Unit Ten Fin 320F

an advantage of AAR is that it is based on book values, not market values

FALSE its a disadvantage

disadvantage of PI

cannot rank mutually exclusive projects

advantages of payback period method for management

- ideal for minor projects - it allows lower level management to make smaller decisions effectively - the payback period method is easy to understand

According to Graham and Harvey's 1999 survey of 392 CFOs (2001), which two capital budgeting methods are widely used by firm in the US and Canada?

- internal rate of return - net present value

in general, NPV is

- positive for discount rates below the IRR - equal to zero when the discount rate equals the IRR - negative for discount rates above the IRR

1. NPV versus IRR. Zayas, LLC, has identified the following two mutually exclusive projects: a. What is the IRR for each of these projects? If you apply the IRR decision rule, which project should the company accept? Is this decision necessarily correct? b. If the required return is 11 percent, what is the NPV for each of these projects? Which project will you choose if you apply the NPV decision rule? c. Over what range of discount rates would you choose Project A? Project B? At what discount rate would you be indifferent between these two projects? Explain. Year cash flow (a) Cash flow (B) 0 - 78500 -78500 1 43000 21000 2 29000 28000 3 23000 34000 4 21000 41000

1. NPV versus IRR. a. The IRR is the interest rate that makes the NPV of the project equal to zero. Project A is: 0 = -$78,500 + $43,000 / (1 + IRR) + $29,000 / (1 + IRR)2 + $23,000 / (1 + IRR)3 + $21,000 / (1 + IRR)4 Using a financial calculator is quite useful to solve for the IRR. Section 3: Cash Flow Analysis, Calculation 4: Calculate IRR: Variable cash flows. We get the IRR of: IRR = 20.70% Project B is: 0 = -$78,500 + $21,000 / (1 + IRR) + $28,000 / (1 + IRR)2 + $34,000 / (1 + IRR)3 + $41,000 / (1 + IRR)4 IRR = 18.73% Examining the IRRs of the projects, we see that the IRRA is greater than the IRRB, so the IRR decision rule implies accepting Project A. This may not be a correct decision, however, because the IRR criterion has a ranking problem for mutually exclusive projects. To see if the IRR decision rule is correct or not, we need to evaluate the project NPVs. b. The NPV of Project A is: NPVA = -$78,500 + $43,000 / 1.11+ $29,000 / 1.112 + $23,000 / 1.113 + $21,000 / 1.114 NPVA = $14,426.54 And the NPV of Project B is: NPVB = -$78,500 + $21,000 / 1.11 + $28,000 / 1.112 + $34,000 / 1.113 + $41,000 / 1.114 NPVB = $15,012.82 The NPVB is greater than the NPVA, so we should accept Project B. While the initial investment is the same, Project B has higher cash flows and produces a higher NPV. If you can invest in only one project, B is the better—wealth increasing—investment. c. We need to find the discount rate at which the NPVA = NPVB. To find this crossover rate, we subtract the cash flows from one project from the cash flows of the other project. Here, we will subtract the cash flows for Project B from the cash flows of Project A. Once we find these differential cash flows, we find the IRR. The equation for the crossover rate is: 0 = $22,000 / (1 + R) + $1,000 / (1 + R)2 - $11,000 / (1 + R)3 - $20,000 / (1 + R)4 Using our financial calculator we find that R = 12.21% At discount rates above 12.21% choose Project A; for discount rates below 12.21% choose Project B; indifferent between A and B at a discount rate of 12.21%. (Chapter 8, 10)

1. Net Present Value. Concerning NPV: Describe how NPV is calculated and describe the information this measure provides about a sequence of cash flows. What is the NPV criterion decision rule? Why is NPV considered to be a superior method of evaluating the cash flows from a project? Suppose the NPV for a project's cash flows is computed to be $2,500. What does this number represent with respect to the firm's shareholders?

