CHAPTER 10 CAPITAL BUDGETING FOCUS Our focus in this first capital budgeting chapter begins by explaining that the field deals with planning and justifying spending large sums of money on non-routine projects. We then move on to decision making techniques and the associated computations. Cash flow estimation and risk are touched upon in anticipation of detailed treatments in later chapters. PEDAGOGY A brief overview of the cost of capital concept is presented early in the chapter even though it is the subject of Chapter 13. This knowledge is necessary to understand and motivate the capital budgeting models. It relates NPV - IRR procedures to the required rate of return idea, something with which students are already familiar. We explicitly tie NPV and IRR together by emphasizing that the IRR comes from the NPV equation as the interest rate that sets NPV = 0. This helps to develop an overall understanding of both procedures. We also present the Accounting (Average) Rate of Return because it is invariably of interest to operating managers whose performance is measured by accounting results. TEACHING OBJECTIVES After this chapter students should: 1. appreciate the discounted cash flow basis of capital budgeting theory, and 2. be able to make the computations associated with the capital budgeting techniques. They should also be marginally aware of the difficulties associated with estimating cash flows and differences in project risk. Along these lines, care should be taken not to give students the impression that capital budgeting is a precise, engineering-like process that always gives exactly the right answer. OUTLINE I. CHARACTERISTICS OF BUSINESS PROJECTS The nature of projects requiring capital budgeting decisions. A. Project Types and Risk Replacement, expansion, and new venture projects and their order of risk. B. Stand-alone and Mutually Exclusive Projects Projects considered by themselves and in competition with one another. C. Project Cash Flows Representing projects as streams of cash for analysis. D. The Cost of Capital A brief introduction to the concept of cost of capital at this point makes the NPV and IRR techniques easier to understand. II. CAPITAL BUDGETING TECHNIQUES A. Payback Period The payback method explained and illustrated. Its uses and drawbacks are discussed. B. Net Present Value (NPV) The NPV concept and the defining equation. The relationship to shareholder wealth. Calculations, decision rules, and applications. C. Internal Rate of Return (IRR) The IRR concept and the relation to a required rate of return. The defining equation and its relationship to NPV. Decision rules, calculations, and examples. D. Comparing IRR and NPV Which is better and why. Possible conflicts E. NPV and IRR Solutions Using Financial Calculators and Spreadsheets Instruction on using calculators and spreadsheets in capital budgeting. F. Projects With A Single Outflow and Regular Inflows Solution techniques when annuity methods are possible. G. Profitability Index (PI) PI as a variation on the NPV concept. Decision rules, calculations, and examples. H. Comparing Projects with Unequal Lives Chaining and Equivalent Annual Annuity methods. I. Capital Rationing Allocating a limited Capital Budget among available projects. J The Accounting (Average) Rate of Return Not as good as cash flow based methods, but often important to operating managers. QUESTIONS 1. Define mutual exclusivity and describe ways in which projects can be mutually exclusive. Answer: A mutually exclusive decision is one in which the selection of any option precludes the selection of all others. In other words, you can't "do both." Mutual exclusivity can be rooted in either the nature of the project or in the availability of resources. Replacements and many expansion projects tend to be mutually exclusive, because there's just one job to be done. Once the method of getting it accomplished is selected, there are simply no other opportunities. Other expansion projects and most new ventures tend to be mutually exclusive because of resource constraints. The firm usually doesn't have enough money to do everything presented as a viable opportunity. 2. Capital budgeting is based on the idea of identifying incremental cash flows, so overheads aren't generally included. Does this practice create a problem for a firm that over a long period of time takes on a large number of projects that are just barely acceptable under capital budgeting rules? Answer: Yes! This is a major problem in incremental thinking. If everything is incrementally just viable, over a long period the firm can wind up with no income to support necessary overhead. 