Chapter 12 The Capital Budgeting Decision Discussion Questions 12-1. What are the important administrative considerations in the capital budgeting process? Important administrative considerations relate to the search for and discovery of investment opportunities, the collection of data, the evaluation of projects, and the reevaluation of prior decisions. 12-2. Why does capital budgeting rely on analysis of cash flows rather than on net income? Cash flow rather than net income is used in capital budgeting analysis because the primary concern is with the amount of actual dollars generated. For example, depreciation is subtracted out in arriving at net income, but this non-cash deduction should be added back in to determine cash flow or actual dollars generated. 12-3. What are the weaknesses of the payback method? The weaknesses of the payback method are: a. There is no consideration of inflows after payback is reached. b. The concept fails to consider the time value of money. 12-4. What is normally used as the discount rate in the net present value method? The cost of capital as determined in Chapter 11. In the Net Present Value (NPV) method, the discount rate typically represents the cost of capital, or the required rate of return on an investment. This rate reflects the opportunity cost of choosing a particular project over alternative investments. Commonly, it is derived from the company's weighted average cost of capital (WACC). In some cases, the discount rate may also be based on the risk profile of the project or industry-specific benchmarks. The rate adjusts future cash flows to their present value, allowing for comparison with the initial investment. 12-5. What does the term mutually exclusive investments mean? The selection of one investment precludes the selection of other alternative investments because the investments compete with one another. For example, if a company is going to build one new plant and is considering five cities, one city will win and the others will lose. 12-6. How does the modified internal rate of return include concepts from both the traditional internal rate of return and the net present value methods? The modified internal rate of return calls for the determination of the interest rate that equates future inflows to the investment, as does the traditional internal rate or return. However, it incorporates the reinvestment rate assumption of the net present value method. That is, inflows are reinvested at the cost of capital. 12-7. If a corporation has projects that will earn more than the cost of capital, should it ration capital? From a purely economic viewpoint, a firm should not ration capital. The firm should be able to find additional funds and increases its overall profitability and wealth through accepting investments to the point where marginal return equals marginal cost. 12-8. What is the net present value profile? What three points should be determined to graph the profile? The net present value profile allows for the graphic portrayal of the net present value of a project at different discount rates. Net present values are shown along the vertical axis and discount rates are shown along the horizontal axis. The points that must be determined to graph the profile are: a. The net present value at zero discount rate. b. The net present value as determined by a normal discount rate. c. The internal rate of return for the investment. 12-9. How does an asset’s ADR (asset depreciation range) relate to its MACRS category? The ADR represents the asset depreciation range or the expected physical life of the asset. Generally, the midpoint of the range or life is utilized. The longer the ADR midpoint, the longer the MACRS category in which the asset is placed. However, most assets can still be written off more rapidly than the midpoint of the ADR. For example, assets with ADR midpoints of 10 years to 15 years can be placed in the 7-year MACRS category for depreciation purposes. Chapter 12 Problems 1. Cash flow (LO12-2) Assume a corporation has earnings before depreciation and taxes of $90,000, depreciation of $40,000, and that it is in a 30 percent tax bracket. Compute its cash flow using the following format. Earnings before depreciation and taxes _____ Depreciation _____ Earnings before taxes _____ Taxes @ 30% _____ Earnings after taxes _____ Depreciation _____ Cash flow _____ 12-1. Solution: Earnings before depreciation and taxes $90,000 Depreciation –40,000 Earnings before taxes 50,000 Taxes @ 30% –15,000 Earnings after taxes $35,000 Depreciation +40,000 Cash flow $75,000 2. Cash flow (LO12-2) Assume a corporation has earnings before depreciation and taxes of $100,000, depreciation of $40,000, and that it has a 40 percent tax bracket. a. Compute its cash flow using the following format. Earnings before depreciation and taxes _____ Depreciation _____ Earnings before taxes _____ Taxes @ 40% _____ Earnings after taxes _____ Depreciation _____ b. Compute the cash flow for the company if depreciation is only $20,000. c How much cash flow is lost due to the reduced depreciation from $40,000 to $20,000. 12-2. Solution: a. Earnings before depreciation and taxes $100,000 Depreciation – 40,000 Earnings before taxes 60,000 Taxes @ 40% 24,000 Earnings after taxes 36,000 Depreciation + 40,000 Cash flow $ 76,000 b. Earnings before depreciation and taxes $100,000 Depreciation – 20,000 Earnings before taxes 80,000 Taxes @ 40% 32,000 Earnings after taxes 48,000 Depreciation + 20,000 Cash flow $ 68,000 c. Cash flow ($40,000) $ 76,000 Cash flow ($20,000) 68,000 Difference in cash flow $ 8,000 3. Cash flow (LO12-2) Assume a firm has earnings before depreciation and taxes of $200,000 and no depreciation. It is in a 40 percent tax bracket. a. Compute its cash flow. b. Assume it has $200,000 in depreciation. Recompute its cash flow. c. How large a cash flow benefit did the depreciation provide? 12-3. Solution: a. Earnings before depreciation and taxes $200,000 Depreciation – 0 Earnings before taxes 200,000 Taxes @ 40% – 80,000 Earnings after taxes 120,000 Depreciation – 0 Cash flow $120,000 b. Earnings before depreciation and taxes $200,000 Depreciation –200,000 Earnings before taxes 0 Taxes @ 40% 0 Earnings after taxes 0 Depreciation 200,000 Cash flow $200,000 c. The $200,000 in depreciation provided a cash flow benefit of $80,000. Cash flow (b) $200,000 Cash flow (a) 120,000 Cash flow benefit $ 80,000 4. Cash flow (LO12-2) Assume a firm has earnings before depreciation and taxes of $440,000 and depreciation of $140,000. a. If it is in a 35 percent tax bracket, compute its cash flow. b. If it is in a 20 percent tax bracket, compute its cash flow. 12-4. Solution: a. Earnings before depreciation and taxes $440,000 Depreciation 140,000 Earnings before taxes 300,000 Taxes @ 35% 105,000 Earnings after taxes 195,000 Depreciation +140,000 Cash flow $335,000 b. Earnings before depreciation + taxes $440,000 Depreciation 140,000 Earnings before taxes 300,000 Taxes @ 20% 60,000 Earnings after taxes 240,000 Depreciation +140,000 Cash flow 380,000 5. Cash flow versus earnings (LO12-2) Al Quick, the president of a New York Stock Exchange-listed firm, is very short-term oriented and interested in the immediate consequences of his decisions. Assume a project that will provide an increase of $2 million in cash flow because of favorable tax consequences, but carries a two-cent decline in earnings per share because of a write-off against first-quarter earnings. What decision might Mr. Quick make? 12-5. Solution: Al Quick Being short-term oriented, he may make the mistake of turning down the project even though it will increase cash flow because of his fear of investors’ negative reaction to the more widely reported quarterly decline in earnings per share. Even though this decline will be temporary, investors might interpret it as a negative signal. 6. Payback method (LO12-3) Assume a $250,000 investment and the following cash flows for two products: Year Product X Product Y 1 $90,000 $50,000 2 90,000 80,000 3 60,000 60,000 4 20,000 70,000 Which alternatives would you select under the payback method? 12-6. Solution: Payback for Product X Payback for Product Y $250,000 – 90,000 1 year $250,000 – 50,000 1 year 160,000 – 90,000 2 years 200,000 – 80,000 2 years 70,000 – 60,000 3 years 120,000 – 60,000 3 years 10,000/20,000 .5 years 60,000/70,000 .86 years Payback Product X = 3.5 years Payback Product Y =3.86 years Product X would be selected because of the faster payback. 