1. Net Present Value. Concerning NPV: a. NPV is the sum of the present values of a project's cash flows. It's a way of doing cost-benefit analysis. For most projects occur at different points in time. A valid comparison is possible only if these cash flows can be restated as of a single point in time. This involves using the opportunity cost, which reflects the basic time value of money (risk free interest rate) and an appropriate risk premium. Again drawing on the concept of cost-benefit analysis, NPV measures whether or not the project increases wealth. Wealth is increased if the inflows exceed the outflows. These inflows and outflows are present values, and thus reflect time and risk, making NPV an especially important decision rule. The NPV decision rule is to accept projects that have a positive NPV, and reject projects with a negative NPV. b. NPV is superior to the other methods of analysis presented in our course because it directly measures a decision's impact on wealth. The only drawback to NPV is that it relies on cash flow and discount rate values that are often estimates and not certain, but this is a problem shared by the other performance criteria as well. A project with NPV = $2,500 implies that the total shareholder wealth of the firm will increase by $2,500 if the project is accepted. This does not mean the shareholders get a check for that amount: it is a statement of the expected increase in wealth given the project. (Chapter 8, 8.5)

1. Payback Period. Concerning payback: a. Describe how the payback period is calculated and describe the information this measure provides about a sequence of cash flows. What is the payback criterion decision rule? b. What are the problems associated with using the payback period as a means of evaluating cash flows? c. What are the advantages of using the payback period to evaluate cash flows? Are there any circumstances under which using payback might be appropriate? Explain.

1. Payback Period. Concerning payback: a. Payback period is simply the break-even point of a series of cash flows. To actually compute the payback period, it is assumed that any cash flow occurring during a given period is realized continuously throughout the period, and not at a single point in time. For example, while you may be paid at the end of the month, you actually earn income for each day worked. The payback is then the point in time for the series of cash flows when the initial cash outlays are fully recovered. Given some predetermined cutoff for the payback period, the decision rule is to accept projects that payback before this cutoff, and reject projects that take longer to payback. b. The worst problem associated with payback period is that it ignores the time value of money. In not using time value, it also does not use an opportunity cost which would reflect the uncertainty of the cash flows. Additionally, the selection of a hurdle point for payback period is an arbitrary exercise that lacks any steadfast rule or method. The payback period is biased towards short-term projects; it fully ignores any cash flows that occur after the cutoff point. c. Despite its shortcomings, payback is often used because the analysis is straightforward and simple. Materiality considerations often warrant a payback analysis as sufficient; maintenance projects are another example where the detailed analysis of other methods is often not needed. Since payback is biased towards liquidity, it may be a useful and appropriate analysis method for short-term projects where cash management is most important. It may also be used when opportunity cost would be difficult to estimate. (Chapter 8, 8.3)

10. Calculating NPV. For the cash flows in the previous problem, what is the NPV at a discount rate of 0 percent? What if the discount rate is 10 percent? If it is 20 percent? If it is 30 percent? year cash flow 0 - 19,400 1 9800 2 11300 3 6900

10. Calculating NPV. The NPV of a project is the PV of the outflows plus by the PV of the inflows. At a zero discount rate (and only at a zero discount rate), the cash flows can be added together across time. So, the NPV of the project at a zero percent required return is: NPV = -$19,400 + 9,800 + 11,300 + 6,900 NPV = $8,600 The NPV at a 10 percent required return is: NPV = -$19,400 + $9,800 / 1.10 + $11,300 / 1.102 + $6,900 / 1.103 NPV = $4,032.01 The NPV at a 20 percent required return is: NPV = -$19,400 + $9,800 / 1.20 + $11,300 / 1.202 + $6,900 / 1.203 NPV = $606.94 And the NPV at a 30 percent required return is: NPV = -$19,400 + $9,800 / 1.30 + $11,300 / 1.302 + $6,900 / 1.303 NPV = -$2,034.50 Notice that as the required return increases, the NPV of the project decreases. This will always be true for projects with conventional cash flows. Conventional cash flows are negative at the beginning of the project and positive throughout the rest of the project. Hope you had your financial calculator for this one. (Chapter 8, 9)