3. Relate the idea of cost of capital to the opportunity cost concept. Is the cost of capital the opportunity cost of project money? Answer: The cost of capital is an opportunity cost because project funds could always be alternatively used to pay down debt and/or distributed to shareholders as dividends. 4. The payback technique is criticized for not using discounted cash flows. Under what conditions will this matter most? That is, under what patterns of cash flow will payback and NPV or IRR be likely to give different answers? Answer: Recognizing the time value of money will matter most when substantial cash flows are projected in the distant future. The discounting methods reduce the value of those flows a lot relative to payback, which gives them their face value. 5. Explain the rationale behind the NPV method in your own words. Why is a higher NPV conceptually better than a lower one? Answer: The NPV method adds up the PV of all of a project's cash flows thereby calculating its effect on the wealth of the firm (and its shareholders). The more NPV a project has, the bigger is its wealth contribution. It is this direct relation with wealth that makes NPV a very good measure of a project's worth. 6. Projects A and B have approximately the same NPV. Their initial outlays are similar in size. Project A has early positive cash flows, and little or nothing is expected to come in later on. Project B has much larger positive cash flows than A, but they're farther in the future. Can you make any general statement about which project might be better? Answer: The project with the cash flows that come in earlier may be better because of the uncertainty of the future. The large flows predicted far out in time are less likely to come true than modest flows predicted in the short run. In fact, this is a major business problem. People tend to predict marvelous results in the distant future that are often very unrealistic. (We'll have a great deal to say about this in later chapters.) 7. Suppose the present value of cash ins and outs is very close to balanced for a project to build a new $50M factory, so that the NPV is + $25,000. The same company is thinking about buying a new trailer truck for $150,000. The NPV of projected cash flows associated with the truck is also about $25,000. Does this mean that the two projects are comparable? Is one more desirable than the other? How are their IRRs likely to compare? If the cash flows have similar risks are the projects equally risky? (Hint: Think in terms of the size of the investment placed at risk relative to the financial rewards expected.) Answer: Projects of grossly different sizes are not readily comparable. In this case, the factory project is marginal, because its NPV is minimally positive relative to the size of the investment required to undertake it. Conversely, the truck is a pretty good deal because its NPV is substantial relative to the investment required to get it. The factory's IRR would be just a hair above the cost of capital while the truck's IRR would exceed k by quite a bit. The factory is really a risky project because a small unfavorable percentage variation in the cash flows planned could result in a big dollar loss relative to the capital budgeting analysis. 8. Think about the cash flows associated with putting $100,000 in the bank for five years, assuming you draw out the interest each year and then close the account. Now think about a set of hypothetical cash flows associated with putting the same money in a business, operating for five years, and then selling out. Write an explanation of why the IRR on the business project is like the bank's interest rate. How are the investments different? Answer: Both uses of the money involve receiving a series of cash inflows over the five-year period and a large inflow at the end. The IRR is defined as the interest rate that makes the present value of these payments just equal to the initial investment of $100K (project NPV = 0). But the bank's interest rate does exactly the same thing. If we take the present value of the interest payments and the final withdrawal at the bank's interest rate, we'll get the amount of the initial deposit. (This is also exactly like a bond's yield.) There are two major differences between the bank account and the business. The bank account's periodic cash flows will be constant while the businesses are likely to vary. Further, all of the bank's flows are nearly certain while the businesses are subject to considerable risk. 9. What is it about the cash flows associated with business projects that makes the NPV profile slope downward to the right? Would the NPV profile of any randomly selected set of positive and negative flows necessarily slope one way or the other? Why? Answer: The bulk of negative project cash flows are generally in the early years, while most of the positive flows are in the more distant future. This means that the discounting factors make a bigger impact on the distant positives than on the near term negatives. This in turn means larger interest rates shrink the positives more than the negatives because they tend to be further into the future. Hence total NPV becomes less positive (declines) as the interest rate increases. This produces a down sloping curve when a project's NPV is graphed versus the interest rate. A randomly selected series of flows would not tend to slope one way or the other. 