CH-12 The Capital Budgeting Decision – Foundations of Financial Management : Book Guide

Chapter 12 Discussion Questions 12-1. 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. 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, amortization is subtracted out in arriving at net income, but this noncash deduction should be added back in to determine cash flow or actual dollars generated. 12-3. The weaknesses of the payback method are: a. There is no consideration of inflows after the cutoff period. b. The concept fails to consider the time value of money. 12-4. The cost of capital as determined in Chapter 11. 12-5. The selection of one investment precludes the selection of other alternative investments. 12-6. From a purely economic viewpoint, a firm should not ration capital. The firm should be able to find additional funds and increase its overall profitability and wealth through accepting investments to the point where marginal return equals marginal cost. 12-7. 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 12-8. In evaluating the forecast IRR and NPV, management must carefully review the assumptions that determined the timing and amount of estimated cash flows. In addition, it must carefully consider the particular project in relation to the firm’s overall business. Although the overall effects may be impossible to quantify, they may be critically important in deciding whether or not to invest. 12-9. The capital cost allowance system generally makes CCA tax shields available earlier than would a straight-line system tied to the asset’s economic life. 12-10. The investment tax credit represents direct dollar givebacks of a portion of an asset’s capital cost regardless of whether or not the firm is taxable. It reduces the amount of capital the firm has to invest in a project. 12-11. The cost of a capital is calculated based on the current market yields for various components of the capital structure. Current market yields incorporate future expectations about interest rates and thus about inflation. Since inflation is incorporated in the evaluation tool to be used in capital budgeting analysis, it is important to be consistent and incorporate the same implied inflation into projected cash flows. 12-12. An efficient market implies that all financial transactions give a return just adequate for the risk assumed and abnormal profits do not exist. Therefore in an efficient market NPV = 0 for all investments. It is highly unlikely that the financial manager faces efficient markets in markets such as technology, machinery, and labour. 12-13. 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 that inflows are reinvested at the cost of capital. Internet Resources and Questions See Finance in Action boxes within chapter. Problems 12-1. Corporate cash flow Earnings before amortization and taxes $100,000 Amortization – 50,000 Earnings before taxes 50,000 Taxes @ 34% 17,000 Earnings after taxes 33,000 Amortization + 50,000 Cash flow $ 83,000 Alternative cash flow calculation: $100,000 17,000 (taxes) $83,000 cash flow 12-2. Corporate cash flow a. Earnings before amortization and taxes $100,000 Amortization – 10,000 Earnings before taxes 90,000 Taxes @ 34% 30,600 Earnings after taxes 59,400 Amortization + 10,000 Cash flow $ 69,400 b. Cash flow (problem 1) $83,000 or [$50,000 – $10,000](T) Cash flow (problem 2a) 69,400 = 40,000 (.34) Difference in cash flow $13,600 = $13,600 12-3. Elias Corporation a. Average accounting return (AAR ) = Year EBAT 1 $40,000 2 45,000 3 50,000 4 55,000 5 60,000 Amortization $20,000 20,000 20,000 20,000 20,000 EBT $20,000 25,000 30,000 35,000 40,000 Average earnings after tax Average accounting return ( AAR ) = Average earnings after tax Average book value Taxes $8,000 10,000 12,000 14,000 16,000 EAT $12,000 15,000 18,000 21,000 24,000 90,000 $18,000 $18,000 = 0.3600 = 36.0% ($100,000 + 0) / 2 b. Seems like a pretty good return, but we need a criteria for acceptance of projects. What AAR is enough? c. AAR does not use the time value of money, cash flows or the market value of assets. 12-4. A Firm Earnings before amortization and taxes (cash flow) Taxes (cash flow) 25% Earning after taxes Cash flow $200,000 50,000 $150,000 $150,000 Earnings before amortization and taxes (cash flow) Amortization (noncash expense) Earnings before taxes Taxes (cash flow) 25% Earning after tax Amortization Cash flow $200,000 200,000 0 0 $ 0 200,000 $200,000 12-5. Bob Cole 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. 12-6. Year EBAT 1 $ 90,000 2 100,000 3 125,000 Mercury Corporation Amortization $60,000 60,000 60,000 EBT $30,000 40,000 65,000 Average earnings after tax Average accounting return ( AAR ) = Taxes $12,000 16,000 26,000 EAT $18,000 24,000 39,000 81,000 $27,000 $27,000 = 0.3000 = 30.00% ($180,000 + 0) / 2 12-7. Payback Payback for Investment A Payback for Investment B $50,000 – $10,000 40,000 – 11,000 29,000 – 13,000 16,000 – 16,000 $50,000 – $20,000 30,000 – 25,000 5,000/ 15,000 1 year 2 years 3 years 4 years 1 year 2 years 0.33 yrs Payback: Investment A = 4.00 years Payback: Investment B = 2.33 years Investment B would be selected because of the faster payback. 12-8. Payback Revisited The $30,000,000 inflow would still leave the payback period for Investment A at 4 years. It would remain inferior to Investment B under the payback method. 