11. Calculating Profitability Index. What is the profitability index for the following set of cash flows if the relevant discount rate is 10 percent? What if the discount rate is 15 percent? If it is 22 percent? year cash flow 0 -27500 1 15800 2 13600 3 8300

11. Calculating Profitability Index. The profitability index is defined as the PV of the future cash flows divided by the initial investment. The equation for the profitability index at a required return of 10 percent is: PI = ($15,800 / 1.10 + $13,600 / 1.102 + $8,300 / 1.103) / $27,500 PI = $31,839.22/$27,500 PI = 1.158 The equation for the profitability index at a required return of 15 percent is: PI = ($15,800 / 1.15 + $13,600 / 1.152 + $8,300 / 1.153) / $27,500 PI = $29,480.07/$27,500 PI = 1.072 The equation for the profitability index at a required return of 22 percent is: PI = ($15,800 / 1.22 + $13,600 / 1.222 + $8,300 / 1.223) / $27,500 PI = $26,659/$27,500 PI = .969 We would accept the project if the required return were 10 percent or 15 percent since the PI is greater than one. We would reject the project if the required return were 22 percent since the PI is less than one. The present values of these cash flows can be computed by using our financial calculator. Sectin 3: Cash Flow Analysis, Calculation 3. Calculate NPV with variable cash flows. Just enter zero for the time zero cash flows and solve for NPV. (Chapter 8, 13)

2. Average Accounting Return. Concerning AAR: a. Describe how the average accounting return is usually calculated and describe the information this measure provides about a sequence of cash flows. What is the AAR criterion decision rule? b. What are the problems associated with using the AAR as a means of evaluating a project's cash flows? What underlying feature of AAR is most troubling to you from a financial perspective? Does the AAR have any redeeming qualities?

2. Average Accounting Return. Concerning AAR: a. The average accounting return is interpreted as an average measure of the accounting performance of a project over time, computed as some average profit measure due to the project divided by some average balance sheet value for the project. This text computes AAR as average net income with respect to average (total) book value. Given some predetermined cutoff for AAR, the decision rule is to accept projects with an AAR in excess of the target measure, and reject all other projects. b. AAR is not a measure of cash flows and market value, but a measure of financial statement accounts that often bear little semblance to the relevant value of a project. In addition, the selection of a cutoff is arbitrary, and the time value of money is ignored. For a financial manager, both the reliance on accounting numbers rather than relevant market data and the exclusion of time value of money considerations are troubling. Despite these problems, AAR continues to be used in practice because (1) the accounting information is usually available, (2) analysts often use accounting ratios to analyze firm performance, and (3) managerial compensation is often tied to the attainment of certain target accounting ratio goals. (Chapter 8, 8.4)

2. Internal Rate of Return. Concerning IRR: Describe how the IRR is calculated, and describe the information this measure provides about a sequence of cash flows. What is the IRR criterion decision rule? What is the relationship between IRR and NPV? Are there any situations in which you might prefer one method over the other? Explain. Despite its shortcomings in some situations, why do most financial managers use IRR along with NPV when evaluating projects? Can you think of a situation in which IRR might be a more appropriate measure to use than NPV? Explain.

2. Internal Rate of Return. Concerning IRR: a. The IRR is the rate of return earned on an investment. It is the discount rate that causes the NPV of a series of cash flows to be equal to zero. IRR can thus be interpreted as a financial break-even rate of return; at the IRR discount rate, the net value of the project is zero. The IRR decision rule is to accept projects with IRRs greater than the discount rate, and to reject projects with IRRs less than the discount rate. b. IRR is the interest rate that a project earns, whereas the required rate of return is the opportunity cost of the project: the rate of return the project should earn given its risk. NPV directly uses the opportunity cost to evaluate the project's cash flows, and is thus is preferred in all situations to IRR. For stand-alone projects with conventional cash flows, IRR and NPV are interchangeable techniques; however, IRR can lead to ambiguous results if there are non-conventional cash flows, and also ambiguously ranks some mutually exclusive projects. c. IRR is frequently used because it is easier for many financial managers and analysts to rate performance in relative terms, such as "12%", than in absolute terms, such as "$46,000." IRR may be a preferred method to NPV in situations where an appropriate discount rate is unknown or uncertain; in this situation, IRR would provide more information about the project than would NPV. (Chapter 8, 8.6)