10. The following set of cash flows changes sign twice and has two IRR solutions. Identify the sign changes. Demonstrate mathematically that 25% and 400% are both solutions to the IRR equation. On the basis of this example, why would you expect multiple solutions to be an unusual problem in practice? Answer: The sign changes from minus to plus from C0 to C1 and from plus to minus from C1 to C2. It's not likely that anyone would mistake the 400% solution as real. Further, multiple sign changes with substantial negative flows in the future are rare. 11. Under what conditions will the IRR and NPV methods give conflicting results for mutually exclusive decisions? Will they ever give conflicting results for stand-alone decisions? Why? Answer: Results can conflict when the project's NPV profiles cross in the first quadrant of the (k, NPV) plane. The methods will never give conflicting results for standalone decisions. Examination of a graph shows that for a single down-sloping NPV profile, IRR>k always implies a positive NPV and IRR 0. PI = $38,363.72 / $35,000 = 1.10 Acceptable since PI > 1.0. b. Because there’s only one table factor in the NPV computation we can substitute into equation 10.2 and treat it as a time value problem in which the interest rate is the unknown. 0 = $35,000 + $56,367.50 [PVFIRR,5] PVFIRR,5 = .6209 IRR = 10% Acceptable since IRR > k. c. NPV = $35,000 + $56,367.50 [PVF12,5] = $35,000 + $56,367.50 (.5674) = $35,000 + $31,982.92 = $3,017.08 Unacceptable since NPV 0. 14. Calculate the IRR, NPV, and PI for projects with the following cash flows. Do each NPV and PI calculation at costs of capital of 8% and 12%. Calculate IRRs to the nearest whole percent. a. An initial outlay of $5,000 and inflows of $1,050 for seven years. b. An initial outlay of $43,500 and inflows of 14,100 for four years c. An investment of $78,000 followed by 12 years of income of $11,500. d. An outlay of $36,423 followed by receipts $8,900 of for six years. Solution: Mutually Exclusive Decisions and Judgment Issues: Concept Connection Example 10-4 (page 450) 15. Island Airlines, Inc. needs to replace a short haul computer plane on one of its busier routes. Two aircraft that satisfy the general requirements of the route are on the market. One is more expensive than the other but has better fuel efficiency and load-bearing characteristics that result in better long-term profitability. The useful life of both planes is expected to be about seven years, after which time both are assumed to have no value. Cash flow projections for the two aircraft follow: a. Calculate the payback period for each plane and select the best choice. b. Calculate the IRR for each plane and select the best option. Use the fact that all the inflows can be represented by an annuity. c. Compare the results of parts a. and b. Both should select the same option, but does one method result in a clearer choice than the other based on the relative sizes of the two payback periods versus the relative sizes of the two IRRs? d. Calculate the NPV and PI of each project assuming a cost of capital of 6%. Use annuity methods. Which plane is selected by NPV? By PI? e. Calculate the NPV and PI of each project assuming the following costs of capital: 2%, 4%, 6%, 8% and 10%. Use annuity methods. Is the same plane selected by NPV and PI at every level of cost of capital? Investigate the relative attractiveness of the two planes under each method. f. Use the results of parts b. and e. to sketch the NPV profiles of the two proposed planes on the same set of axes. Show the IRRs on the graph. Would NPV and IRR ever give conflicting results? Why? Solution: NPV and PI rank these projects fairly consistently relative to one another (mutually exclusive decision) and in absolute terms (stand-alone decision). NPV and IRR would not give conflicting results in this case because the NPV profiles do not cross in the first quadrant. Replacement Chain and Equivalent Annual Annuity (EAA) : Concept Connection Example 10.8 and 10.9 (pages 466 - 468) 16. Bagel Pantry Inc. is considering two mutually exclusive projects with widely differing lives. The company's cost of capital is 12%. The project cash flows are summarized as follows: a. Compare the projects by using Payback. b. Compare the projects by using NPV. c. Compare the projects by using IRR. d. Compare the projects by using the replacement chain approach. e. Compare the projects by using the EAA method. f. Chose a project and justify your choice. Solution: f. Project A is preferred on all counts except the original NPV calculation, and that disparity is due to the time horizon problem. Hence A is the best choice. CALCULATOR PROBLEMS The problems in this section should be solved using a financial calculator. See pages 461-462. 