12-9. Payback versus NPV NPV for Investment A Year 1 2 3 4 5 Cash flow $ 10,000 11,000 13,000 16,000 30,000 Present value of inflows Initial investment NPV (net present value) Present value @ 15% $ 8,696 8,318 8,548 9,148 14,915 $49,625 50,000 $ (375) NPV for Investment B Year 1 2 3 Cash flow $20,000 25,000 15,000 Present value of inflows Initial investment NPV (net present value) Present value @ 15% $17,391 18,904 9,863 $46,158 50,000 $(3,842) Neither project is attractive, with investment B less attractive. 12-10. Short-Line Railroad a. Payback for Electric Co. $100,000 – $70,000 30,000 – 15,000 15,000 – 0 1 year 2 years 3 years Payback for Water Works $100,000 – $15,000 85,000 – 15,000 70,000 – 0 1 year 2 years 3 years Both projects have equal payback = 3 years b. The Electric Co. has a cash flow of $70,000 in the first year but because the time value of money is ignored, the $70,000 has the same value as the cash flow in year three for Water Works. 12-11. Britney Javelin Company a. Payback for Project M $15,000 – $8,100 6,900 – 5,400 1 year 2 years Payback for Project N $15,000 – $6,750 8,250 – 4,050 1 year 2 years 1,500/ 4,050 2.37 years 4,200 / 10,800 2.39 years Based on payback the projects are virtually identical. b. NPV for Project M Year Cash flow 1 $8,100 2 5,400 3 4,050 Present value of inflows Initial investment NPV (net present value) Present value @ 7% $7,570 4,717 3,306 $15,593 15,000 $ 593 NPV for Project N Year Cash flow 1 $ 6,750 2 4,050 3 10,800 Present value of inflows Initial investment NPV (net present value) Present value @ 7% $6,308 3,537 8,816 $18,661 15,000 $ 3,661 Both projects are attractive, but project N adds the most value to the firm. It has the higher NPV. c. The NPV is preferred and gives more confidence because it incorporates the time value of money and considers all the cash flows. 12-12. A Firm PV $24,907 = = 5.535 ( Appendix D) A $4,500 For N = 8, we find 5.535 under the 9% column. Therefore IRR = 9% PVIFA = Calculator: Compute: 12-13. PV = $24,907 FV = 0 N=8 %I/Y =? %I/Y = 9.00% PMT = $4,500 Ned Worth PV $31,782 = = 10.594 ( Appendix D) $3,000 A For N = 20, we find 10.594 under the 7% column. Therefore IRR = 7% PVIFA = Calculator: Compute: 12-14. PV = $31,782 FV = 0 N = 20 %I/Y =? %I/Y = 7.00% PMT = $3,000 King’s Department Store PV $13,869 = = 4.623 ( Appendix D) A $3,000 For N = 6, we find 4.623 under the 8% column. Therefore IRR = 8% PVIFA = Calculator: Compute: PV = $13,869 FV = 0 N=6 %I/Y =? %I/Y= 8.00% PMT = $3,000 The machine should not be purchased since its return is less than 12%. 12-15. a. Year 1 2 3 Elgin Restaurant Supplies Cash flow $10,000 9,000 6,500 Present value of inflows Initial investment NPV (net present value) PV @ 14% @15% $ 8,772 $ 8,696 6,925 6,805 4,387 4,274 $20,084 $19,775 20,000 20,000 $ 84 $ (225) IRR is the discount rate at which the NPV = 0. This is a trial and error process. In this case IRR is between 14% and 15% (14% + 84/ 309 × 1% = 14.27%) b. Year 1 2 3 Cash flow $10,000 9,000 6,500 Present value of inflows Initial investment NPV (net present value) Present value @ 12% $ 8,929 7,175 4,627 $20,731 20,000 $ 731 The machine should be purchased as the NPV is positive. c. Profitability index = PV of inflows $20,731 = = 1.037 PV of outflows $20,000 12-16. Year 1 2 3 4 5 Altman Hydraulic Corporation Cash flow $54,000 66,000 (60,000) 57,000 120,000 Present value of inflows Present value of outflows NPV(net present value) Present value @ 11% $48,649 53,567 (43,871) 37,548 71,214 $167,107 160,000 $ 7,107 The NPV is positive and the project should be undertaken. 12-17. Year 0 1 2 3 3 Hamilton Control Systems Cash flow Present value @ 10% $(90,000) $(90,000) 23,000 20,909 38,000 31,405 60,000 45,079 (15,000) (11,270) Net present value $(3,877) The NPV is negative. The project should not be undertaken. Note, the $15,000 outflow could have been subtracted out of the $60,000 inflow in the third year and the same answer would result. 12-18. Twelve Inch Toes Corp. Find the present value of a deferred annuity: PV A = A × PV IFA (n = 8, i = 11%) (Appendix D) PV A = $43,000 × 5.146 = $221,278 Calculator: Compute: PV =? FV = 0 PMT = $43,000 N=8 %I/Y = 11% PV = $221,283 Discount this value to PV from the beginning of the third period (end of 2nd). PV = FV × PV IF (n = 2, i = 11%) (Appendix B) PV = $221,278 × .812 = $179,678 Calculator: Compute: PV =? FV = $221,283 N=2 %I/Y = 12% PV = $179,598 Present value of inflows Present value of outflows NPV (net present value) The project should be undertaken. $179,598 175,000 $ 4,598 PMT = 0 12-19. a. NPV Year 1 2 3 4 5 DeBarry Corporation Cash flow Present value @ 9% $ 10,000 $ 9,174 10,000 8,417 16,000 12,355 18,000 12,752 20,000 12,999 Present value of inflows $55,697 50,000 Present value of outflows (cost) NPV (net present value) $ 5,697 b. IRR Since we have a positive net present value, the internal rate of return must be larger than 9%. Because of uneven cash flows, we need to use trial and error. Counting the net present value calculation as the first trial, we now try 11% for our second trial. Year 1 2 3 4 5 Cash flow $ 10,000 10,000 16,000 18,000 20,000 Present value of inflows Present value @ 11% $ 9,009 8,116 11,699 11,857 11,869 $52,550 A two percent increase in the discount rate has eliminated over one-half of the net present value so another two percent should be close to the answer. Year 1 2 3 4 5 Cash flow $ 10,000 10,000 16,000 18,000 20,000 Present value of inflows Present value @13% $ 8,850 7,831 11,089 11,040 10,855 $49,665 The correct answer must fall between 11% and 13%. We interpolate. $52,550 49,665 $ 2,885 PV @ 11% PV @ 13% $52,550 50,000 $ 2,550 PV @ 11% (Cost) $2,550 (0.02) = 0.11 + 0.8839(0.02) $2,885 = 0.11 + .0177 = 0.1277 = 12.77% IRR (interpolate ) = 0.11 + Calculator: Compute: CF i = – 50,000; 10,000; 10,000; 16,000; 18,000; 20,000 %I/Y =? IRR = 12.76% c. The project should be accepted because the NPV is positive and the IRR exceeds the cost of capital. 