2. Problems with Profitability Index. The Matterhorn Corporation is trying to choose between the following two mutually exclusive design projects: year cash flow (I) Cash flow (II) 0 - 78000 - 28,800 1 28, 300 9600 2 34800 17400 3 43700 15600 a. If the required return is 11 percent and the company applies the profitability index decision rule, which project should the firm accept? b. If the company applies the NPV decision rule, which project should it take? c. Explain why your answers in parts (a) and (b) are different.

2. Problems with Profitability Index. a. The profitability index is defined as the PV of the future cash flows divided by the initial investment. The equation for the profitability index for each project is: PII = ($28,300 / 1.11 + $34,800 / 1.112 + $43,700 / 1.113) / $78,000 PII = 1.099 PIII = ($9,600 / 1.11 + $17,400 / 1.112 + $15,600 / 1.113) / $28,800 PIII = 1.187 The profitability index decision rule implies that we accept Project II, since PIII is greater than the PII. b. The NPV of each project is: NPVI = -$78,000 + $28,300 / 1.11 + $34,800 / 1.112 + $43,700 / 1.113 NPVI = $7,693.02 NPVII = -$28,800 + $9,600 / 1.11 + $17,400 / 1.112 + $15,600 / 1.113 NPVII = $5,377.46 The NPV decision rule implies accepting Project I, since the NPVI is greater than the NPVII. c. Profitability Index, like IRR, is a relative measure. For standard independent projects NPV, IRR and PI should give the same accept/reject decision. For mutually exclusive projects the relative rankings of IRR and PI may differ from the ranking given by NPV. Using the profitability index to compare mutually exclusive projects can be ambiguous when the magnitudes of the cash flows for the two projects are of different scale. In this problem, Project I is roughly 2.5 times as large as Project II and produces a larger NPV, yet the profitability index criterion implies that Project II is more acceptable. (Chapter 8, 14)

3. Calculating Payback. Global Toys Inc. imposes a payback cutoff of three years for its international investment projects. If the company has the following two projects available, should it accept either of them? year cash flow (A) Cash flow (B) 0 -60,000 - 105,0000 1 23,000 21,0000 2 28000 26000 3 19000 29000 4 9000 260000

3. Calculating Payback. Payback measures the time it takes to recoup a projects initial investments. Project A This project requires an investment of $60,000 today. The first two years have inflows totaling $51,000. Cash flows = $23,000 + 28,000 = $51,000 The cash flows are still short by $9,000 of recapturing the initial investment, and we need 47% of the third year to get this last $9,000. $9,000 / $19,000 = .47 The payback for Project A is: Payback = 2.47 years Project B This project requires an initial investment of $105,000. The first three years have inflows totaling $51,000. Cash flows = $21,000 + 26,000 + 29,000 = $76,000 The cash flows are still short by $29,000 of recapturing the initial investment, and we need 11% of the third year to get this last $29,000. $29,000 / $260,000 = .11 The payback for Project B is: Payback = 3.11 years Using the payback criterion and a cutoff of 3 years, accept Project A and reject Project B. (Chapter 8, 3)

3. NPV and Profitability Index. Robben Manufacturing has the following two possible projects. The required return is 12 percent. year project y project z 0 - 43,400 - 78,000 1 19,800 32,000 2 17,500 30,100 3 20,700 29,500 4 14,600 27,300 a. What is the profitability index for each project? b. What is the NPV for each project? c. Which, if either, of the projects should the company accept?