17. Callaway Associates, Inc. is considering the following mutually exclusive projects. Callaway’s Cost of capital is 12%. a. Calculate each project’s NPV and IRR. b. Which project should be undertaken? Why? Solution: a. Set the CF mode on your calculator, enter each project’s cash flows, and solve for NPV and IRR as follows b. First note that the results of the NPV and IRR methods conflict. Project A should be selected because NPV is the preferred method in the case of such conflicts. 18. Tutak Industries is considering a project requiring an initial investment of $200,000 followed by annual cash inflows of $45,000 for the next six years. A second six-year project has an initial outlay of $325,000. a. How much would the second project have to generate in annual cash flows to have the same IRR as the first? b. If Tutak’s cost of capital is 8%, how much would the second project have to generate in annual cash flows to have the same NPV as the first project. Solution: 19. Provide the missing information for the following projects using the present value of an annuity function [time value of money (TVM) keys rather than the cash flow (CF) function keys]. (Hint: The present value of the annuity of the annual cash flows minus the initial outlay must equal the NPV. For example, for project A calculate the present value of five $35,000 cash inflows and subtract the initial outlay (C0) to get the project’s NPV.) Solution: A. PMT = 35,000 N = 5 I/Y = 8 FV = 0 PV = ? = 139,744.85 which make the NPV = $39,744.85 B. PV = (235,000) N = 4 I/Y = 13 FV = 0 PMT = ? = $79,005.64 C. PV = (315,000) PMT = 50,000 N = 7 FV = 0 I/Y = ? = 2.71% D. PV = (420,000) I/Y = 9 PMT = 56,098 FV = 0 N = ? = 13 E. PMT = 75,000 N = 6 I/Y = 10 FV = 0 PV = ? = 326,644.55 which means the Initial outlay was $25,000 less or $301,644.55 20. Calculate IRRs for the projects in the previous problem. Solution: At the IRR the present value of the cash inflows is equal to the initial outlay so the TVM keys can be used as follows. Alternately just use the CF mode on the results of the previous problem. 21. Huron Valley Homes is considering a project requiring a $1 million initial investment. Expected cash inflows will be $25,000 in the first year, $100,000 in the second year, and $200,000 per year for the next six years. a. Calculate the project’s IRR and the NPV assuming an 8% cost of capital. b. How much would each of the last six payments have to be to make the project’s NPV $100,000? Solution: Use the NPV/IRR feature of the calculator rather than the TVM keys. a. CFo = (1,000,000) CF1 = 25,000 CF2 = 100,000 CF3 = 200,000 F03 = 6 I = 8 NPV = ? = (98,443.13) IRR = 5.74% b. First, compute the NPV of the initial outlay and the first two unequal cash flows and add the $100,000 required NPV. CFo = (1,000,000) CF1 = 25,000 CF2 = 100,000 I = 8 NPV = ? = (891,117.97) + (100,000) = (991,117.97) Now switch to the TVM mode and calculate the future value of that amount two periods out: PV = (991,117.97) N = 2 PMT = 0 I/Y = 8 FV = ? = 1,156,040 This amount becomes the PV of the six year annuity which begins in the third year. PV = 1,156,040 N = 6 I/Y = 8 FV = 0 PMT = ? = $250,069.24 Alternatively use an iterative approach in the NPV/IRR mode by trying new values for C03 until one produces an NPV that’s close to $100,000. Press CF to reenter the cash flow mode where the inputs from part a are still in place. Press ↓ repeatedly until C03 appears and input a new value. Press enter and then NPV. I=8 will reappear. Press enter, ↓, CPT, and read the new NPV. To try another value press CF again and repeat the procedure. Keep adjusting C03 until NPV = $100,000. 