12-20. a. NPV Year 1 2 3 4 5 Green Goddess Salad Oil Company Cash flow Present value @ 10% $15,000 $13,636 20,000 16,529 25,000 18,783 10,000 6,830 5,000 3,105 Present value of inflows $58,883 Present value of outflows (cost) 45,000 NPV (net present value) $13,883 b. IRR Since we have a positive net present value, the internal rate of return must be larger than 10%. Because of uneven cash flows, we need to use trial and error. Counting the net present value calculation as the first trial, we now try 20% for our second trial. Year 1 2 3 4 5 Cash flow $15,000 20,000 25,000 10,000 5,000 Present value of inflows Present value @ 20% $12,500 13,889 14,468 4,823 2,009 $47,689 Since 20% is not high enough, we try a higher rate, say 25%. Year 1 2 3 4 5 Cash flow $15,000 20,000 25,000 10,000 5,000 Present value of inflows Present value @ 25% $12,000 12,800 12,800 4,096 1,638 $43,334 The correct answer must fall between 20% and 25%. We interpolate. $47,689 43,334 $ 4,355 PV @ 20% PV @ 25% $47,689 45,000 $ 2,689 PV @ 20% (Cost) $2,689 (0.05) = 0.20 + 0.6175(0.05) $4,355 = 0.20 + .0309 = 0.2309 = 23.09% IRR (interpolation ) = 0.20 + Interpolation is more accurate using a small difference between trials. Calculator: CF i = – 45,000; 15,000; 20,000; 25,000; 10,000; 5,000 %I/Y =? Compute: IRR = 22.99% c. The project should be accepted because the net present value is positive and the IRR exceeds the cost of capital. 12-21. Boring Corporation NPV for Project X (Weather Report DVDs) Year Cash flow Present value @ 10% 1 $5,000 $ 4,545 2 3,000 2,479 3 4,000 3,005 4 3,600 2,459 Present value of inflows 12,488 10,000 Present value of outflows (cost) NPV (net present value) $ 2,488 Profitability index = PV of inflows $12,488 = = 1.2488 PV of outflows $10,000 NPV for Project Y (Slow-Mo Commercials) Year Cash flow Present value @ 10% 1 $15,000 $ 13,636 2 8,000 6,612 3 9,000 6,762 4 11,000 7,513 Present value of inflows $34,523 30,000 Present value of outflows (cost) NPV (net present value) $ 4,523 Profitability index = PV of inflows $34,523 = = 1.1508 PV of outflows $30,000 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. What can be earned on the differential investment of $20,000 (between projects) is relevant. If there are no other investment opportunities Project Y with the higher NPV may be the preferred investment. 12-22. Turner Video a. Reinvestment assumption of NPV Year 1 2 3 4 5 Inflows Rate No. of Periods $10,000 12,000 16,000 20,000 24,000 9% 9% 9% 9% – 4 3 2 1 0 Future value $14,116 15,540 19,010 21,800 24,000 $94,466 b. Reinvestment assumption of IRR Year 1 2 3 4 5 Inflows Rate No. of Periods $10,000 12,000 16,000 20,000 24,000 14% 14% 14% 14% – 4 3 2 1 0 Future value $ 16,890 17,779 20,794 22,800 24,000 $102,263 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. 21st Century Corporation 12-23. a. Year 1 2 3 PVIF = Inflows Rate # of Periods Future value $10,000 9,000 6,800 8% 8% 8% 2 1 0 $11,664 9,720 6,800 $28,184 PV $20,000 = = 0.7096 ( Appendix B) FV $28,184 At 3 periods, appendix B suggests a modified IRR of 12% Calculator: Compute: PV = $20,000 FV = $28,184 N=3 %I/Y = ? %I/Y = 12.11% PMT = 0 b. Calculator: CF i = – 20,000; 10,000; 9,000; 6,800 Compute: IRR = 14.91% %I/Y = ? The difference occurs because the traditional IRR assumes reinvestment at the IRR whereas the modified IRR (MIRR) assumes reinvestment at the lower cost of capital. 12-24. Strawb Music a. Year 1 2 3 PVIF = Inflows Rate # of Periods Future value $17,000 13,200 16,100 9% 9% 9% 2 1 0 $20,198 14,388 16,100 $50,686 PV $43,000 = = 0.8484 ( Appendix B) FV $50,686 At 3 periods, appendix B suggests a modified IRR of about 5.65% Calculator: Compute: PV = $43,000 FV = $50,686 N=3 %I/Y = ? %I/Y = 5.63% PMT = 0 b. Calculator: CF i = – 43,000; 17,000; 13,200; 16,100 %I/Y = ? Compute: IRR = 3.83% The project would not be acceptable because both the IRR and MIRR are below the firm’s cost of capital of 9%. 12-25. Tosca Spoons Company a. Year 1 2 3 PVIF = Inflows Rate # of Periods Future value $12,000 17,500 24,600 11% 11% 11% 2 1 0 $14,785 19,425 24,600 $58,810 PV $38,000 = = 0.6461 ( Appendix B) FV $58,810 At 3 periods, appendix B suggests a modified IRR of about 15.70% Calculator: Compute: PV = $38,000 FV = $58,810 N=3 %I/Y = ? %I/Y = 15.67% PMT = 0 b. Calculator: CF i = – 38,000; 12,000; 17,500; 24,600 %I/Y = ? Compute: IRR = 17.58% The project would be acceptable because both the IRR and MIRR are above the firm’s cost of capital of 11%. 12-26. Suboptimal Glass Company You should rank the investments in terms of IRR. Project IRR Project Size Total Budget E D C G A B F 23% 17.0 16.5 16.0 15.0 14.0 11.0 $10,000 10,000 25,000 15,000 10,000 30,000 20,000 $ 10,000 20,000 45,000 60,000 70,000 100,000 120,000 a. Because of capital rationing, only $60,000 worth of projects can be accepted. The four projects to accept are E, D, C and G. Projects A and B provide positive benefits also, but cannot be undertaken under capital rationing. b. If Projects D and E are mutually exclusive, you would select Project E in preference to D. In summary, you would accept E, C, G and A. The last project would replace D and is of the same $10,000 magnitude. 