3. NPV and Profitability Index a. The profitability index for each project is: Y: PI = ($19,800 / 1.12 + $17,500 / 1.122 + $20,700 / 1.123 + $14,600 / 1.124) / $43,400 PI = 1.282 Z: PI = ($32,000 / 1.12 + $30,100 / 1.122 + $29,500 / 1.123 + $27,300 / 1.124) / $78,000 PI = 1.166 Profitability index criterion implies accept Project Y because its PI is greater than Project Z's. b. The NPV for each project is: Y: NPV = -$43,400 + $19,800 / 1.12 + $17,500 / 1.122 + $20,700 / 1.123 + $14,600 / 1.124 NPV = $12,241.88 Z: NPV = -$78,000 + $32,000 / 1.12 + $30,100 / 1.122 + $29,500 / 1.123 + $27,300 / 1.124 NPV = $12,914.13 NPV criterion implies we accept Project Z because Project Z has a higher NPV than Project Y. c. Accept Project Z since the NPV is higher. As we said in problem 2, PI is a relative measure and may not lead to the best choice. This potential conflict between PI and NPV is present when the projects are mutually exclusive and differ in size or timing of the cash flows. (Chapter 8, 17)

3. Profitability Index. Concerning the profitability index: a. Describe how the profitability index is calculated and describe the information this measure provides about a sequence of cash flows. What is the profitability index decision rule? b. What is the relationship between the profitability index and the NPV? Are there any situations in which you might prefer one method over the other? Explain.

3. Profitability Index. Concerning the profitability index: a. The profitability index is the present value of the future cash flows, discounted by the opportunity cost, divided by the initial investment. It measures the wealth created per dollar invested, providing a measure of the relative profitability of a project. The profitability index decision rule is to accept projects with a PI greater than one, and to reject projects with a PI less than one. A PI greater than one indicates that the project will return more than a dollar for each dollar invested, with this comparison using proper time value analysis. b. Whereas NPV measures the total wealth creation of a project, PI gives the wealth creation per dollar invested. Most firms, like all organizations and most everyone other than Warren Buffet or Bill Gates, has limited capital. As we will see in Lesson 2, if a firm has a basket of positive NPV projects and is subject to capital rationing, PI may provide a good ranking measure of the projects, indicating the "bang for the buck" of each particular project. (Chapter 8, 8.7)

4. Calculating AAR. You're trying to determine whether or not to expand your business by building a new manufacturing plant. The plant has an installation cost of $12.5 million, which will be depreciated straight-line to zero over its four-year life. If the plant has projected net income of $1,368,000, $1,935,000, $1,738,000, and $1,310,000 over these four years, what is the project's average accounting return (AAR)?

4. AAR is the average net income divided by the average book value. The average net income for this project is: Average net income = ($1,368,000 + 1,935,000 + 1,738,000 + 1,310,000)/4 = $1,587,750 And the average book value is: Average book value = ($12,500,000 + 0)/2 = $6,250,000 So, the AAR for this project is: AAR = Average net income / Average book value = $1,587,750 / $6,250,000 = .2540, or 25.40% Let's summarize the two traditional decision rules. The payback approach is probably the simplest, followed by the AAR. These measures don't require a discount rate. While this makes these measures a bit easier to use, the lack of a discount rate also means that the projects are not evaluated for risk. A manager might see a project with a good payback, but not realize that the project might be quite risky. The AAR does not take time value or risk into account, and uses historic revenues and expenses. (Chapter 8, 4)

4. Capital Budgeting Problems. What are some of the difficulties that might come up in actual applications of the various criteria we discussed in this course. Which one would be the easiest to implement in actual applications? The most difficult?