22. Consider two mutually exclusive projects, A and B. Project A requires an initial cash outlay of $100,000 followed by five years of $30,000 cash inflows. Project B requires an initial cash outlay of $240,000 with cash inflows of $40,000 in the first two years, $80,000 in the next two years and $100,000 in the fifth year. a. Compute the IRR for each project. b. Compute the NPV for each project for each of the following costs of capital: 0%, 4%, 8%, 12% and 16%, and record your results in a table. c. For which costs of capital do the IRR and NPV methods select the same project? d. Examine the table created in part b and determine the costs of capital between which the methods begin to select different projects? Is your answer consistent with the result of part a. Explain your answer in terms of NPV profiles. Solution: c. The IRR method selects A. The NPV method selects A at 12%. At 16%, both projects have negative NPVs, but A’s is less negative. d. The NPV selection shifts when the cost of capital is between 8% and 12%. This implies that the NPV profiles cross in the first quadrant between 8% and 12%. That’s consistent with part a because the crossover must be to the left of both IRRs. Mutually Exclusive Decisions and Judgment Issues: Concept Connection Example 10-4 (page 450) 23. Kneelson and Botes Inc. (K&B) is a construction company that does road and bridge work for the state highway authority. The state government solicits bids on construction projects from private contractors. The winning contractor is chosen based on its bid price as well as its perceived ability to do the work. Sophisticated contractors develop bids using capital budgeting techniques because most projects require cash outlays for hiring, equipment and materials before getting started (C0). After that the state makes progress payments to cover costs and profits until the job is finished (C1…..Cn). Contractors know that even after they’ve won a bid, realizing the planned profits and cash flows isn’t assured in part because government budgets can change while construction progresses. If funding is up, officials tend to add to the work originally ordered leading to increased profits and cash flows. But if funding is down, officials start to nit pick the contract looking for cost savings, which generally leads to lower cash inflows. State budget projections are fairly good for a year or two, but tend to be inaccurate over longer periods. K&B has been offered two, four year contracts, but doesn’t have enough cash or management depth to take on both (mutually exclusive because of resource limitations). One project involves road repair, most of which will be done and paid quickly. The other requires working on a new bridge. The bulk of the cash inflows on bridge projects generally occur near completion. K&B’s estimating department has put together the following projections of the two projects’ cash flows: K&B doesn’t know its exact cost of capital, but feels it’s between 10% and 15%. This is not uncommon in smaller companies. (In Chapter 13 we’ll learn that estimating the cost of capital can be difficult and less than precise for firms of any size.) The company has hired you as a financial consultant to make a recommendation as to which project to accept. a. Calculate the payback period for both projects. Which does payback choose? b. Calculate the IRR for both projects. Which does the IRR method choose. Is the choice clear or is it a close decision? Is the choice consistent with the result of the payback method. c. Calculate NPVs for both projects for costs of capital from 10% to 15% in 1% increments. Then plot both projects’ NPV profiles on a graph similar to that shown in Figure 10-2 on page XXX. Does the NPV method give a meaningful result. If so is it consistent with the results of the payback and IRR methods. Which method is theoretically the best? Does that help in this situation? d. You must make a recommendation to K&B’s management regardless of any technical difficulties you’ve encountered. Provide another, less quantitative argument that tends to support one project over the other. (Hint: See question 6 on page XXX and Business Analysis 4 on page XXX.) e. What is your recommendation and why? Solution: ($000) a. The Road project pays back the initial investment of $3,000K in exactly one year. The Bridge project recovers $2,100K of the initial outlay in the first two years leaving $2,400, which is recovered in ($2,400/$3,000 = .8) 8/10 of the third year. Hence the payback period is 2.8 years The payback method chooses the Road project by a wide margin. b. Enter the project’s cash flows in your calculator in accordance with the instructions in the chapter as follows: Then for each project press IRR and then compute: IRR 56.9% 27.1% The Road project has the highest IRR by a wide margin, hence the IRR method clearly chooses the Road project which is consistent with the payback method. c. With a project’s cash flows in your calculator, press NPV. The machine prompts for the cost of capital which it calls I (we’ve called it k). Type in a value and press enter. Then press the ↓ and then compute. The calculator displays the NPV at that value of the cost of capital. Continue with all the values of the