12-27. Keller Construction a. Zero discount rate Project E Inflows Outflow $8,000 = ($5,000 + $6,000 + $7,000 + $10,000) – $20,000 Project H Inflows $5,000 = ($16,000 + $5,000 + $4,000) Outflow – $20,000 b. 9% discount rate Project E Year 1 2 3 4 Cash Flow Present Value @ 9% $ 5,000 $ 4,587 6,000 5,050 7,000 5,405 10,000 7,084 Present value of inflows 22,126 20,000 Present value of outflows (cost) NPV (net present value) $ 2,126 Project H Year 1 2 3 Cash Flow Present Value @ 9% $16,000 $14,679 5,000 4,208 4,000 3,089 Present value of inflows 21,976 20,000 Present value of outflows (cost) NPV (net present value) $ 1,976 c. Net Present Value Profile Net present value profile NPV 800 Project E 600 400 Project Crossover point 200 IR H = 0 0 5 10 15 IR C 20 = - Discount rate (%) d. Since the projects are not mutually exclusive, they both can be selected if they have a positive net present value. At a 10% rate, 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% cost of capital ! select Project E (ii) 13% cost of capital ! select Project H (iii) 118% cost of capital - Do not select either project 12-28. Luft Watch Company a. NPV @ 0% discount rate Inflows $4,000 = (8,000 + $7,000 + $4,000) Outflow – $15,000 b. 10% discount rate Year 1 2 3 Cash Flow $8,000 7,000 4,000 Present value of inflows Present value of outflows NPV (net present value) Present Value @ 10% $7,273 5,785 3,005 16,063 15,000 $ 1,063 c. 20% discount rate Year 1 2 3 Cash Flow $8,000 7,000 4,000 Present value of inflows Present value of outflows Net Present Value Present Value @ 20% $ 6,667 4,861 2,315 13,843 15,000 $(1,157) d. Net present value profile Net present value 4,000 2,000 0 5% 10% 20% 15% Discount rate (%) e. Interpolate between 14% and 15%: Year 1 2 3 Cash Flow $8,000 7,000 4,000 Present value of inflows $15,104 14,880 $ 224 PV @ 14% PV @ 15% Present Value @ 14% @ 15% $ 7,018 $ 6,957 5,386 5,293 2,700 2,630 $15,104 $14,880 $15,104 15,000 $ 104 PV @ 14% (Cost) $104 (0.01) = 0.14 + 0.4643(0.01) $224 = 0.14 + .0046 = 0.1446 = 14.46% IRR (interpolatation ) = 0.14 + Calculator: CF i = – 15,000; 8,000; 7,000; 4,000 Compute: IRR = 14.46% %I/Y =? 12-29. XYZ Corporation a. The original cost of the building would be deducted from the Class 3 pool as the lower of sale price or original cost is used when disposing of an asset. The Class 3 UCC is: $12,000,000 4,500,000 $ 7,500,000 The present value of the tax shield lost on disposal would be: Salvage × d T c / (d + r) = $4,500,000 × .05 × .25/ (.05 + .12) = $4,500,000 × .0735294 = $330,882 The $500,000 difference ($5,000,000 – $4,500,000) would be a capital gain for tax purposes. Fifty percent of a capital gain is taxable. XYZ’s tax on the taxable capital gain is: 0.50 × capital gain × T × PV IF (n = 1, i = 12%) = 0.50 × $500,000 × .25 × PV IF (n = 1, i = 12%) = $55,804 The total present value of tax consequences = $330,882 + $55,804 = b. Class 3 UCC $386,686 $4,000,000 4,500,000 $ (500,000) The negative balance of $500,000 is recaptured amortization. This is added to income in the year of disposal thus increasing tax by: Income increase × T × PV IF (n = 1, i = 12%) = $500,000 × .25 × PV IF (n = 1, i = 12%) = $111,607 The present value of the tax shield lost on disposal would be: Salvage × d T c / (d + r) = $4,000,000 × .05 × .25 / (.05 + .12) = $4,000,000 × .0735294 = $294,118 Since there was only $4,000,000 in the pool, that is the basis for calculating the tax shield lost on disposal. The tax on the taxable capital gain is $55,804 (as in part a). The total present value of tax consequences = $111,607 + $294,118 + $55,804 = c. Class 3 UCC $461,529 $6,000,000 4,500,000 $1,500,000 The $1,500,000 left over in the Class 3 pool is a terminal loss and can be written off against income in the year of disposal. The tax savings is: Terminal loss × T × PV IF (n = 1, i = 12%) = $1,500,000 × .25 × PV IF (n = 1, i = 12%) = $334,821 The present value of the tax shield lost on disposal would be: Amount in pool × = $6,000,000 × = $6,000,000 × = $441,176 d T c / (d + r) .05 × .25 / (.05 + .12) .0735294 The tax on the taxable capital gain is $55,804 (as in part a). The total present value of tax consequences = $(334,821) + $441,176 + $55,804 = $162,159 12-30. Capital Cost Allowance a. The assets will fall under Class 10 (auto equipment) with an allowable CCA rate of 30%. b. Year 1 Increase in pool’s UCC Allowable CCA in 1st year Year 2 Remaining increase in UCC Additional CCA allowable = $95,000 = 1/2 ($95,000 × .30) = $14,250 = = = = $95,000 – $14,250 $80,750 $80,750 × .30 $24,225 c. The assets would then fall under Class 8 (machinery): The allowable CCA rate would be 20%. d. There would be no effects except to the extent of any dollar amounts realized on disposal. 12-31. Coastal Shipping Corporation a. The original cost of the vessel would be deducted from the Class 7 pool as the lower of sale price or original cost is used when disposing of an asset. The Class 7 UCC is: $2,000,000 1,000,000 $1,000,000 The present value of the tax shield lost on disposal would be: Amount lost from pool (salvage) × dT c / (d + r) = $1,000,000 × .15 × .25 / (.15 + .10) = $1,000,000 × .15 = $150,000 This is the extent of the tax consequences. b. Class 3 UCC $ 800,000 1,000,000 $ (200,000) The negative balance of $200,000 is recaptured amortization. This is added to income in the year of disposal increasing tax by: Income increase × T × PV IF (n = 1, i = 10%) = $200,000 × .25 × PV IF (n = 1, i = 10%) = $45,454 The present value of the tax shield lost on disposal would be: Amount lost from pool (salvage) × dT c / (d + r) = $800,000 × .15 × .25 / (.15 + .10) = $800,000 × .15 = $120,000 Since there was only $800,000 in the pool, that