7. Payback method (LO12-3) Assume a $40,000 investment and the following cash flows for two alternatives. Year Investment X Investment Y 1 $ 6,000 $15,000 2 8,000 20,000 3 9,000 10,000 4 17,000 — 5 20,000 — Which of the alternatives would you select under the payback method? 12-7. Solution: Payback for Investment X Payback for Investment Y $40,000–$6,000 1 year $40,000–$15,000 1 year 34,000–8,000 2 years 25,000–20,000 2 years 26,000–9,000 3 years 5,000/10,000 .5 years 17,000–17,000 4 years Payback Investment X = 4.00 years Payback Investment Y = 2.50 years Investment Y would be selected because of the faster payback. 8. Payback method (LO12-3) Assume a $90,000 investment and the following cash flows for two alternatives. Year Investment A Investment B 1 $25,000 $40,000 2 30,000 40,000 3 25,000 28,000 4 19,000 — 5 25,000 — a. Calculate the payback for investment A and B. b. If the inflow in the fifth year for Investment A was $25,000,000 instead of $25,000, would your answer change under the payback method? 12-8. Solution: a. Payback for Investment A Payback for Investment B $90,000 – $25,000 1 year $90,000 – $40,000 1 year 65,000 – 30,000 2 years 50,000 – 40,000 2 years 35,000 – 25,000 3 years 10,000/28,000 .36 years 10,000/19,000 0.53 years Payback Investment A = 3.53 years Payback Investment B = 2.36 years Investment B would be selected because of the faster payback. b. The $25,000,000 inflow would still leave the payback period for Investment A at 3.53 years. It would remain inferior to Investment B under the payback method. 9. Payback method (LO12-3) The Short-Line Railroad is considering a $140,000 investment in either of two companies. The cash flows are as follows: Year Electric Co. Water Works 1 $85,000 $30,000 2 25,000 25,000 3 30,000 85,000 4–10 10,000 10,000 a. Using the payback method, what will the decision be? b. Explain why the answer in part a can be misleading. 12-9. Solution: Short-Line Railroad a. Payback for Electric Co. Payback for Water Works $140,000 – $85,000 1 year $140,000 – $30,000 1 year 55,000 – 25,000 2 years 110,000 – 25,000 2 years 30,000 – 30,000 3 years 85,000 – 85,000 3 years Payback (Electric Co.) = 3 years Payback (Water Works) = 3 years b. The answer in part a is misleading because the two investments seem to be equal with the same payback period of three years. Nevertheless, the Electric Co. is a superior investment because it covers large cash flows in the first year, while the large recovery for Water Works is not until the third year. The problem is that the payback method does not consider the time value of money. 10. Payback and net present value (LO12-3 and 4) X-treme Vitamin Company is considering two investments, both of which cost $10,000. The cash flows are as follows: Year Project A Project B 1 $12,000 $10,000 2 8,000 6,000 3 6,000 16,000 a. Which of the two projects should be chosen based on the payback method? b. Which of the two projects should be chosen based on the net present value method? Assume a cost of capital of 10 percent. c. Should a firm normally have more confidence in answer a or answer b. 12-10. Solution: X-treme Vitamin Company a. Payback Method Payback for Project A Payback for Project B Under the Payback Method, you should select Project A because of the shorter payback period. b. Net Present Value Method Project A Year Cash Flow PVIFA Present Value 1 $12,000 .909 $10,908 2 $ 8,000 .826 $ 6,608 3 $ 6,000 .751 $ 4,506 Present value of inflows $22,022 Present value of outflows 10,000 Net present value $12,022 Project B Year Cash Flow PVIFA Present Value 1 $10,000 .909 $ 9,090 2 $ 6,000 .826 $ 4,956 3 $16,000 .751 $12,016 Present value of inflows $26,062 Present value of outflows 10,000 Net present value $16,062 Under the net present value method, you should select Project B because of the higher net present value. c. A company should normally have more confidence in answer b because the net present value considers all inflows as well as the time value of money. The heavy late inflow for Project B was partially ignored under the payback method. Calculator Solution: (b-1) Project A using a financial calculator: Use the NPV keys by pressing and entering the following: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 10,000 +|– key, press the Enter key. Press down arrow, enter 12,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 8,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 6,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 10 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 12,028.55, which is the net present value of Project A. (b-2) Project B Using Financial Calculator Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 10,000 +|– key, press the Enter key. Press down arrow, enter 10,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 6,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 16,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 10 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 16,070.62, which is the net present value of Project B. Under the net present value method, you should select Project B because of the higher net present value. 11. Internal rate of return (LO12-4) You buy a new piece of equipment for $16,230, and you receive a cash inflow of $2,500 per year for 12 years. What is the internal rate of return? 12-11. Solution: Appendix D IRR = 11% For n = 12, we find 6.492 under the 11% column. Calculator Solution: Using a financial calculator, Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 16,230 +|– key, press the Enter key. Press down arrow, enter 2,500, and press Enter. Press down arrow, enter 12, and press Enter. Press IRR; calculator shows IRR = 0.00. Press CPT; calculator shows IRR = 11. Answer: IRR = 11% 12. Internal rate of return (LO12-4) King’s Department Store is contemplating the purchase of a new machine at a cost of $22,802. The machine will provide $3,500 per year in cash flow for nine years. King’s has a cost of capital of 10 percent. Using the internal rate of return method, evaluate this project and indicate whether it should be undertaken. 12-12. Solution: King’s Department Store Appendix D PVIFA = $22,802/$3,500 = 6.515 IRR = 7% For n = 9, we find 6.515 under the 7% column. The machine should not be purchased since its return is less than the 10 percent cost of capital. Calculator Solution: (a) Using a financial calculator, Press the following keys: 2nd, CF, 2nd, CLR WORK. Calculator displays CFo, 22,802 +|– key, press the Enter key. Press down arrow, enter 3,500, and press Enter. Press down arrow, enter 9, and press Enter. Press IRR; calculator shows IRR = 0.00. Press CPT; calculator shows IRR = 7. Answer: IRR = 7% 13. Internal rate of return (LO12-4) Home Security Systems is analyzing the purchase of manufacturing equipment that will cost $50,000. The annual cash inflows for the next three years will be: Year Cash Flow 1 $25,000 2 23,000 3 18,000 a. Determine the internal rate of return. b. With a cost of capital of 18 percent, should the machine be purchased? 12-13. Solution: Home Security Systems a. Step 1 Average the inflows. Step 2 Divide the inflows by the assumed annuity in Step 1. Step 3 Go to Appendix D for the first approximation. The value in Step 2 (for n = 3) falls between 15 and 16 percent. Step 4 Try a first approximation of discounting back the inflows. Because the inflows are biased toward the early years, we will use the higher rate of 16 percent. Year Cash Flow PVIF at 16% Present Value 1 $25,000 .862 $21,550 2 $23,000 .743 $17,089 3 $18,000 .641 $11,538 $50,177 Step 5 Since the NPV is slightly over $50,000, we need to try a higher rate. We will try 17 percent. 12-13. (Continued) Year Cash Flow PVIF at 17% Present Value 1 $25,000 .855 $21,375 2 $23,000 .731 $16,813 3 $18,000 .624 $11,232 $49,420 Because the NPV is now below $50,000, we know the IRR is between 16 and 17 percent. We will interpolate. $50,177 PV @ 16% $50,177 PV @ 16% –49,420 PV @ 17% –50,000 Cost $ 757 $ 177 16% + ($177/$757) (1%) 14% + .234 (1%) = 16.23% IRR The IRR is 16.23% If the student skipped from 16 percent to 18 percent, the calculations to find the IRR would be as follows: Year Cash Flow PVIF at 18% Present Value 1 $25,000 .847 $ 21,175 2 $23,000 .718 $ 16,514 3 $18,000 .609 $ 10,962 $ 48,651 12-13. (Continued) $50,177 PV @ 16% $50,177 PV @ 16% –48,651 PV @ 18% –50,000 Cost $ 1,526 $ 177 16% + ($177/$1,526) (2%) 16% + (.12)(2%) = 16.24% This answer is very close to the previous answer, the difference is due to rounding and that the differences between the numbers in the table are not linear. b. Since the IRR of 16.23 percent (or 16.24 percent) is less than the cost of capital of 18 percent, the project should not be accepted. Calculator Solution: Alternatively, use a financial calculator as follows to obtain the correct answer rather than an approximation. Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 50,000 +|– key, press Enter. Press down arrow, enter 25,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 23,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 18,000, and press Enter. Press down arrow, enter 1, and press Enter. Press IRR; calculator shows IRR = 0.00. Press CPT; calculator shows IRR = 16.23. Answer: IRR = 16.23% 14. Net present value method (LO12-4) Aerospace Dynamics will invest $110,000 in a project that will produce the following cash flows. The cost of capital is 11 percent. Should the project be undertaken? (Note that the fourth year’s cash flow is negative.) Year Cash Flow 1 $36,000 2 44,000 3 38,000 4 (44,000) 5 81,000 12-14. Solution: Aerospace Dynamics Year Cash Flow PVIF at 11% Present Value 1 $36,000 .901 $ 32,436 2 44,000 .812 35,728 3 38,000 .731 27,778 4 (44,000) .659 (28,996) 5 81,000 .593 48,033 Present Value of Inflows $114,979 Present Value of Outflows 110,000 Net Present Value $ 4,979 The net present value is positive and the project should be undertaken. Calculator Solution: Using a financial calculator, Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 110,000 +|– key, press Enter. Press down arrow, enter 36,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 44,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 38,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 44,000 +|–, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 81,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 11 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; the calculator shows NPV = 5,014.49, which is the net present value of the project. The net present value is positive and the project should be undertaken. 15. Net present value method (LO12-4) The Horizon Company will invest $60,000 in a temporary project that will generate the following cash inflows for the next three years. Year Cash Flow 1 $15,000 2 25,000 3 40,000 The firm will also be required to spend $10,000 to close down the project at the end of the three years. If the cost of capital is 10 percent, should the investment be undertaken? 12-15. Solution: Horizon Company Present Value of Inflows Year Cash Flow × PVIF at 10% Present Value 1 $15,000 .909 $13,635 2 25,000 .826 20,650 3 40,000 .751 30,040 $64,325 Present Value of Outflows 0 $60,000 1.000 $60,000 3 10,000 .751 7,510 $67,510 Present Value of Inflows $64,325 Present Value of Outflows 67,510 Net Present Value ($ 3,185) The net present value is negative and the project should not be undertaken. Note, the $10,000 outflow could have been subtracted out of the $40,000 inflow in the third year and the same answer would result. Calculator Solution: Using a financial calculator, Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 60,000 +|– key, press the Enter key Press down arrow, enter 15,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 25,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 30,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 10 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = –3,163.04, which is the net present value of the project. Note, the $10,000 outflow in year 3 has been subtracted from the $40,000 inflow in the third year, and thus the year 3 net cash flow is $30,000. 16. Net present value method (LO12-4) Skyline Corp. will invest $130,000 in a project that will not begin to produce returns until after the 3rd year. From the end of the 3rd year until the end of the 12th year (10 periods), the annual cash flow will be $34,000. If the cost of capital is 12 percent, should this project be undertaken? 12-16. Solution: Skyline Corporation Present Value of Inflows Find the present value of a deferred annuity A = $34,000, n = 10, i = 12% PVA = A × PVIFA (Appendix D) PVA = $34,000 × 5.650 = $192,100 Discount from beginning of the third period (end of second period to present): FV = $192,100, n = 2, i = 12% PV = FV × PVIF (Appendix B) PV = $192,100 × .797 = $153,104 Present Value of Inflows $153,104 Present Value of Outflows 130,000 Net Present Value $ 23,104 The net present value is positive and the project should be undertaken. Calculator Solution: Using a financial calculator, Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 130,000 +|– key, press Enter. Press down arrow, enter 0, and press Enter. Press down arrow, enter 2, and press Enter. Press down arrow, enter 34,000, and press Enter. Press down arrow, enter 10, and press Enter. Press NPV; calculator shows I = 0; enter 12 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 23,146.99, which is the net present value of the project. 17. Net present value and internal rate of return methods (LO12-4) The Hudson Corporation makes an investment of $24,000 that provides the following cash flow: Year Cash Flow 1 $ 13,000 2 13,000 3 4,000 a. What is the net present value at an 8 percent discount rate? b. What is the internal rate of return? c. In this problem, would you make the same decision under both parts a and b? 12-17. Solution: Hudson Corporation a. Net Present Value Year Cash Flow × 8% PVIF Present Value 1 $13,000 .926 $ 12,038 2 13,000 .857 11,141 3 4,000 .794 3,176 Present Value of Inflows $26,355 Present Value of Outflows 24,000 Net Present Value $ 2,355 b. Internal Rate of Return We will average the inflows to arrive at an assumed annuity value. $13,000 13,000 4,000 $30,000/3 = $10,000 12-17. (Continued) We divide the investment by the assumed annuity value. Using Appendix D for n = 3, the first approximation appears to fall between 12 percent and 14 percent. Since the heavy inflows are in the early years, we will try 14 percent. Year Cash Flow × 14% PVIF Present Value 1 $13,000 .877 $ 11,401 2 13,000 .769 9,997 3 4,000 .675 2,700 Present Value of Inflows $24,098 Since 14 percent is not high enough to get $24,000 as the present value, we will try 16 percent. (We could have only gone up to 15 percent, but we wanted to be sure to include $24,000 in this calculation. Of course, students who use 15 percent are doing fine.) Year Cash Flow × 16%PVIF Present Value 1 $13,000 .862 $ 11,206 2 13,000 .743 9,659 3 4,000 .641 2,564 Present Value of Inflows $23,429 The correct answer must fall between 14 percent and 16 percent. We interpolate. $24,098 PV @ 14% $24,098 PV @ 14% 23,429 PV @ 16% 24,000 Cost $ 669 $ 98 As an alternative answer, students who use 15 percent as the second trial and error rate will show the following: Year Cash Flow × 15%PVIF Present Value 1 $13,000 .870 $ 11,310 2 13,000 .756 9,828 3 4,000 .658 2,632 Present Value of Inflows $23,770 The correct answer falls between 14 percent and 15 percent. We interpolate. $24,098 PV @ 14% $24,098 PV @ 14% 23,770 PV @ 15% 24,000 Cost 328 $ 98 c. Yes. Both the NPV is greater than 0 and the IRR is greater than the cost of capital. Calculator Solution: (a) Press the following keys: 2nd, CF, 2nd, and Clear. Calculator displays CFo, 24,000 +|– key, press Enter. Press down arrow, enter 13,000, and press Enter. Press down arrow, enter 2, and press Enter. Press down arrow, enter 4,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 8 and press Enter. Press down arrow; calculator shows NPV = 0.00 Press CPT; calculator shows NPV = 2,357.77, which is the net present value of the project. (b) Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 24,000 +|– key, press Enter. Press down arrow, enter 13,000 and press Enter. Press down arrow, enter 2, and press Enter. Press down arrow, enter 4,000, and press Enter. Press down arrow, enter 1, and press Enter. Press IRR; calculator shows IRR = 0.00. Press CPT; calculator shows IRR = 14.29. Answer: IRR = 14.29% 18. Net present value and internal rate of return methods (LO12-4) The Pan American Bottling Co. is considering the purchase of a new machine that would increase the speed of bottling and save money. The net cost of this machine is $60,000. The annual cash flows have the following projections. Year Cash Flow 1 $23,000 2 26,000 3 29,000 4 15,000 5 8,000 a. If the cost of capital is 13 percent, what is the net present value of selecting a new machine? b. What is the internal rate of return? c. Should the project be accepted? Why? 12-18. Solution: Pan American Bottling Co. a. Net Present Value Year Cash Flow × 13% PVIF Present Value 1 $23,000 .885 $20,355 2 26,000 .783 20,358 3 29,000 .693 