4. Capital Budgeting Problems. The single biggest difficulty, by far, is coming up with reliable cash flow estimates. Every company operates in a market environment and is subject to changes in changes to fiscal policies and regulations not just for their government, but major governments throughout the world. Technology, consumer preferences and competitive pressures all make cash flow estimates difficult. Determining an appropriate discount rate is also not a simple task. Most major governments have an active monetary and exchange-rate policy that affect interest rates. The discount rate is also subject to inflationary pressures. We have not seen inflation get out of hand in this century, but have experienced inflation shocks in the past. While these are difficulties, far more dangerous difficulties would occur if managers did not use proper time value decision rules. (Chapter 8, 8.10)

5. Capital Budgeting in Not-for-Profit Entities. Are the capital budgeting criteria we discussed applicable to not-for-profit corporations? How should such entities make capital budgeting decisions? What about the U.S. Government? Should it evaluate spending proposals using these techniques?

5. Capital Budgeting in Not-for-Profit Entities. Capital budgeting is crucial for not-for-profit entities and governments. Non-profits need to allocate limited capital efficiently to accomplish their goals, just as for-profits do. Sites such as Charity Navigator, www.charitynavigator.org and Give Well, www.givewell.org exist to provide information to prospective donors. Charity Navigator had over 7 million visitors last year, so there is interest in the efficient use of donated funds. Capital budgeting techniques can help charities be more efficient and thus attract more donations! It is frequently the case that the "revenues" from not-for-profit ventures are not tangible, but rather benefits that are difficult to measure, such as quality of life for the disabled. These organizations also have no stock price or market determined discount rate to use in their decisions. However, like for-profit corporations, cost-benefit analysis is important and must be done as effectively as possible given these limitations. Finally, realistic cost/benefit analysis should definitely be used by the U.S. government and would go a long way toward balancing the budget! In fact, cost-benefit analysis is often written into the laws passed by Congress and state legislatures. The major difficulty here is that government benefits/contracts/payments for some groups are considered "fat" by others, so the allocation is often done along political, not economic or true social lines. (Chapter 8, 8.11)

6. Calculating IRR. A firm evaluates all of its projects by applying the IRR rule. If the required return is 11 percent, should the firm accept the following project? year cash flow 0 -168,500 1 86,000 2 91,000 3 53,000

6. Calculating IRR. The IRR is the rate of return earned on an investment. For our simple one-period investment the IRR is: IRR for multiperiod cash flows is best done with a financial calculator. Go to our calculator guide, Section 3: Cash Flow Analysis, Calculation 4: Calculate IRR: Variable cash flows. Plugging in these numbers gives an IRR of 18.8% The required rate of return—the opportunity cost offered on equivalent investments—is 14%. As you would be satisfied with this rate, earning 18.8% is very attractive and you should accept this investment. (Chapter 8, 5)

8. Calculating NPV and IRR. A project that provides annual cash flows of $2,145 for eight years costs $8,450 today. Is this a good project if the required return is 8 percent? What if it's 24 percent? At what discount rate would you be indifferent between accepting the project and rejecting it?

8. Calculating NPV and IRR. This problem integrates NPV and IRR and thus reinforces the elements of the previous two problems. The NPV of a project is the PV of the outflows plus the PV of the inflows. Since the cash inflows are an annuity, the equation for the NPV of this project at an 8 percent required return is: NPV = -$8,450 + $2,145(PVIFA8%, 8) NPV = $3,876.54 At an 8 percent required return, the NPV is positive, so we would accept the project. Going to the calculator guide gives us the efficient way of calculating NPV. Section 3: Cash Flow Analysis, Calculation 1: Calculate NPV with level cash flows. The equation for the NPV of the project at a 24 percent required return is: NPV = -$8,450 + $2,145(PVIFA24%, 8) NPV = -$1,111.48 With the calculator we need only change the discount rate and get the revised NPV. At a 24 percent required return, the NPV is negative, so we would reject the project. While the cash flows have not changed, something has happened to the discount rate. Inflation could have spiked and caused an increase in the risk-free rate, or the project's risk might have increased. Our decision changes with this change in information. We would be indifferent to the project if the required return was equal to the IRR of the project, since at that required return the NPV is zero. The IRR of the project is: 0 = -$8,450 + $2,145(PVIFAIRR, 8) IRR = .1913, or 19.13% By now we know that if the project cash flows are already in our calculator, we need only punch the IRR button to get this answer! The IRR rule agrees with the NPV rule. (Chapter 8, 7)