is the basis for calculating the tax shield lost on disposal. The total present value of tax consequences = $45,454 + $120,000 = c. Class 3 UCC $165,454 $ 600,000 1,000,000 $(400,000) The negative balance of $400,000 is recaptured amortization. This is added to income in the year of disposal thus increasing tax by: Income increase × T × PV IF (n = 1, i = 10%) = $400,000 × .25 × PV IF (n = 1, i = 10%) = $90,909 The present value of the tax shield lost on disposal would be: Amount lost from pool (salvage) × dT c / (d + r) = $600,000 × .15 × .25 / (.15 + .10) = $600,000 × .15 = $90,000 Since there was only $600,000 in the pool, that is the basis for calculating the tax shield lost on disposal. The total present value of tax consequences = $90,909 + $90,000 = $180,909 12-32. Nexus Corp. a. The CCA class for aircraft is Class 9, with a CCA rate of 25%. b. CCA allowable in 1st year $1,500,000 × 25% × .5 = $187,500 CCA allowable in 2nd year [$1,500,000 − $187,500] × 25% = $328,125 c. The CCA class for hangars is class 6, with a CCA rate of 10%. d. After 10 years the UCC of Class 9 will be(including CCA for the 10th year): $1,500,000[1 − (.25/2) (1 − .25)10 – 1] = $1,500,000 [(.875) (.75)9] = $1,500,000 [.0656991] = $98,549 If the plane is scrapped after the 10th year the consequences are: Recapture of $200,000 98,549 $101,451 Thus $101,451 will be added to taxable income in the eleventh year. To determine the taxes payable: multiple by Nexus’ tax rate. 12-33. Brunswick Corporation Increased sales Increased costs Earnings before amortization and taxes Amortization ($40,000 × .20 × 1/2) Earnings before taxes Taxes @ 38% Earnings after tax Amortization Net cash flow 12-34. $65,000 35,000 30,000 4,000 26,000 9,880 16,120 4,000 $20,120 Acme Auto Parts Ltd. a. The investment qualifies for a 35% ITC. $1,700,000 × .35 = $595,000 b. The original cost base is: $1,700,000 – $595,000 = $1,105,000 c. The effects of ITC and CCA are realized at year-end. Therefore: PV (ITC) = ITC × PV IF (n = 1, i = 10%) = $595,000 × PV IF (n = 1, i = 10%) = $540,909  dT  1 + .5r  PV (CCA) = [C PV - S PV ] C    r + d  1 + r   .20 × .22  1 + .5 × .10  = [$1,105,000]   = $154,700 + . 10 . 20 1 + . 10    Total combined present value of tax benefits is: = $540,909 + $154,700 = $695,609 12-35. a. Follett Enterprises (Beginning) Year UCC Purchases Sales Rate 0 0 $300,000 – (.10)(.50) 1 $285,000 – – (.10) 2 256,500 – – (.10) 250,000 – (.10)(.50) 3 4 468,350 421,515 This year 759,363 Remaining UCC 259,363 – – 400,000 – – – (.10) (.10) (.10)(.50) Tax shield CCA @ 30% $15,000 $ 4,500 28,500 8,550 25,650 12,500 38,150 11,445 46,835 14,051 42,152 20,000 62,152 18,646 500,000 Terminal loss 77,809 b. As in (a) only no terminal loss. CCA lost from this year forward on $500,000, but $259,363 remains in the pool. Year 1 2 3 4 5 Tax shield Present value @ 14% $ 4,500 $ 3,947 8,550 6,579 11,445 7,725 14,051 8,319 18,646 9,684 Present value of tax shields $36,254 (without terminal loss) c. With formula: PV of impacts on pool: Year Purchase/ sell 0 $300,000 2 250,000 4 400,000 5 (500,000) PV @ 14% $300,000 192,367 236,832 (259,684) $469,515  dT  1 + .5r  PV (CCA ) = [C - S PV ] C    r + d  1 + r   0.10 × 0.30  1 + .5 × .14  = [$469,515]    0.14 + 0.10  1 + .14  = [$469,515](0.125)(0.938596 ) = $55,086 Difference between formula and year by year calculation: = $55,086 – $36,254 = $18,832 Without formula: $759,363 remains in the pool before $500,000 sale.  0.10 × 0.30   0.10 × 0.30  1 + .5 × .14  PV (CCA ) = [$759,363]  − [$500,000]    0.14 + 0.10  1 + .14   0.14 + 0.10  = [$759,363](.125) − $500,000(.11732456) = $94,920 − $58,662 PV = = $36,258 × PV IF (n = 5, %I/Y = 14) $18,818 (rounding difference) Calculator: Compute: Note: = $36,258 PV =? FV = $36,258 N=5 %I/Y = 14% PV = $18,831 PMT = 0 The half year rule has already been applied to arrive at the $759,363. 12-36. Bryant Car Rental Corporation N=2 Year Event T = 30% r = 11% Expected Cash Flow d = 40% (class 16) Aftertax Cash Flow Present Value @ 11% 0 0 1-2 Investment $(625,000) – Working capital (5,000) – Revenue $16,500 × 25 = 412,500 288,750 1-2 Expenses $0.12(40,000) × 25 = 120,000 84,000 2 Sale (.60) (625,000) = 375,000 – 2 WC recovery 5,000 – 0 CCA pool  dT  1 + .5r  PV (CCA ) = [C PV - S PV ] C    r + d  1 + r  $(625,000) ( 5,000) 494,491 (143,852) 304,358 4,058  0.40 × 0.30  1 + .5 × .11  = [$625,000 − $304,358]    0.11 + 0.40  1 + .11  = [$320,642](0.23529412 )(0.95045045) = 71,707 NPV = $100,762 Bryant Car Rental Corporation should purchase the autos as the firm’s value will decrease by $100,762. 12-37. MicroElectronics Ltd. N=9 T = 15% r = 14% Expected Year Event Cash Flow 0 Investment $(60,000) 1 ITC .20($60,000) = 12,000 1-2 Costs (15,000) 2 Working capital .10(116,000) = (11,600) 3-9 Revenues 116,000 3-7 8-9 9 0 Expenses Expenses WC recovery CCA pool (88,000) (101,000) d = 20% (class 8) ITC = 20% Aftertax Cash Flow – Present Value @ 14% $ (60,000) – (12,750) 10,526 (20,995) – 98,600 422,827 (74,800) (256,794) (85,850) (141,366) (8,926) 11,600 325,352 (197,595) (56,495) 3,567  dT  1 + .5r  PV (CCA ) = [C PV - S PV ] C    r + d  1 + r   0.20 × 0.15  1 + .5 × .14  = [$60,000 − 0]    0.14 + 0.20  1 + .14  = [$60,000](0.08823529 )(0.938596491) = 4,969 ITC from CCA pool  dT   0.20 × 0.15  PV (CCA ) = [- ITC PV ] C  = [− $12,000]   0.14 + 0.20  r +d (941) = [− $12,000](0.08823529 ) = ($1,059 ) NPV = ($538) MicroElectronics should not purchase the new machine. 