20,097 4 15,000 .613 9,195 5 8,000 .543 4,344 Present Value of Inflows $74,349 Present Value of Outflows –60,000 Net Present Value $14,349 12-18. (Continued) b. Internal Rate of Return We will average the inflows to arrive at an assumed annuity. $23,000 26,000 29,000 15,000 8,000 $101,000/5 = $20,200 We divide the investment by the assumed annuity value. Using Appendix D for n = 5, 20 percent appears to be a reasonable first approximation (2.991). We try 20 percent. Year Cash Flow × 20% PVIF Present Value 1 $23,000 .833 $19,159 2 26,000 .694 18,044 3 29,000 .579 16,791 4 15,000 .482 7,230 5 8,000 .402 3,216 Present Value of Inflows $64,440 Since 20 percent is not high enough, we try the next highest rate at 25 percent. Year Cash Flow × 25% PVIF Present Value 1 $23,000 .800 $18,400 2 26,000 .640 16,640 3 29,000 .512 14,848 4 15,000 .410 6,150 5 8,000 .328 2,624 Present Value of Inflows $58,662 12-18. (Continued) The correct answer must fall between 20 and 25 percent. We interpolate. $64,440 PV @ 20% $64,440 PV @ 20% 58,662 PV @ 25% 60,000 Cost $ 5,778 $ 4,440 c. The project should be accepted because the net present value is positive and the IRR exceeds the cost of capital. Calculator Solution: Find the NPV using a financial calculator: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 60,000 +|– key, press Enter. Press down arrow, enter 23,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 26,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 29,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 15,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 8,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 10 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 14,356.11, which is the net present value of the project. (b) Calculator Solution: Find the IRR using a financial calculator: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 60,000 +|– key, press the Enter key. Press down arrow, enter 23,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 26,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 29,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 15,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 8,000, and press Enter. Press down arrow, enter 1, and press Enter. Press IRR; calculator shows IRR = 0. Press CPT; calculator shows IRR = 23.77%, which is the IRR of the project. 19. Use of profitability index (LO12-4) You are asked to evaluate the following two projects for the Norton Corporation. Using the net present value method combined with the profitability index approach described in footnote 2 of this chapter, which project would you select? Use a discount rate of 14 percent. Project X (Videotapes of the Weather Report) ($20,000 Investment) Project Y (Slow-Motion Replays of Commercials) ($40,000 investment) Year Cash Flow Year Cash Flow 1 $10,000 1 $20,000 2 8,000 2 13,000 3 9,000 3 14,000 4 8,600 4 16,000 12-19. Solution: Norton Corporation NPV for Project X Year Cash Flow × PVIF at 14% Present Value 1 $10,000 .877 $ 8,770 2 8,000 .769 6,152 3 9,000 .675 6,075 4 8,600 .592 5,091 Present Value of Inflows $26,088 Present Value of Outflows (Cost) –20,000 Net Present Value $ 6,088 NPV for Project Y Year Cash Flow × PVIF at 14% Present Value 1 $20,000 .877 $ 17,540 2 13,000 .769 9,997 3 14,000 .675 9,450 4 16,000 .592 9,472 Present Value of Inflows $46,459 Present Value of Outflows (Cost) –40,000 Net Present Value $ 6,459 You should select Project X because it has the higher profitability index. This is true in spite of the fact that it has a lower net present value. The profitability index may be appropriate when you have different size investments. Calculator Solution: (a) Find NPV using a financial calculator: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 20,000 +|– key, press the Enter key. Press down arrow, enter 10,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 8,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 9,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 8,600, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; the calculator shows I = 0; enter 14 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 6,094.30, which is the net present value of Project X. Profitability index using a financial calculator: Profitability Index = Present Value of Inflows / Present Value of Outflows Present Value of Inflows = NPV + Outflows = 6,094.30 + 40,000 = $26,094.30 Profitability Index = 26,094.30/40,000 = 1.30 (b) Find NPV using a financial calculator: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 40,000 +|– key, press the Enter key. Press down arrow, enter 20,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 13,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 14,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 16,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 14 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 8,771.93, which is the net present value of Project Y. Profitability Index Using Financial Calculator: Profitability Index = Present Value of Inflows / Present Value of Outflows Present Value of Inflows = NPV + Outflows = 8,771.93 + 40,000 = $46,469.82 Profitability Index = $46,469.82/40,000 = 1.16 20. Reinvestment rate assumption in capital budgeting (LO12-4) Turner Video will invest $58,500 in a project. The firm’s cost of capital is 12 percent. The investment will provide the following inflows. Year Inflow 1 $15,000 2 17,000 3 21,000 4 25,000 5 29,000 The internal rate of return is 11 percent. a. If the reinvestment assumption of the net present value method is used, what will be the total value of the inflows after five years? (Assume the inflows come at the end of each year.) b. If the reinvestment assumption of the internal rate of return method is used, what will be the total value of the inflows after five years? c. Generally is one investment assumption likely to be better than another? 12-20. Solution: Turner Video a. Reinvestment assumption of NPV No. of Future Year Inflows Rate Periods Value Factor Value 1 $15,000 12% 4 1.574 $23,610 2 17,000 12% 3 1.405 23,885 3 21,000 12% 2 1.254 26,334 4 25,000 12% 1 1.120 28,000 5 29,000 – 0 1.000 29,000 $130,829 b. Reinvestment assumption of IRR No. of Future Year Inflows Rate Periods Value Factor Value 1 $15,000 11% 4 1.518 $ 22,770 2 17,000 11% 3 1.368 23,256 3 21,000 11% 2 1.232 25,872 4 25,000 11% 1 1.110 27,750 5 29,000 – 0 1.000 29,000 $128,648 c. No. However, for investments with a very high IRR, it may be unrealistic to assume that reinvestment can take place at an equally high rate. The net present value method makes the more conservative assumption of reinvestment at the cost of capital. (a) Calculator Solution: Find PV of cash inflow using a financial calculator at 12 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 0, press the Enter key. Press down arrow, enter 15,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 17,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 21,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 25,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 29,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 12 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 74,235.87, which is the present value of the inflow. Next, find the FV of the 74,235.87 as of year 5 at a 12 percent annual rate. N I/Y PV PMT FV 5 12 74,235.87 0 CPT FV - 130,828.97 Answer: $130,828.97 (b) Calculator Solution: Find PV of cash inflow using a financial calculator at 11 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 0, press the Enter key. Press down arrow, enter 15,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 17,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 21,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 25,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 29,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 11 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 76,344.48, which is the present value of the inflow. Next, find the FV of the 76,344.48 as of year 5 at an 11 percent annual rate. N I/Y PV PMT FV 5 11 76,344.48 0 CPT FV - 128,644.88 Answer: $128,644.88 21. Modified internal rate of return (LO12-4) The Caffeine Coffee Company uses the modified internal rate of return. The firm has a cost of capital of 11 percent. The project being analyzed is as follows ($26,000 investment): Year Cash Flow 1 $12,000 2 11,000 3 9,000 a. What is the modified internal rate of return? An approximation from Appendix B is adequate. (You do not need to interpolate.) b. Assume the traditional internal rate of return on the investment is 17.5 percent. Explain why your answer in part a would be lower. 