back in a nominal sense? </li></ul><ul><li>Computation </li></ul><ul><ul><li>Estimate the cash flows </li></ul></ul><ul><ul><li>Subtract the future cash flows from the initial cost until the initial investment has been recovered </li></ul></ul><ul><li>Decision Rule – Accept if the payback period is less than some preset limit </li></ul>
12. 12. Computing Payback For the Project <ul><li>Assume we will accept the project if it pays back within two years. </li></ul><ul><ul><li>Year 1: 165,000 – 63,120 = 101,880 still to recover </li></ul></ul><ul><ul><li>Year 2: 101,880 – 70,800 = 31,080 still to recover </li></ul></ul><ul><ul><li>Year 3: 31,080 – 91,080 = -60,000 project pays back during year 3 </li></ul></ul><ul><ul><li>Payback = 2 years + 31,080/91,080 = 2.34 years </li></ul></ul><ul><li>Do we accept or reject the project? </li></ul>
13. 13. Decision Criteria Test - Payback <ul><li>Does the payback rule account for the time value of money? </li></ul><ul><li>Does the payback rule account for the risk of the cash flows? </li></ul><ul><li>Does the payback rule provide an indication about the increase in value? </li></ul><ul><li>Should we consider the payback rule for our primary decision criteria? </li></ul>
14. 14. Advantages and Disadvantages of Payback <ul><li>Advantages </li></ul><ul><ul><li>Easy to understand </li></ul></ul><ul><ul><li>Adjusts for uncertainty of later cash flows </li></ul></ul><ul><ul><li>Biased towards liquidity </li></ul></ul><ul><li>Disadvantages </li></ul><ul><ul><li>Ignores the time value of money </li></ul></ul><ul><ul><li>Requires an arbitrary cutoff point </li></ul></ul><ul><ul><li>Ignores cash flows beyond the cutoff date </li></ul></ul><ul><ul><li>Biased against long-term projects, such as research and development, and new projects </li></ul></ul>
15. 15. Average Accounting Return <ul><li>There are many different definitions for average accounting return </li></ul><ul><li>The one used in the book is: </li></ul><ul><ul><li>Average net income / average book value </li></ul></ul><ul><ul><li>Note that the average book value depends on how the asset is depreciated. </li></ul></ul><ul><li>Need to have a target cutoff rate </li></ul><ul><li>Decision Rule: Accept the project if the AAR is greater than a preset rate. </li></ul>
16. 16. Computing AAR For the Project <ul><li>Assume we require an average accounting return of 25% </li></ul><ul><li>Average Net Income: </li></ul><ul><ul><li>(\$13,620 + 3,300 + 29,100) / 3 = \$15,340 </li></ul></ul><ul><li>AAR = \$15,340 / 72,000 = .213 = 21.3% </li></ul><ul><li>Do we accept or reject the project? </li></ul>
17. 17. Decision Criteria Test - AAR <ul><li>Does the AAR rule account for the time value of money? </li></ul><ul><li>Does the AAR rule account for the risk of the cash flows? </li></ul><ul><li>Does the AAR rule provide an indication about the increase in value? </li></ul><ul><li>Should we consider the AAR rule for our primary decision criteria? </li></ul>
18. 18. Advantages and Disadvantages of AAR <ul><li>Advantages </li></ul><ul><ul><li>Easy to calculate </li></ul></ul><ul><ul><li>Needed information will usually be available </li></ul></ul><ul><li>Disadvantages </li></ul><ul><ul><li>Not a true rate of return; time value of money is ignored </li></ul></ul><ul><ul><li>Uses an arbitrary benchmark cutoff rate </li></ul></ul><ul><ul><li>Based on accounting net income and book values, not cash flows and market values </li></ul></ul>
19. 19. Internal Rate of Return <ul><li>This is the most important alternative to NPV </li></ul><ul><li>It is often used in practice and is intuitively appealing </li></ul><ul><li>It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere </li></ul>