9. Calculating IRR. What is the IRR of the following set of cash flows? year cash flow 0 - 19,400 1 9800 2 11300 3 6900

9. Calculating IRR. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is: 0 = -$19,400 + $9,800 / (1+IRR) + $11,300 / (1+IRR)2 + $6,900 / (1+IRR)3 Using the calculator guide: Section 3: Cash Flow Analysis, Calculation 4: Variable cash flows, gives us the IRR. IRR = 22.09% (Chapter 8, 8)

payback period rule _____________ a project if it has payback period that is less than or equal to a particular cutoff date

Accepts

The Management of Premium Manufacturing Company is evaluating two forklift systems to use in its plant that produces the towers for a windmill power farm. The costs and the cash flows from these systems are shown below. If the company uses a 12 percent discount rate for all projects, determine which forklift system should be purchased using the net present value (NPV) approach.

NPV for Otis Forklifts: NPV = PVinflows - PVoutflows $337,075 = $979,225/(1.12) + $1,358,886/(1.12)^2 + $2,111,497/(1.12)^3 - $3,123,450 NPV for Craigmore Forklifts: $90,606 = $875/236/(1.12) + $1,765,225/(1.12)^2 + $2,865,110/(1.12)^3 - $4,137,410 As these are mutually-exclusive projects, Premium should purchase Otis forklift since it has a larger NPV.

a firm is evaluating two possible projects, both of which require the use of the same production facilities, these projects would be considered

mutually exclusive

average accounting return ARR

average net income/ average book value

according to the average account return rule, a project is acceptable if its average accounting return exceeds

- a target average accounting return

weakness of payback method

- cut off date is arbitrary - time value of money principles are ignored - cash flows received after the payback period are ignored

IRR rule

- reject a project if the IRR is less than the required return

7. Calculating NPV. For the cash flows in the previous problem, suppose the firm uses the NPV decision rule. At a required return of 9 percent, should the firm accept this project? What if the required return was 21 percent? year cash flow 0 -168,500 1 86,000 2 91,000 3 53,000

6. Calculating NPV. I'd like to use this problem to not only calculate NPV but review the inputs and logic of this very important decision rule. The NPV of a project is the PV of the outflows minus by the PV of the inflows. The equation for the NPV of this project at a 9 percent required return is: NPV = -$168,500 + $86,000 /1.09 + $91,000 /(1.09)2 + $53,000 /(1.09)3 = -$168,500 + $196,418 = $27,918 As the NPV is positive at 9%, the project's benefits exceed the costs and we should adopt the project. Here, again, is where the financial calculator comes in handy. Go back to the calculator guide. Section 3: Cash Flow Analysis, Calculation 3: Calculate NPV with variable cash flows. In fact, if you already have the cash flows entered from problem 6, you can use those to calculate NPV. Changing the discount rate is a breeze. Just enter the new discount rate and ask for the revised NPV. At a 21% percent required return, the NPV is -$5,354. While the cash flows did not change, the discount rate did increase substantially, so we would reject the project. While this is a simple computational problem, it demonstrates some major economic relationships. The opportunity cost: Economic decisions are comparisons of alternatives. We generally compare investments or other economic decisions in terms of the rate of return earned. The opportunity cost is the rate we should earn on equivalent investments, with equivalent being largely based on risk, which we examined in Unit 5. Economic value: We calculate how much the future cash flows of an investment are worth to us today: their present value, which takes into account the amount of the cash flows, when they occur, and their risk. The present value is the economic value. NPV: Note that the PVInflows, a major component of the NPV calculation is, by the previous definition, the economic value of the benefits (expected future cash flows). NPV thus calculates the economic value of an investment and then subtracts the amount you'd have to pay to get the future cash flows (economic value) of the investment. If the value exceeds the cost, it's a good investment. A good deal is a good deal: When the opportunity cost was 9%, both the NPV and IRR decision rules recommended that the project be accepted. With a discount rate of 21% we get a negative NPV. The IRR does not change—it's calculation does not depend on the opportunity cost and thus remains at 18.8%--however, with an opportunity cost of 21% the IRR rule would also reject this project. In this problem, and for many types of projects both the NPV and IRR decision rules will agree. However, as we will see in Lesson 2, this is not always the case! Relative vs. absolute measures: NPV is an absolute dollar measure of the wealth increase (addition to cash purchasing power) a decision is expected to produce. IRR is a relative measure, the rate of increase of an investment. We mention this distinction now, as it will have a major impact on the usefulness of these decision rules when examining some of the special capital budgeting cases in Lesson 2. (Chapter 8, 6)