12-21. Solution: Caffeine Coffee Company Terminal Value (end of year 3) a. FV Factor Period of (11%) Future Growth (Appendix A) Value Year 1 $12,000 2 1.232 $14,784 Year 2 11,000 1 1.110 12,210 Year 3 9,000 0 1.000 9,000 Terminal Value $35,994 To determine the modified internal rate of return, calculate the yield on the investment. Use Appendix B for three periods, the answer is approximately 11 percent (.731). b. The answer is lower than 17.5 percent under the Modified IRR because inflows are reinvested at the cost of capital of 11 percent. Under the traditional IRR, inflows are reinvested at the internal rate of return of 17.5 percent, which leads to a higher terminal value. Calculator Solution: Using a financial calculator: Find the PV of cash inflow using a financial calculator at 11 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 0, press the Enter key. Press down arrow, enter 12,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 11,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 9,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 11 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 26,319.38, which is the present value of the inflow. Next find the FV of the 26,319.38 as of year 3 at an 11 percent annual rate. (a) N I/Y PV PMT FV 3 11 26,319.38 0 CPT FV 35,995.20 Answer: $35,995.20 Next, find the discount rate that produces a PV of 26,000. N I/Y PV PMT FV 3 CPT I I/Y 11.45 26,000 0 –35,995.20 Answer: MIRR = 11.45 22. Capital rationing and mutually exclusive investments (LO12-4) The Suboptimal Glass Company uses a process of capital rationing in its decision making. The firm’s cost of capital is 10 percent. It will only invest $77,000 this year. It has determined the internal rate of return for each of the following projects. Project Project Size Internal Rate of Return A $10,500 21% B 30,500 22 C 25,500 18 D 10,500 13 E 10,500 20 F 20,500 11 G 10,500 16 a. Pick out the projects that the firm should accept. b. If Projects A and B are mutually exclusive, how would that affect your overall answer? That is, which projects would you accept in spending the $77,000? 12-22. Solution: Suboptimal Glass Company You should rank the investments in terms of IRR. Project IRR Project Size Total Budget B 22% $30,500 $ 30,500 A 21 10,500 41,000 E 20 10,500 51,500 C 18 25,500 77,000 G 16 10,500 87,500 D 13 10,500 98,000 F 11 20,500 118,500 a. Because of capital rationing, only $77,000 worth of projects can be accepted. The four projects to accept are B, A, E, and C. Projects G and D provide positive benefits also, but cannot be undertaken under capital rationing. b. If Projects A and B are mutually exclusive, you would select Project B in preference to A. You would then include Project G with the freed up funds. In summary, you would accept B, E, C, and G. The last project would replace A and is of the same $10,500 magnitude. 23. Net present value profile (LO12-4) Keller Construction is considering two new investments. Project E calls for the purchase of earthmoving equipment. Project H represents an investment in a hydraulic lift. Keller wishes to use a net present value profile in comparing the projects. The investment and cash flow patterns are as follows: Project E ($20,000 Investment) Project H ($20,000 Investment) Year Cash Flow Year Cash Flow 1 $ 5,000 1 $16,000 2 6,000 2 5,000 3 7.000 3 4,000 4 10,000 a. Determine the net present value of the projects based on a zero discount rate. b. Determine the net present value of the projects based on a 9 percent discount rate. c. The internal rate of return on Project E is 13.25 percent, and the internal rate of return on Project H is 16.30 percent. Graph a net present value profile for the two investments similar to Figure 12-3. (Use a scale up to $8,000 on the vertical axis, with $2,000 increments. Use a scale up to 20 percent on the horizontal axis, with 5 percent increments.) d. If the two projects are not mutually exclusive, what would your acceptance or rejection decision be if the cost of capital (discount rate) is 8 percent? (Use the net present value profile for your decision; no actual numbers are necessary.) e. If the two projects are mutually exclusive (the selection of one precludes the selection of the other), what would be your decision if the cost of capital is (1) 6 percent, (2) 13 percent, and (3) 18 percent? Once again, use the net present value profile for your answer. 12-23. Solution: Keller Construction Company a. Zero discount rate Project E Inflows Outflow 8,000 = ($5,000 + $6,000 + $7,000 + $10,000) – $20,000 Project H Inflows Outflow $ 5,000 = ($16,000 + $5,000 + $4,000) – $20,000 b. 9 percent discount rate Project E Year Cash Flow PVIF at 9% Present Value 1 $ 5,000 .917 $ 4,585 2 6,000 .842 5,052 3 7,000 .772 5,404 4 10,000 .708 7,080 Present Value of Inflows $22,121 Present Value of Outflows 20,000 Net Present Value $ 2,121 12-23. (Continued) Project H Year Cash Flow PVIF at 9% Present Value 1 $16,000 .917 $14,672 2 5,000 .842 4,210 3 4,000 .772 3,088 Present Value of Inflows $21,970 Present Value of Outflows 20,000 Net Present Value $ 1,970 c. Net Present Value Profile d. Since the projects are not mutually exclusive, they both can be selected if they have a positive net present value. At a 9 percent cost of capital, they should both be accepted. As a side note, we can see Project E is superior to Project H. e. With mutually exclusive projects, only one can be accepted. Of course, that project must still have a positive net present value. Based on the visual evidence, we see: (i) 6 percent cost of capital—select Project E (ii) 13 percent cost of capital—select Project H (iii) Do not select either project Calculator Solution: (b) Using a financial calculator: Project E: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, press 20,000 +|–, press the Enter key. Press down arrow, enter 5,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 6,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 7,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 10,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 9 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 2,126.77, which is the NPV of Project E. Project H: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, press 20,000 +|–, press the Enter key. Press down arrow, enter 16,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 5,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 4,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 9 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 1,976.03, which is the NPV of Project H. 24. Net present value profile (LO12-4) Davis Chili Company is considering an investment of $35,000, which produces the following inflows: Year Cash Flow 1 $16,000 2 15,000 3 12,000 You are going to use the net present value profile to approximate the value for the internal rate of return. Please follow these steps: a. Determine the net present value of the project based on a zero discount rate. b. Determine the net present value of the project based on a 10 percent discount rate. c. Determine the net present value of the project based on a 15 percent discount rate (it will be negative). d. Draw a net present value profile for the investment and observe the discount rate at which the net present value is zero. This is an approximation of the internal rate of return based on the interpolation procedure presented in this chapter. 12-24. Solution: Davis Chili Company a. NPV @ 0% discount rate Inflows Outflow $8,000 = ($16,000 + $15,000 + $12,000) – $35,000 b. Year Cash Flow PVIF at 10% Present Value 1 $16,000 .909 $ 14,544 2 15,000 .826 12,390 3 12,000 .751 9,012 Present Value of Inflows $35,946 Present Value of Outflows 35,000 Net Present Value $ 946 c. Year Cash Flow PVIF at 15% Present Value 1 $16,000 .870 $ 13,920 2 15,000 .756 11,340 3 12,000 .658 7,896 Present Value of Inflows $33,156 Present Value of Outflows 35,000 Net Present Value ($ 1,844) d. Net Present Value Profile Calculator Solution: (b) Using a financial calculator at 10 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, press 35,000 +|–, press the Enter key. Press down arrow, enter 16,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 15,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 12,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 10 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 957.93, which is the NPV of the project. (c) Using a financial calculator at 20 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, press 35,000 +|–, press the Enter key. Press down arrow, enter 16,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 15,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 12,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 20 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = –1,854.61, which is the NPV of the project. 