cost of capital for both projects. The results are as follows: The NPV Method does not give a meaningful result in this case, because we can’t clearly place the cost of capital (k) on either side of the crossover of the NPV profile. Even if we could, the result wouldn’t be meaningful because the projects’ NPVs are very close in the neighborhood of the crossover which is between 13% and 14%. That means the NPV method is more or less indifferent between the projects at that cost of capital. The NPV result doesn’t support the IRR result but there isn’t really a conflict either, because NPV is essentially neutral in this case. NPV is theoretically the best method, but that doesn’t help us much here since it doesn’t give us a clear answer. d. Another less quantitative argument involves the timing of the two projects’ cash flows. The Bridge is inherently more risky than the Road because its positive cash flows are further in the future and therefore are less likely to be realized. In this case we were told that’s especially problematic because of the state government’s tendency to run out of money. The fact that most managements are risk averse (just like the investors we studied in chapter 9) argues in favor of choosing the Road project. The Road project also requires placing a smaller investment at risk which is generally positive to managements. Along the same lines, the payback method is unusually telling in this case, because it shows that the Road project recovers its outlay almost immediately, so the risk of loss is minimal. e. Recommend the road project because 1. Its IRR and payback are better without conflicting with NPV, 2. It’s less risky, and 3. It gets K&B’s money back faster. Replacement Chain and EAA: Concept Connection Example 10.8 and 10.9 (pages 466-468) 24. Haley Motors is considering a maintenance contract for its heavy equipment. One firm has offered Haley a four-year contract for $100,000 to be paid in advance. Another firm has offered an eight year contract for $165,000 also to be paid in advance. Both contracts require full payment in advance. Haley will be able to save $34,000 per year under either contract because its employees will no longer have to do the work themselves. a. If Haley’s cost of capital is 10%, which project should be selected? Use both the replacement chain and the equivalent annual annuity (EAA) method to justify your answer. b. If Haley’s cost of capital is 12%, does it change the decision? What about 14%? Solution: a. At 10%, both the EAA and replacement chain favor the 8-year contract b. At 12%, the NPV of the replacement chain is higher on the 4-year contract. At 14%, both of the projects have a negative NPV, so neither should be selected. 25. Cassidy and Sons is reviewing a project with an initial cash outflow of $250,000. An additional $100,000 will have to be invested after the first year, followed by an additional investment of $50,000 at the end of the second year. Beginning at the end of year three, the project is expected to generate cash flows of $90,000 per year for the next eight years. a. Calculate the project’s Payback Period, and IRR, and its NPV and PI at a cost of capital of 8%. b. What concerns might Cassidy have regarding this project beyond the financial calculations in part a? Solution: Payback Period = 6 + 40/90 = 6.44 years IRR (based on cash flows shown above) = 10.75% NPV = $57,954 The present value of the three outflows is (385,460). Hence the present value of the positive cash flows is 385,460 + 57,954 so the PI is calculated as follows. PI = (385,460 + 57,954)/(385,460) = 1.15 b. The length of the payback period is an important concern. Projects that don’t pay back for that long a time are very risky simply because of the uncertainty of the future. 26. Zuker Distributors handles the warehousing of perishable foods and is considering replacing one of its primary cold storage units. One supplier has offered a unit for $250,000 with an expected life of 10 years. The unit is projected to reduce electricity costs by $50,000 per year. However, it requires a $20,000 refurbishing every two years, beginning two years after purchase. Another supplier has offered a cold storage unit with similar capabilities for $300,000. It will produce the same savings in electricity costs, but requires refurbishing every five years at a cost of $40,000. Zuker’s cost of capital is 8.5%. Use NPV to determine which cold storage unit Zuker should select. Solution: Capital Rationing: (page 469) 27. Griffin-Kornberg is reviewing the following projects for next year’s capital program. Projects A and B are mutually exclusive and so are Projects D and E. Griffin-Kornberg has a 9% cost of capital and a maximum of $14 million to spend on capital