12-38. Nelson Technology N=5 T = 30% Year Event 0 0 1 Investment Trade- in ITC 1 2 3 4 5 0 Cost savings Cost savings Cost savings Cost savings Cost savings CCA pool r = 11% Expected Cash Flow d = 20% (class 8) ITC = 10% Aftertax Cash Flow Present Value @ 11% – – $(320,000) 78,000 $(320,000) 78,000 .10(320,000) = 32,000 95,000 86,000 72,000 60,000 58,000 – 66,500 60,200 50,400 42,000 40,600 28,829 59,910 48,860 36,852 27,667 24,094  dT  1 + .5r  PV (CCA ) = [C PV - S PV ] C    r + d  1 + r   0.20 × 0.30  1 + .5 × .11  = [$320,000 − $78,000]    0.11 + 0.20  1 + .11  = [$242,000](0.19354839 )(0.95045045) = 44,518 1 ITC from CCA pool  dT   0.20 × 0.30  PV (CCA ) = [- ITC PV ] C  = [− $32,000]   0.11 + 0.20  r +d (5,580) = [− $32,000](0.19354939 ) = ($6,194 ) NPV = $23,150 Nelson should purchase the new machine. Comprehensive Problems 12-39. Ontario Corporation Tax Year 1 2 3 4 5 6-10 EBIT $650,000 $700,000 $720,000 $720,000 $690,000 $700,000 - Interest = $93,750 $93,750 $93,750 $93,750 $93,750 $93,750 EBT $556,250 $606,250 $626,250 $626,250 $596,250 $606,250 (30%) $166,875 $181,875 $187,875 $187,875 $178,875 $181,875 Net = Income $389,375 $424,375 $438,375 $438,375 $417,375 $424,375 Capital + Amort. - Investment $140,000 $200,000 $140,000 $200,000 $140,000 $200,000 $140,000 $200,000 $140,000 $200,000 $140,000 $ 80,000 Cash *PV of = Flow Cash Flow $329,375 $ 291,482 $364,375 $ 285,359 $378,375 $ 262,233 $378,375 $ 232,064 $357,375 $ 193,969 $484,375 $ 924,678 $2,189,785 *13% was used since this is an equity only investment. From the table we see that the present value of the cash flows estimates for the next ten years is $2,189,785. We must now calculate a value for the cash flows expected more than 10 years hence. To do this we will calculate a terminal value at the end of year 10 and discount that back to the present. Terminal value Present value = = = = = Annual cash flow/ discount rate $484,375/ 0.13 $3,725,962 $3,725,962 x PV IF (n = 10, i = 13%) ($1,099,159 – tables) $1,097,625 (Calculator) Therefore, the present value of all future cash flow estimates is $2,189,785 + $1,097,625 = $3,287,410 Since the market value of the firm’s shares is $3,000,000 (2,000,000 × $1.50/share) Ontario might consider pursuing Target Firm if management is reasonably confident in the assumptions underlying the analysis and has examined qualitative factors. 12-40. M and C Hammer Machinery Ltd. N = 10 a. Year 0 0 1-10 10 0 T = 30% Event r = 14% Expected Cash Flow d = 20% Aftertax Cash Flow Purchase machine $(54,000) – Installation (5,000) – Cost savings 15,000 10,500 Salvage 8,000 – CCA pool  dT  1 + .5r  PV (CCA ) = [C - S PV ] C    r + d  1 + r  Present Value @ 14% $(54,000) (5,000) 54,769 2,158  0.20 × 0.30  1 + .5 × .14  = [$54,000 + $5000 − $2,158]    0.14 + 0.20  1 + .14  = [$56,842](0.176470588)(0.938596491) = 9,415 NPV = $ 7,342 M and C Hammer Machinery should purchase the new machine. b. Sell old machine Remove from CCA pool: 7,000 (.165634675) Net increase in NPV Overall the new The NPV improves. $ 7,000 (1,159) 5,841 NPV = $ 13,183 c. Year 0 0 1-10 10 0 Expected Cash Flow Aftertax Cash Flow Purchase machine $(54,000) Installation (5,000) Cost savings 15,000 Salvage 8,000 CCA pool – – 10,500 – Event Present Value @ 17% $(54,000) ( 5,000) 48,915 1,664  dT  1 + .5r  PV (CCA ) = [C - S PV ] C   + + r d 1 r      0.20 × 0.30  1 + .5 × .17  = [$54,000 + $5,000 − $1,664]    0.17 + 0.20  1 + .17  = [$57,336](0.162162162 )(0.927350427 ) = 8,622 NPV = $ 201 NPV = ─ $1,901 $ 201 PV @ 17% $201 PV @ 17% – (1,901) PV @ 18% 000 (Cost) $2,102 $201 $201 (0.01) = 0.17 + 0.096(0.01) IRR (interpolatation ) = 0.17 + $2,102 = 0.17 + .0010 = 0.1710 = 17.10% @18% Profitability index (PI ) = PV of inflows $66,342 = = 1.124 PV of outflows $59,000 12-41. Lakeland Drive-In Theatres Ltd. N=7 Grand Year Event T = 25% r = 16% Expected Cash Flow d = 30% Aftertax Cash Flow Present Value @ 16% 0 1-7 7 Purchase machine $(40,000) – $(40,000) Operating costs (16,000) (12,000) (48,463) Salvage 4,000 – 1,415  0.30 × 0.25  1 + .5 × .16  PV (CCA ) = [$40,000 − $1,415]    0.16 + 0.30  1 + .16  = [$38,585](0.163043478)(0.93103448) = 5.857 NPV = $(81,191) Ultra Year Event Expected Cash Flow Aftertax Cash Flow Present Value @ 16% 0 1-7 7 Purchase machine $(60,000) – $(60,000) Operating costs (10,500) (7,875) (31,804) Salvage 6,000 – 2,123  0.30 × 0.25  1 + .5 × .16  PV (CCA ) = [$60,000 − $2,123]    0.16 + 0.30  1 + .16  = [$57,877](0.163043478)(0.93103448) = 8,786 NPV = $(80,895) The salvage value of $2,500 for the old machine would be deducted from the CCA pool, but since it is common to both alternatives it is ignored for the analysis and decision making purposes. The Ultra should be selected as its NPV is somewhat less costly. Our assumption is that the revenue stream is worthwhile and the least costly replacement is to be selected. 12-42. Crash Test Dummy Shop N=9 a. Year 0 1-9 5 9 0 Event T = 25% r = 13% Expected Cash Flow d = 20% Aftertax Cash Flow Present Value @ 13% Purchase machine $(550,000) – $(550,000) Cash flow 180,000 135,000 692,773 Capital upgrade 120,000 – (65,131) Salvage 20,000 – 6,658 CCA pool (PV of tax savings)  0.20 × 0.25  1 + .5 × .13  = [$550,000 + $65,131 − $6,658]    0.13 + 0.20  1 + .13  = [$608,473](0.151515152 )(0.94247788) = 86,890 NPV = $ 171,190 Note: The $100,000 deposit is a sunk cost and is irrelevant for this decision. b. Year 0 1-9 5 9 0 Event Expected Cash Flow Aftertax Cash Flow Present Value @ 21% Purchase machine $(550,000) – $(550,000) Cash flow 180,000 135,000 527,234 Capital upgrade (120,000) – (46,265) Salvage 20,000 – 3,597 CCA pool (PV of tax savings)  0.20 × 0.25  1 + .5 × .21  = [$550,000 + $46,265 − $3,597]    0.21 + 0.20  1 + .21  = [$592,668](0.12195122 )(0.91222314 ) = 66,005 NPV = $ 571 @22% NPV = -$15,892 $ 571 PV @ 21% $ 571 PV @ 21% – (15,892) PV @ 22% 000 (Cost) $16,463 $ 571 $571 (0.01) = 0.21 + 0.0347(0.01) IRR (interpolatation ) = 0.21 + $16,463 = 0.21 + .0003 = 0.2103 = 21.03% This is an approximation. PV of inflows $786,321 = = 1.278 PV of outflows $615,131 This is calculated @13%. c. Profitability index (PI ) = d. Crash Test Dummy should purchase the new machine. Value will increase by $171,190 (the NPV), the IRR exceeds the cost of capital and the PI exceeds 1. 