25. MACRS depreciation and cash flow (LO12-2) Telstar Communications is going to purchase an asset for $380,000 that will produce $180,000 per year for the next four years in earnings before depreciation and taxes. The asset will be depreciated using the three-year MACRS depreciation schedule in Table 12-12. (This represents four years of depreciation based on the half-year convention.) The firm is in a 35 percent tax bracket. Fill in the schedule below for the next four years. Earnings before depreciation and taxes _____ Depreciation _____ Earnings before taxes _____ Taxes _____ Earnings after taxes _____ + Depreciation _____ Cash flow _____ 12-25. Solution: Telstar Communications Corporation First, determine annual depreciation. Percentage Depreciation Depreciation Annual Year Base (Table 12-9) Depreciation 1 $380,000 .333 $ 126,540 2 380,000 .445 169,100 3 380,000 .148 56,240 4 380,000 .074 28,120 $380,000 Then, determine the annual cash flow. Earnings before depreciation and taxes (EBDT) will be the same for each year, but depreciation and cash flow will differ. 1 2 3 4 EBDT $180,000 $180,000 $180,000 $180,000 – D 126,540 169,100 56,240 28,120 EBT 53,460 10,900 123,760 151,880 T (35%) 18,711 3,815 43,316 53,158 EAT 34,749 7,085 80,444 98,722 + D 126,540 169,100 56,240 28,120 Cash Flow $161,289 $176,185 $136,684 $126,842 26. MACRS depreciation categories (LO12-4) Assume $65,000 is going to be invested in each of the following assets. Using Tables 12-11 and 12-12, indicate the dollar amount of the first year’s depreciation. a. Office furniture. b. Automobile. c. Electric and gas utility property. d. Sewage treatment plant. 12-26. Solution: a. Office furniture – Based on Table 12-8, this falls under 7-year MACRS depreciation. Then, examining Table 12-9, the first year depreciation rate is .143. Thus: b. Automobile – This falls under 5-year MACRS depreciation. This first year depreciation rate is .200. c. Electric and gas utility property – This falls under 20-year MACRS depreciation. The first year depreciation rate is .038. d. Sewage treatment plant – This falls under 15-year MACRS depreciation. This first year depreciation rate is .050. 27. MACRS depreciation and net present value (LO12-4) The Summit Petroleum Corporation will purchase an asset that qualifies for three-year MACRS depreciation. The cost is $160,000 and the asset will provide the following stream of earnings before depreciation and taxes for the next four years: Year 1 $70,000 Year 2 85,000 Year 3 42,000 Year 4 40,000 The firm is in a 35 percent tax bracket and has an 8 percent cost of capital. Should it purchase the asset? Use the net present value method. 12-27. Solution: Summit Petroleum Corporation First, determine annual depreciation. Percentage Depreciation Depreciation Annual Year Base (Table 12-9) Depreciation 1 $160,000 .333 $53,280 2 160,000 .445 71,200 3 160,000 .148 23,680 4 160,000 .074 11,840 $160,000 Then, determine the annual cash flow. 1 2 3 4 EBDT $70,000 $85,000 $42,000 $40,000 – D 53,280 71,200 23,680 11,840 EBT 16,720 13,800 18,320 28,160 T (35%) 5,852 4,830 6,412 9,856 EAT 10,868 8,970 11,908 18,304 + D 53,280 71,200 23,680 11,840 Cash Flow $64,148 $80,170 $35,588 $30,144 12-27. (Continued) Then, determine the net present value. Cash Flow Present Year (inflows) PVIF at 8% Value 1 $64,148 .926 $59,401 2 80,170 .857 68,706 3 35,588 .794 28,257 4 30,144 .735 22,156 Present Value of Inflows $178,520 Present Value of Outflows 160,000 Net Present Value $ 18,520 The asset should be purchased based on the net present value. Calculator Solution: (a) Using a financial calculator, Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, press 160,000 +|–, press the Enter key. Press down arrow, enter 64,148, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 80,170, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 35,588, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 30,144, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 8 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 18,536.79, which is the NPV of the project. 28. MACRS depreciation and net present value (LO12-4) Oregon Forest Products will acquire new equipment that falls under the five-year MACRS category. The cost is $300,000. If the equipment is purchased, the following earnings before depreciation and taxes will be generated for the next six years. Year 1 $112,000 Year 2 105,000 Year 3 82,000 Year 4 53,000 Year 5 37,000 Year 6 32,000 The firm is in a 30 percent tax bracket and has a 14 percent cost of capital. Should Oregon Forest Products purchase the equipment? Use the net present value method. 12-28. Solution: Oregon Forest Products First, determine annual depreciation. Percentage Depreciation Depreciation Annual Year Base (Table 12-9) Depreciation 1 $300,000 .200 $ 60,000 2 300,000 .320 96,000 3 300,000 .192 57,600 4 300,000 .115 34,500 5 300,000 .115 34,500 6 300,000 .058 17,400 $300,000 12-28. (Continued) Then, determine the annual cash flow. Annual Cash Flow 1 2 3 4 5 6 EBDT $112,000 $105,000 $82,000 $53,000 $37,000 $32,000 – D 60,000 96,000 57,600 34,500 34,500 17,400 EBT 52,000 9,000 24,400 18,500 2,500 14,600 T (30%) 15,600 2,700 7,320 5,550 750 4,380 EAT 36,400 6,300 17,080 12,950 1,750 10,220 + D 60,000 96,000 57,600 34,500 34,500 17,400 Cash Flow $ 96,400 $102,300 $74,680 $47,450 $36,250 $27,620 Then, determine the net present value. Cash Flow Present Year (Inflows) PVIF @ 14% Value 1 $ 96,400 .877 $ 84,543 2 102,300 .769 78,669 3 74,680 .675 50,409 4 47,450 .592 28,090 5 36,250 .519 18,814 6 27,620 .456 12,595 Present Value of Inflows $273,120 Present Value of Outflows 300,000 Net Present Value ($ 26,880) The equipment should not be purchased. Calculator Solution: Press the following keys: 2nd, CF, 2nd, CLR WORK. Calculator displays CFo, press 300,000 +|–, press the Enter key. Press down arrow, enter 96,400, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 102,300, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 74,680, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 47,450, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 36,250, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 27,620, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 14 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = –26,810.57, which is the NPV of the project. The equipment should not be purchased because NPV is negative. 29. MACRS depreciation and net present value (LO12-4) Universal Electronics is considering the purchase of manufacturing equipment with a 10-year midpoint in its asset depreciation range (ADR). Carefully refer to Table 12-11 to determine in what depreciation category the asset falls. (Hint: It is not 10 years.) The asset will cost $120,000, and it will produce earnings before depreciation and taxes of $37,000 per year for three years, and then $19,000 a year for seven more years. The firm has a tax rate of 40 percent. With a cost of capital of 12 percent, should it purchase the asset? Use the net present value method. In doing your analysis, if you have years in which there is no depreciation, merely enter a zero for depreciation. 