projects next year. Use capital rationing to determine which projects should be included in Griffin-Kornberg’s capital program. Solution: (000) At the IRR the present values of the annuities of cash inflows are just equal to the initial outlays so we can find the projects’ IRRs by solving time value of annuity problems for the interest rates as follows. Modified Internal Rate of Return (MIRR): (Insights Box, page 458) 28. Find the MIRR and the IRR for the following capital budgeting project and comment on the difference between the two. The cost of capital is 12%. Solution: MIRR: Calculate the present value at time 0 of the year 2 outflow: FV=-150 n=2 I/Y=12 PV = -119.58 Combine with initial outlay for total present outflow Present Outflow = -$800.00 -$119.58 = -$919.58 Calculate the future value at time 3 of the year 1 inflow PV=550 n=2 I/Y=12 FV = 689.92 Combine with year 3 cash flow to get total future inflow. Future Inflow = $700.00 + $689.92 = $1,389.92 Find the interest rate that makes the present value of the future inflow equal to the present outflow. FV = 1389.92 PV=919.58 n=2 I/Y = 14.76 MIRR = 14.8% IRR: Find the IRR using the cash flow mode and input as follows Comment: IRR is higher than MIRR because of the unrealistic assumption implicit in the IRR calculation that cash inflows are reinvested at the IRR. The MIRR assumes reinvestment at the lower and more realistic cost of capital. Accounting Rate of Return (ARR): Concept Connection Example 10-10 (page 471) 29. The Griffin Company is launching a maritime project by purchasing a small, previously owned cargo ship for $2M which will be used to ferry iron ore across the Great Lakes The ship will be depreciated over four years straight line. Freight revenue and expenses from the venture are forecast below Calculate the project’s ARR and comment on its likelihood of acceptance by management. Also estimate project cash flows and calculate its NPV and IRR at a 5% cost of capital. Solution: First create an income statement for the project along with an estimate of cash flows. Average Accounting Return (ARR) calculations: The Asset’s net book value starts $2M and ends at $0. Hence its average book value is ($2M + $0) ÷ 2 = $1M The average net income is (-$.3 + $.6 + $.9 + $1.1) ÷ 4 = $2.3 ÷ 4 = $.6 Hence the average Accounting Rate of Return is $.6M ÷ $1M = 60% NPV and IRR calculations using a financial calculator yield: k=5% NPV = $417,120 IRR = 11.93% Analysis and Comments The project has a healthy return under both accounting and cash flow methods. There is a negative in the first year, but that should be explainable by management as a startup cost. COMPUTER PROBLEMS: DEVELOPING SOFTWARE 30. Write a spreadsheet program to calculate the NPV of a project with an irregular pattern of cash flows for up to 10 periods without using the spreadsheet software's NPV function. Essentially, the task is to program Equation 10.1a with n = 10. First, input the interest rate (k) in a single cell. Next, set up three horizontal rows of 11 cells (including C0). The top row will receive the cash flows as inputs. Program the present value factor for each period into the second row of cells using the interest rate you input earlier as follows. Note that we're calling the interest rate k, but it will appear as a cell name in your program. Next, form the third row by multiplying the top two cells in each column together. This makes the third row the present value of each cash flow. Finally, sum the values along the third row in another cell to form the project's NPV. Notice that your program will handle a project of less than ten periods if you simply input zero (or leave blank) the cash flow cells from n+1 to ten. Also notice that you can easily extend your program to any reasonable number of periods by extending the horizontal rows and the programming logic. Test your program on the data in Example 10.4 to make sure it works correctly. 31. The Tallahassee Motor Company is thinking of automating one of its production facilities. The equipment required will cost a total of $10.0 million and is expected to last 10 years. The company's cost of capital is 9%. The project's benefits include labor savings, and a quality improvement that will lower warranty costs. Savings are estimated as follows. a. Use the program developed in the previous problem to find the project's NPV. Is the project acceptable? b. Use the program to develop the data for an NPV profile. Evaluate the NPV for interest rates (costs of capital) from 6 to 14 percent. c. Use the program to iteratively find the project's IRR to one tenth of a percent. Solution Manual for Practical Financial Management William R. Lasher 9781305637542
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