20. 20. IRR – Definition and Decision Rule <ul><li>Definition: IRR is the return that makes the NPV = 0 </li></ul><ul><li>Decision Rule: Accept the project if the IRR is greater than the required return </li></ul>
21. 21. Computing IRR For the Project <ul><li>If you do not have a financial calculator, then this becomes a trial-and-error process </li></ul><ul><li>Calculator </li></ul><ul><ul><li>Enter the cash flows as you did with NPV </li></ul></ul><ul><ul><li>Press IRR and then CPT </li></ul></ul><ul><ul><li>IRR = 16.13% > 12% required return </li></ul></ul><ul><li>Do we accept or reject the project? </li></ul>
22. 22. NPV Profile For the Project IRR = 16.13%
23. 23. Decision Criteria Test - IRR <ul><li>Does the IRR rule account for the time value of money? </li></ul><ul><li>Does the IRR rule account for the risk of the cash flows? </li></ul><ul><li>Does the IRR rule provide an indication about the increase in value? </li></ul><ul><li>Should we consider the IRR rule for our primary decision criteria? </li></ul>
24. 24. Advantages of IRR <ul><li>Knowing a return is intuitively appealing </li></ul><ul><li>It is a simple way to communicate the value of a project to someone who doesn’t know all the estimation details </li></ul><ul><li>If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task </li></ul>
25. 25. Summary of Decisions For the Project Accept Internal Rate of Return Reject Average Accounting Return Reject Payback Period Accept Net Present Value Summary
26. 26. Calculating IRRs With a Spreadsheet <ul><li>You start with the cash flows the same as you did for the NPV </li></ul><ul><li>You use the IRR function </li></ul><ul><ul><li>You first enter your range of cash flows, beginning with the initial cash flow </li></ul></ul><ul><ul><li>You can enter a guess, but it is not necessary </li></ul></ul><ul><ul><li>The default format is a whole percent – you will normally want to increase the decimal places to at least two </li></ul></ul>
27. 27. NPV vs. IRR <ul><li>NPV and IRR will generally give us the same decision </li></ul><ul><li>Exceptions </li></ul><ul><ul><li>Nonconventional cash flows – cash flow signs change more than once </li></ul></ul><ul><ul><li>Mutually exclusive projects </li></ul></ul><ul><ul><ul><li>Initial investments are substantially different </li></ul></ul></ul><ul><ul><ul><li>Timing of cash flows is substantially different </li></ul></ul></ul>
28. 28. IRR and Nonconventional Cash Flows <ul><li>When the cash flows change signs more than once, there is more than one IRR </li></ul><ul><li>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 </li></ul><ul><li>If you have more than one IRR, which one do you use to make your decision? </li></ul>
29. 29. Another Example – Nonconventional Cash Flows <ul><li>Suppose an investment will cost \$90,000 initially and will generate the following cash flows: </li></ul><ul><ul><li>Year 1: \$132,000 </li></ul></ul><ul><ul><li>Year 2: \$100,000 </li></ul></ul><ul><ul><li>Year 3: -\$150,000 </li></ul></ul><ul><li>The required return is 15%. </li></ul><ul><li>Should we accept or reject the project? </li></ul>
30. 30. NPV Profile IRR = 10.11% and 42.66%
31. 31. Summary of Decision Rules <ul><li>The NPV is positive at a required return of 15%, so you should Accept </li></ul><ul><li>If you use the financial calculator, you would get an IRR of 10.11% which would tell you to Reject </li></ul><ul><li>You need to recognize that there are nonconventional cash flows, and that you need to look at the NPV profile </li></ul>
32. 32. IRR and Mutually Exclusive Projects <ul><li>Mutually exclusive projects </li></ul><ul><ul><li>If you choose one, you can’t choose the other </li></ul></ul><ul><ul><li>Example: You can choose to attend graduate school next year at either Harvard or Stanford, but not both </li></ul></ul><ul><li>Intuitively, you would use the following decision rules: </li></ul><ul><ul><li>NPV – choose the project with the higher NPV </li></ul></ul><ul><ul><li>IRR – choose the project with the higher IRR </li></ul></ul>