12-29. Solution: Universal Electronics Because the manufacturing equipment has a 10-year midpoint of its asset depreciation range (ADR), it falls into the 7-year MACRS category as indicated in Table 12-8. Furthermore, we see that most types of manufacturing equipment fall into the 7-year MACRS category. With seven-year MACRS depreciation, the asset will be depreciated over eight years (based on the half-year convention). Also, we observe that the equipment will produce earnings for 10 years, so in the last 2 years there will be no depreciation write-off. We first determine the annual depreciation. Percentage Depreciation Depreciation Annual Year Base (Table 12-9) Depreciation 1 $120,000 .143 $17,160 2 120,000 .245 29,400 3 120,000 .175 21,000 4 120,000 .125 15,000 5 120,000 .089 10,680 6 120,000 .089 10,680 7 120,000 .089 10,680 8 120,000 .045 5,400 $120,000 12-29. (Continued) Next, determine the net present value. Cash Flow Present Year (Inflows) PVIF at 12% Value 1 $29,064 .893 $ 25,954 2 33,960 .797 27,066 3 30,600 .712 21,787 4 17,400 .636 11,066 5 15,672 .567 8,886 6 15,672 .507 7,946 7 15,672 .452 7,084 8 13,560 .404 5,478 9 11,400 .361 4,115 10 11,400 .322 3,671 Present Value of Inflows $123,053 Present Value of Outflows 120,000 Net Present Value $ 3,053 New asset should be purchased. Calculator Solution: Using a financial calculator, Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, press 120,000 +|–, press the Enter key. Press down arrow, enter 29,064, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 33,960, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 30,600, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 17,400, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 15,672, and press Enter. Press down arrow, enter 3, and press Enter. Press down arrow, enter 13,560, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 11,400, and press Enter. Press down arrow, enter 2, and press Enter. Press NPV; calculator shows I = 0; enter 12 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 3,053, which is the NPV of the project. The asset should be purchased because NPV is positive. 30. Working capital requirements in capital budgeting (LO12-4) The Spartan Technology Company has a proposed contract with the Digital Systems Company of Michigan. The initial investment in land and equipment will be $120,000. Of this amount, $70,000 is subject to five-year MACRS depreciation. The balance is in non-depreciable property. The contract covers six years; at the end of six years, the non-depreciable assets will be sold for $50,000. The depreciated assets will have zero resale value. The contract will require an additional investment of $55,000 in working capital at the beginning of the first year and, of this amount, $25,000 will be returned to the Spartan Technology Company after six years. The investment will produce $50,000 in income before depreciation and taxes for each of the six years. The corporation is in a 40 percent tax bracket and has a 10 percent cost of capital. Should the investment be undertaken? Use the net present value method. 12-30. Solution: Spartan Technology Company Although there are some complicated features to this problem, we are still comparing the present value of cash flows to the total initial investment. The initial investment is: Land and equipment $120,000 Working capital 55,000 Initial investment $175,000 In computing the present value of the cash flows, we first determine annual depreciation based on a $70,000 depreciation base. Percentage Depreciation Depreciation Annual Year Base (Table 12-9) Depreciation 1 $70,000 .200 $14,000 2 70,000 .320 22,400 3 70,000 .192 13,440 4 70,000 .115 8,050 5 70,000 .115 8,050 6 70,000 .058 4,060 $70,000 We then determine the annual cash flow. In addition to normal cash flow from operations; we also consider the funds generated in the sixth year from the sale of the non-depreciable property (land) and from the recovery of working capital. Then, determine the annual cash flow. Annual Cash Flow 1 2 3 4 5 6 EBDT $50,000 $50,000 $50,000 $50,000 $50,000 $50,000 – D 14,000 22,400 13,440 8,050 8,050 4,060 EBT 36,000 27,600 36,560 41,950 41,950 45,940 T (40%) 14,400 11,040 14,624 16,780 16,780 18,376 EAT 21,600 16,560 21,936 25,170 25,170 27,564 + D 14,000 22,400 13,440 8,050 8,050 4,060 + Sale of Non-depreciable Assets 50,000 + Recovery of Working Capital 25,000 Cash Flow $35,600 $38,960 $35,376 $33,220 $33,220 $106,624 We then determine the net present value. Cash Flow Present Year (Inflows) PVIF @ 10% Value 1 $ 35,600 .909 $ 32,360 2 38,960 .826 32,181 3 35,376 .751 26,567 4 33,220 .683 22,689 5 33,220 .621 20,630 6 106,624 .564 60,136 Present Value of Inflows $194,563 Present Value of Outflows 175,000 Net Present Value $ 19,563 The investment should be undertaken. Calculator Solution: Using a financial calculator: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, press 175,000 +|–, press the Enter key. Press down arrow, enter 35,600, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 38,960, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 35,376, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 33,220, and press Enter. Press down arrow, enter 2 and press Enter. Press down arrow, enter 106,624, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 10 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 19,643.68, which is the NPV of the project. 31. Tax losses and gains in capital budgeting (LO12-2) An asset was purchased three years ago for $120,000. It falls into the five-year category for MACRS depreciation. The firm is in a 35 percent tax bracket. Compute the following: a. Tax loss on the sale and the related tax benefit if the asset is sold now for $15,060. b. Gain and related tax on the sale if the asset is sold now for $56,060. (Refer to footnote 4 in the chapter.) 12-31. Solution: First determine the book value of the asset. Percentage Depreciation Depreciation Annual Year Base (Table 12-9) Depreciation 1 $120,000 .200 $24,000 2 120,000 .320 38,400 3 120,000 .192 23,040 Total Depreciation to Date $85,440 Purchase Price $120,000 – Total Depreciation to Date 85,440 Book Value $ 34,560 a. $15,060 sales price Book Value $34,560 Sales Price 15,060 Tax Loss on the Sale $19,500 Tax Loss on the Sale $19,500 Tax Rate 35% Tax Benefit $ 6,825 b. $56,060 sales price Sales Price $56,060 Book Value 34,560 Taxable Gain 21,500 Tax Rate 35% Tax Obligation $ 7,525 32. Capital budgeting with cost of capital computation (LO12-5) DataPoint Engineering is considering the purchase of a new piece of equipment for $240,000. It has an eight-year midpoint of its asset depreciation range (ADR). It will require an additional initial investment of $140,000 in non-depreciable working capital. Thirty-five thousand dollars of this investment will be recovered after the sixth year and will provide additional cash flow for that year. Income before depreciation and taxes for the next six years will be: Year Amount 1 $185,000 2 160,000 3 130,000 4 115,000 5 95,000 6 85,000 The tax rate is 40 percent. The cost of capital must be computed based on the following (round the final value to the nearest whole number): Cost (aftertax) Weights Debt Kd 9.5% 25% Preferred stock Kp 13.2 25 Common equity (retained earnings). Ke 18.0 50 a. Determine the annual depreciation schedule. b. Determine annual cash flow. Include recovered working capital in the sixth year. c. Determine the weighted average cost of capital. d. Determine the net present value. Should DataPoint purchase the new equipment? 12-32. Solution: DataPoint Engineering a. An eight-year midpoint of the ADR leads to five-year MACRS depreciation. Percentage Depreciation Depreciation Annual Year Base (Table 12-9) Depreciation 1 $ 240,000 .200 $ 48,000 2 240,000 .320 76,800 3 240,000 .192 46,080 4 240,000 .115 27,600 5 240,000 .115 27,600 6 240,000 .058 13,920 $240,000 b. Annual Cash Flow 1 2 3 4 5 6 EBDT $185,000 $160,000 $130,000 $115,000 $95,000 $85,000 – D 48,000 76,800 46,080 27,600 27,600 13,920 EBT $137,000 $ 83,200 $ 83,920 87,400 $67,400 71,080 T (40%) 54,800 33,280 33,568 34,960 26,960 28,432 EAT 82,200 49,920 50,352 52,440 40,440 42,648 + D 48,000 76,800 46,080 27,600 27,600 13,920 + Recovery of Working Capital 35,000 Cash Flow $130,200 $126,720 $ 96,432 $ 80,040 $68,040 $91,568 c. Weighted Average Cost of Capital Cost (aftertax) Weights Weighted Debt Kd 9.5% 25% 2.38% Preferred Stock Kp 13.2% 25% 3.30% Common Equity (retained earnings) Ke 18.0% 50% 9.00% Weighted Average Cost of Capital 14.68% d. Net Present Value Cash Flow Present Year (inflows) PVIF at 15% Value 1 $130,200 .870 $113,274 2 126,720 .756 95,800 3 96,432 .658 63,452 4 80,040 .572 45,783 5 68,040 .497 33,816 6 91,568 .432 39,557 Present Value of Inflows $391,682 * Present Value of Outflows 380,000 Net Present Value $ 11,682 *This represents the $240,000 for the equipment plus the $140,000 in initial working capital. The net present value ($11,682) is positive and DataPoint Engineering should purchase the equipment. Calculator Solution: Using a financial calculator: (d) Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, press 380,000 +|–, press the Enter key. Press down arrow, enter 130,200 and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 126,720, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 96,432, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 80,040, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 68,040, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 91,568, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 15 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 11,619.93, which is the NPV of the project. The net present value 11,619.93 is positive and DataPoint Engineering should purchase the equipment. 