12-43. Good T N = 12 a. Year Event T = 39% r = 14% Expected Cash Flow d = 30% Aftertax Cash Flow 0 Capital expenditure($2,000,000) – 0 Previously purchased equipment (opportunity cost of forgoing sale) (525,000) – 0 Working capital (75,000) – 1-6 Cash flow 650,000 396,500 7-12 Cash flow 750,000 457,500 1-12 Rent forgone (100,000) (61,000) (opportunity cost) 12 Salvage 50,000 – 12 WC Recovery 75,000 – 0 CCA pool PV (CCA) Present Value @ 14% ($2,000,000) (525,000) ( 75,000) 1,541,857 810,518 (345,278) 10,378 15,567  0.30 × 0.39  1 + .5 × .14  = [$2,000,000 + $525,000 − $10,378]   + 1 . 14 0 . 14 0 . 30 +    = [$2,514,622](0.26590909 )(0.93859649 ) = 627,603 NPV = $ 60,645 Good T should proceed. Value will be added to the firm. b. A changing cost of capital can be handled by discounting with multiple discount rates appropriate to each year. 12-44. Torch Concerts Ltd. N=7 Year 0 0 1-7 7 7 8 Event T = 25% r = 15% Expected Cash Flow Purchase land $(325,000) Working capital (60,000) Cash flow 50,000 Sell land 700,000 WC recovery 60,000 Tax on taxable capital gain [700,000 – 325,000] × 0.50 × .25 = $46,875 d = 20% Aftertax Cash Flow – – 37,500 – – Present Value @ 15% $(325,000) (60,000) 156,016 263,156 22,556 (15,324) NPV = $41,388 Note: The tax is paid one year after the realization of the capital gain (year 8). This assumption is consistent with other treatments for analysis purposes. Torch Concerts Ltd. should purchase the vacant lot. Its purchase will increase the value of the firm by $41,388. If the tax on the capital gain is taken at year 7 its PV is negative $17,622 and the overall present value is a positive $39,090 and the project is still acceptable. 12-45. Twining Company N = 15 Year 0 0 Event T = 30% r = 12% (1 + .25) = 15% Expected Cash Flow Aftertax Cash Flow Investment $(400,000) – Working capital 150,000 × 60/ 365 = (24,657) – 1-15 Revenues 150,000 105,000 1-15 Expenses (74,000) (51,800) 15 Salvage 15,000 – 15 WC Recovery 24,657 – 0 CCA pool PV (CCA ) d = 30% Present Value @ 15% $(400,000) (24,657) 613,974 (302,894) 1,843 3,030  0.30 × 0.30  1 + .5 × .15  = [$400,000 − $1,843]   + 0 . 15 0 . 30 1 . 15 +    = [$398,157](0.20 )(0.9347826 ) = 74,438 NPV =$ (34,266) Twinning should not proceed. Value will not be added to the firm. This analysis has used an adjusted discount rate to account for the higher risk that would be assumed if the project were undertaken. 12-46. Quixotic Enterprises N = 10 T = 25% r = 20% d = 5% a. Expected Cash Flow Aftertax Cash Flow Construct windmills$(400,000) Working capital (10,000) Revenues 150,000 Big wind tax (7,500) Rent forgone (opportunity cost) (5,000) 5 Capital upgrade (100,000) 10 Salvage 25,000 10 WC Recovery 10,000 0 CCA pool PV (CCA ) – – 112,500 (5,625) $(400,000) (10,000) 471,653 (23,583) (3,750) – – – (15,721) (40,188) 4,038 1,615 Year 0 0 1-10 1-10 1-10 Event Present Value @ 20%  0.05 × 0.25  1 + .5 × .20  = [$400,000 + $40,188 − $4,038]    0.20 + 0.05  1 + .20  = [$436,150](0.05)(0.9166667 ) = 19,990 NPV = $ 7,804 b. IRR Year Event 0 0 1-10 1-10 1-10 5 10 10 0 Expected Cash Flow Aftertax Cash Flow Present Value @ 21% Construct windmills$(400,000) Working capital (10,000) Revenues 150,000 Big wind tax (7,500) Rent forgone (opportunity cost) (5,000) Capital upgrade (100,000) Salvage 25,000 WC Recovery 10,000 CCA pool – – 112,500 (5,625) $(400,000) (10,000) 456,084 (22,804) (3,750) – – – (15,202) (38,554) 3,716 1,486 PV (CCA )  0.05 × 0.25  1 + .5 × .21  = [$400,000 + $38,554 − $3,716]    0.21 + 0.05  1 + .21  = [$434,834](0.048076923)(0.91322314 ) = 19,091 NPV = ($6,183) $ 7,804 – (6,183) $13,987 PV @ 20% PV @ 21% $7,804 0,000 $7,804 PV @ 20% (Cost) $7,804 (0.01) = 0.20 + 0.5579(0.01) $13,987 = 0.20 + .0056 = 0.2056 = 20.56% IRR (interpolatation ) = 0.20 + PV of inflows $497,296 = = 1.016 PV of outflows $489,492 Just above 1 indicating profitability. (Info from part (a)) c. Profitability index (PI ) = d. Dream the impossible dream as it will add value to Quixotic Enterprises. 12-47. J. Letterman Ltd. N = 10 Year 0 0 0 1-10 Event T = 28% r = 12% Expected Cash Flow d = 30% Aftertax Cash Flow Purchase machine $(210,000) – Sell old machine 32,500 – Deinvest WC 10,000 – Incremental annual(75,000 – 42,500) cost savings 32,500 23,400 10 Incremental salvage(50,000 – 12,000) 38,000 – 10 Reinvest WC (10,000) – 0 CCA pool PV (CCA ) Present Value @ 12% $(210,000) 32,500 10,000 132,215 12,235 (3,220)  0.30 × 0.28  1 + .5 × .12  = [$210,000 − $32,500 − $12,235]    0.12 + 0.30  1 + .12  = [$165,265](0.20 )(0.9464286 ) = 31,282 NPV = $ 5,012 J. Letterman should not replace the older machine, as the NPV of the replacement, relative to the older machine is negative. 