An engineer is considering upgrading four production-lines. She has determined that upgrading all four lines is economically justifiable and proposes to invest the $64,000 necessary to make these improvements. Her boss declines her request for all of the funds and states she may spend only $40,000 for improvements this year. Given her discount rate of 8%, what is the highest NPV she can obtain from her total investment? Do not enter dollar sign or commas, just the number. Project Initial NPV Investment A $12,000 $1,250 B $15,000 $1,150 C $12,000 $1,640 D $25,000 $2,840

As we are interested in creating the highest NPV given our limited funds, we will use PI to rank the projects by the wealth created per dollar invested. Begin by ranking the projects by their PI. While not given the present value of inflows, we know that as NPV = PVInflows - PVOutlflows, the present value of the inflows can be obtained as: PVInflows = NPV + PVOutlflows,. Using this trick we can calculate the PIs. Project PVInflows / PVOutlfows PI Rank A $13,250/$12,000 = 1.10 3 B $16,150/$15,000 = 1.08 4 C $13,640/$12,000 = 1.14 1 D $27,840/$25,000 = 1.11 2 As PI measures the NPV per dollar of investment and is a relative measure of wealth created, we would choose the the highest PI, then next highest, etc. This would result in the engineer fully investing in projects C and D. C + D $12,000 $25,000 = $37,000 This leaves $3,000 remaining for additional investment. $40,000 - $37,000 = $3,000 The engineer would invest this $3,000 in Project A, which would allow her to obtain 25% of A. $3,000/$12,000 = 0.25 or 25%. Investing in all of C and D and 25% of A would use up the total capital budget: $40,000 This would produce a total NPV: $4,792.50 $1,640 + $2,840 + $1,250(0.25) This is the maximum possible NPV for the $40,000 investment. The engineer has done the best she could do with limited funds.

Our engineer is now considering three new production lines. While each of these lines appear to have a positive NPV, their total cost would be $39 million. Her capital budget cannot exceed $30 million. The designs on each line have been optimally engineered, so no further design changes will be possible: these projects are not divisible. Given her discount rate of 8%, what projects should she invest in? Project Initial NPV Investment A $12 $1.250 B $15 $1.150 C $12 $1.640

With a capital budget of $30 million she can't take on all projects. Additionally, each project must be accepted or rejected as a whole, so we cannot take part of a project. The engineer must therefore identify the portfolios of assets that are acceptable. This would produce the following alternatives. Project/Projects Initial NPV Investment A $12 $1.2 B $15 $1.1 C $12 $1.6 A+B $27 $2.3 A+C $24 $2.8 B+C $27 $2.7 A+B+C $39 $3.9 A+B+C is not on the table because it would exceed the capital budget. The optimal choice is A+C, which produces the highest NPV. She could invest more in A+B, but this produces a lower total NPV. The objective is to increase wealth, not spend money!

PI rule for an independent project is to _____ the project if the PI is greater than 1

accept

how does timing and the size of cash flow affect the payback method?

an increase in the size of the first cash inflow will decease the payback period, all else held constant