33. Replacement decision analysis (LO12-4) Hercules Exercise Equipment Co. purchased a computerized measuring device two years ago for $58,000. The equipment falls into the five-year category for MACRS depreciation and can currently be sold for $24,800. A new piece of equipment will cost $148,000. It also falls into the five-year category for MACRS depreciation. Assume the new equipment would provide the following stream of added cost savings for the next six years. Year Cash Savings 1 $62,000 2 54,000 3 52,000 4 50,000 5 47,000 6 36,000 The firm’s tax rate is 35 percent and the cost of capital is 12 percent. a. What is the book value of the old equipment? b. What is the tax loss on the sale of the old equipment? c. What is the tax benefit from the sale? d. What is the cash inflow from the sale of the old equipment? e. What is the net cost of the new equipment? (Include the inflow from the sale of the old equipment.) f. Determine the depreciation schedule for the new equipment. g. Determine the depreciation schedule for the remaining years of the old equipment. h. Determine the incremental depreciation between the old and new equipment and the related tax shield benefits. i. Compute the after tax benefits of the cost savings. j. Add the depreciation tax shield benefits and the after tax cost savings, and determine the present value. (See Table 12-17 as an example.) k. Compare the present value of the incremental benefits (j) to the net cost of the new equipment (e). Should the replacement be undertaken? 12-33. Solution: Hercules Exercise Equipment Co. a. Percentage Depreciation Depreciation Annual Year Base (Table 12-9) Depreciation 1 $58,000 .200 $11,600 2 58,000 .320 18,560 Total Depreciation to Date $30,160 Purchase Price $58,000 – Total Depreciation to Date 30,160 Book Value $27,840 b. Book Value $27,840 Sales Price 24,800 Tax Loss on the Sale $ 3,040 c. Tax Loss on the Sale $ 3,040 Tax Rate 35% Tax Benefit $ 1,064 d. Sales Price of the Old Equipment $ 24,800 Tax Benefit from the Sale 1,064 Cash Inflow from the Sale of the Old Equipment $ 25,864 e. Price of the New Equipment $148,000 – Cash Inflow from the Sale of the Old Equipment 25,864 Net Cost of the New Equipment $122,136 f. Depreciation schedule on the new equipment Percentage Depreciation Depreciation Annual Year Base (Table 12-9) Depreciation 1 $148,000 .200 $ 29,600 2 148,000 .320 47,360 3 148,000 .192 28,416 4 148,000 .115 17,020 5 148,000 .115 17,020 6 148,000 .058 8,584 $148,000 g. Depreciation schedule for the remaining years of the old equipment Percentage Depreciation Depreciation Annual Year* Base (Table 12-9) Depreciation 1 $58,000 .192 $11,136 2 58,000 .115 6,670 3 58,000 .115 6,670 4 58,000 .058 3,364 * The next four years represent the last four years on the old equipment. 12-33. (Continued) h. Incremental depreciation and tax shield benefits (1) (2) (3) (4) (5) (6) Year Depreciation on new Equipment Depreciation on old Equipment Incremental Depreciation Tax Rate Tax Shield Benefits 1 $29,600 $11,136 $18,464 .35 $ 6,462 2 47,360 6,670 40,690 .35 14,242 3 28,416 6,670 21,746 .35 7,611 4 17,020 3,364 13,656 .35 4,780 5 17,020 17,020 .35 5,957 6 8,584 8,584 .35 3,004 i. After tax cost savings Year Savings (1 – Tax Rate) After tax Savings 1 $62,000 .65 $40,300 2 54,000 .65 35,100 3 52,000 .65 33,800 4 50,000 .65 32,500 5 47,000 .65 30,550 6 36,000 .65 23,400 j. Present value of the total incremental benefits (1) (2) (3) (4) (5) (6) Year Tax Shield Benefits from Depreciation After tax Cost Savings Total Annual Benefits Present Value Factor 12% Present Value 1 $ 6,462 $40,300 $46,762 .893 $ 41,758 2 14,242 35,100 49,342 .797 39,326 3 7,611 33,800 41,411 .712 29,485 4 4,780 32,500 37,280 .636 23,710 5 5,957 30,550 36,507 .567 20,699 6 3,004 23,400 26,404 .507 13,387 Present Value of Incremental Benefits $168,365 k. Present Value of Incremental Benefits $168,365 Net Cost of New Equipment 122,136 Net Present Value $ 46,229 Based on the present value analysis, the equipment should be replaced. Calculator Solution: Using a financial calculator, Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CF0, press 122,136 +|–, press the Enter key. Press down arrow, enter 46,762, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 49,342, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 41,411, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 37,280, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 36,507, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 26,404, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 12 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT, calculator shows NPV = 46,210.46, which is the NPV of the project. Based on the present value analysis, the equipment should be replaced. COMPREHENSIVE PROBLEM The Woodruff Corporation purchased a piece of equipment three years ago for $230,000. It has an asset depreciation range (ADR) midpoint of eight years. The old equipment can be sold for $90,000. A new piece of equipment can be purchased for $320,000. It also has an ADR of eight years. Assume the old and new equipment would provide the following operating gains (or losses) over the next six years. New Equipment Old Equipment 1 $80,000 $25,000 2 76,000 16,000 3 70,000 9,000 4 60,000 8,000 5 50,000 6,000 6 45,000 (7,000) The firm has a 36 percent tax rate and a 9 percent cost of capital. Should the new equipment be purchased to replace the old equipment? CP 12-1. Solution: Woodruff Corporation Book Value of Old Equipment (ADR of 8 years indicates the use of the 5-year MACRS schedule) Year Depreciation Base Percentage Depreciation (Table 12-9) Annual Depreciation 1 $230,000 .200 $ 46,000 2 230,000 .320 73,600 3 230,000 .192 44,160 Total Depreciation to Date $163,760 Purchase Price $230,000 – Total Depreciation to Date 163,760 Book Value $ 66,240 Tax Obligation on the Sale Sales Price $ 90,000 Book Value 66,240 Taxable Gain 23,760 Tax Rate 36% Taxes $ 8,554 Cash Inflow from the Sale of the Old Equipment Sales Price $90,000 Taxes 8,554 $81,446 Net Cost of the New Equipment Purchase Price $320,000 – Cash Inflow from the Sale of the Old Equipment 81,446 Net Cost $238,554 Depreciation Schedule of the New Equipment (ADR of 8 years indicates the use of the 5-year MACRS schedule) Year Depreciation Base Percentage Depreciation (Table 12-9) Annual Depreciation 1 $320,000 .200 $ 64,000 2 320,000 .320 102,400 3 320,000 .192 61,440 4 320,000 .115 36,800 5 320,000 .115 36,800 6 320,000 .058 18,560 $320,000 Depreciation Schedule for the Remaining Years of the Old Equipment Year* Depreciation Base Percentage Depreciation (Table 12-9) Annual Depreciation 1 $230,000 .115 $26,450 2 230,000 .115 26,450 3 230,000 .058 13,340 *The next three years represent the last three years of the old equipment. CP 12-1. (Continued) Incremental Depreciation and Tax Shield Benefits (1) (2) (3) (4) (5) (6) Year Depreciation on New Equipment Depreciation on Old Equipment Incremental Depreciation Tax Rate Tax Shield Benefits 1 $ 64,000 $26,450 $37,550 .36 $13,518 2 102,400 26,450 75,950 .36 27,342 3 61,440 13,340 48,100 .36 17,316 4 36,800 36,800 .36 13,248 5 36,800 36,800 .36 13,248 6 18,560 18,560 .36 6,682 After tax cost savings New Equipment Old Equipment Cost Savings (1 – Tax Rate) After tax Savings $80,000 $25,000 $55,000 .64 $35,200 76,000 16,000 60,000 .64 38,400 70,000 9,000 61,000 .64 39,040 60,000 8,000 52,000 .64 33,280 50,000 6,000 44,000 .64 28,160 45,000 (7,000) 52,000 .64 33,280 CP 12-1. (Continued) Present value of the total incremental benefits. (1) (2) (3) (4) (5) (6) Year Tax Shield Benefits from Depreciation After tax Cost Savings Total Annuity Benefits Present Value Factor 9% Present Value 1 $13,518 $35,200 $48,718 .917 $ 44,674 2 27,342 38,400 65,742 .842 55,355 3 17,316 39,040 56,356 .772 43,507 4 13,248 33,280 46,528 .708 32,942 5 13,248 28,160 41,408 .650 26,915 6 6,682 33,280 39,962 .596 23,817 Present Value of Incremental Benefits $227,210 Net Present Value Present Value of Incremental Benefits $227,210 Net Cost of New Equipment 238,554 Net Present Value ($ 11,344) Based on the net present value analysis, the equipment should not be replaced. Solution Manual for Foundations of Financial Management Stanley B. Block, Geoffrey A. Hirt, Bartley R. Danielsen 9780077861612, 9781260013917, 9781259277160
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