33. 33. Example With Mutually Exclusive Projects The required return for both projects is 10%. Which project should you accept and why? 60.74 64.05 NPV 22.17% 19.43% IRR 200 325 2 325 325 1 -400 -500 0 Project B Project A Period
34. 34. NPV Profiles IRR for A = 19.43% IRR for B = 22.17% Crossover Point = 11.8%
35. 35. Conflicts Between NPV and IRR <ul><li>NPV directly measures the increase in value to the firm </li></ul><ul><li>Whenever there is a conflict between NPV and another decision rule, you should always use NPV </li></ul><ul><li>IRR is unreliable in the following situations </li></ul><ul><ul><li>Non-conventional cash flows </li></ul></ul><ul><ul><li>Mutually exclusive projects </li></ul></ul>
36. 36. Modified Internal Rate of Return (MIRR) <ul><li>Compute IRR of modified cash flows </li></ul><ul><li>Controls for some problems with IRR </li></ul><ul><li>Discounting Approach – Discount future outflows to present and add to CF 0 </li></ul><ul><li>Reinvestment Approach - Compound all CFs except the first one forward to end </li></ul><ul><li>Combination Approach – Discount outflows to present; compound inflows to end </li></ul><ul><li>MIRR will be a unique number for each method, but is difficult to interpret; discount/compound rate is externally supplied </li></ul>
37. 37. Example: MIRR <ul><li>Project cash flows: </li></ul><ul><li>Time 0: -\$500 today; Time 1: + \$1,000; Time 2: -\$100 </li></ul><ul><li>Use combined method and RRR = 11% </li></ul><ul><li>PV (outflows) = -\$500 + -\$100/(1.11) 2 = -\$581.16 </li></ul><ul><li>FV (inflow) = \$1,000 x 1.11 = \$1,110 </li></ul><ul><li>MIRR: N=2; PV=-581.16; FV=1,110; CPT I/Y = MIRR = 38.2% </li></ul>
38. 38. Profitability Index <ul><li>Measures the benefit per unit cost, based on the time value of money </li></ul><ul><li>A profitability index of 1.1 implies that for every \$1 of investment, we receive \$1.10 worth of benefits, so we create an additional \$0.10 in value </li></ul><ul><li>This measure can be very useful in situations in which we have limited capital </li></ul>
39. 39. Advantages and Disadvantages of Profitability Index <ul><li>Advantages </li></ul><ul><ul><li>Closely related to NPV, generally leading to identical decisions </li></ul></ul><ul><ul><li>Easy to understand and communicate </li></ul></ul><ul><ul><li>May be useful when available investment funds are limited </li></ul></ul><ul><li>Disadvantages </li></ul><ul><ul><li>May lead to incorrect decisions in comparisons of mutually exclusive investments </li></ul></ul>
40. 40. Capital Budgeting In Practice <ul><li>We should consider several investment criteria when making decisions </li></ul><ul><li>NPV and IRR are the most commonly used primary investment criteria </li></ul><ul><li>Payback is a commonly used secondary investment criteria </li></ul>
41. 41. Quick Quiz <ul><li>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 the required payback is 4 years. </li></ul><ul><ul><li>What is the payback period? </li></ul></ul><ul><ul><li>What is the NPV? </li></ul></ul><ul><ul><li>What is the IRR? </li></ul></ul><ul><ul><li>Should we accept the project? </li></ul></ul><ul><li>What should be the primary decision method? </li></ul><ul><li>When is the IRR rule unreliable? </li></ul>
42. 42. Comprehensive Problem <ul><li>An investment project has the following cash flows: CF0 = -1,000,000; C01 – C08 = 200,000 each </li></ul><ul><li>If the required rate of return is 12%, what decision should be made using NPV? </li></ul><ul><li>How would the IRR decision rule be used for this project, and what decision would be reached? </li></ul><ul><li>How are the above two decisions related? </li></ul>