12-48. Midnight Oil and Gas N = 10 Year Event T = 30% r = 14% Expected Cash Flow d (pipeline) = 20% d (buildings) = 4% Aftertax Cash Flow 0 Construct pipeline$(1,000,000) – 0 Construct buildings (200,000) – 0 Use land (opportunity cost) (2,000,000) – 1-10 Cash flow 625,000 437,500 10 Enviro: cleanup (1,200,000) (840,000) 10 Salvage 0 – 10 Sell land 4,500,000 – 11 Tax on capital gain (4,500,000 – 500,000) × .50 × .30 (600,000) 1 Tax on capital gain forgone (2,000,000 – 500,000) × .50 × .30 225,000 0 CCA pool (building ) = [$200,000] 0.04 × 0.30  1 + .5 × .14   0.14 + 0.04  1 + .14  = [$200,000](0.066666667 )(0.93859649 ) Present Value @ 14% $(1,000,000) (200,000) (pipeline) = [$1,000,000] 0.20 × 0.30  1 + .5 × .14  (2,000,000) 2,282,051 (226,585) 0 1,213,847 (141,970) 197,368 = 12,515  0.14 + 0.20  1 + .14  = [$1,000,000](0.176470588)(0.93859649 ) = 165,635 NPV = $302,861 Build the pipeline. Value will be added to the firm. 12-49. Bowser Venture N = 12 Year Event T = 30% r = 16% Expected Cash Flow d (machinery) d (buildings) Aftertax Cash Flow = 30% = 4% Present Value @ 16% 0 1 2 3-12 3-12 12 12 12 Acquire land $(500,000) – $(500,000) Payment building (1,000,000) – (862,069) Purchase machinery (150,000) – (111,474) Revenues 900,000 630,000 2,262,881 Expenses (350,000) (245,000) (880,009) Sell building 200,000 – 33,693 Sell machinery 40,000 – 6,739 12 Sell land 500,000 (1.11) 1,749,225 – 294,679 13 Tax on capital gain (1,749,225 – 500,000) × .50 × .30 (187,384) (27,213) 0 CCA pool (building ) = [$862,069 − $33,693] 0.04 × 0.30  1 + .5 × .16   0.16 + 0.04  1 + .16  = [$828,376](0.060 )(0.9310345) = 46,275 (machinery) = [$111,474 − $6,739] 0.30 × 0.30  1 + .5 × .16   0.16 + 0.30  1 + .16  = [$104,586](0.195652174 )(0.9310345) = 19,051 NPV = $282,553 Bowser should proceed with the venture. Value will be added to the firm. 12-50. Marceline Enterprises N=9 Year 0 0 3 3 6 6 1-2 3-5 6-9 9 9 0 Event T = 25% r = 11% Expected Cash Flow Expansion $(1,000,000) Working capital (50,000) Additional capital (200,000) Additional WC (10,000) Additional capital (200,000) Additional WC (10,000) Revenues 250,000 Revenues 325,000 Revenues 375,000 Salvage 150,000 WC Recovery 70,000 CCA pool d = 15% Aftertax Cash Flow − − − − − − 187,500 243,750 281,250 − − Present Value @ 11% $(1,000,000) (50,000) (146,238) (7,312) (106,928) (5,346) 321,098 483,447 517,824 58,639 27,365 [1,000,000 + 146,238 + 106,928 − 58,639] (.15)(.30)  1 + .5(.11)  = 1,194,527 (.1730076923) (.9504505)  .11 + .15  1 + .11  196,501 NPV = $289,050 Marceline Enterprises should proceed with the amusement park expansion, as the NPV is positive. MINI CASES Aerocomp Corporation (Methods of Investment Evaluation) This case places emphasis on comparing the payback method, the internal rate of return, and the net present value approaches for a series of investments. As the student progresses through the calculations, the various advantages and disadvantages of the different approaches become evident. The reinvestment assumption of a high return project under the internal rate of return can be highlighted and evaluated. Capital rationing is also introduced into the case and plays a part in the analysis. Finally, the issue of reported earnings to shareholders versus sophisticated capital budgeting techniques is brought up and makes for interesting classroom discussion. Are shareholders more concerned with next quarter’s earnings or long-term benefits? a. Total Reported Earnings increases for each projects: Project A Project B Project C Project D Year 1: $(13,250) $ 29,313 $(60,000) $ 192,206 Year 2: $ (450) $ 87,938 $(16,000) $ 129,846 Year 3: $ 25,494 $146,563 $ 61,640 $ (43,350) Year 4: $101,003 $234,500 $162,140 $ (62,475) Year 5: $ 63,315 $322,438 $262,640 $ (94,350) Total: $176,112 $820,752 $410,420 $ 121,877 We are told in the case that Kay Marsh is sensitive to Aerocomp’s level of earnings. Therefore, Project B, with over $820,000 in reported earnings increases (twice as much as any of the other projects), will be the one that attracts Kay’s attention. (She may initially be swayed by the $192,206 that Project D brings in during the first year, but the losses in years three through five will probably cause her to reject that alternative quickly.) Note: Projects A and C both produce earnings decreases for the first two years. We would suspect that if Emily thinks that either of these two should be selected (on the basis of some other ranking method, such as NPV), she had better have some convincing arguments prepared! b. Payback Period, IRR, and NPV of each alternative: Project A Project B Project C Project D Payback Period: 4 years 5 Years 5 Years 2 Years IRR: 14.08% 7.18% 11.95% 12.48% NPV @ 10%: $39,971 ($63,848) $52,192 $20,609 (Students may get slightly different values due to rounding.) Note: A few students may question the fact that Project B’s cost has not been completely recovered in the five-year period shown, as the cost of the other projects has been. Therefore, they will claim, we are not using the proper time frame for our comparison of the projects. Of course, they are correct, and deserve extra points for their astute observation. In the case, Project B’s amortization, or depreciation, was limited on purpose to highlight the effect of amortization on reported income and cash flows. c. 1. According to the Payback period, Project D should be selected. The initial investment of $510,000 is recovered in the second year. 2. The chief disadvantage of the Payback Period is obvious at once: the method ignores cash flows occurring after the payback period. In this case such an omission is disastrous, since Project D’s reported earnings and cash flows fall off significantly after the payback period and never recover. Another disadvantage of the Payback Period is that it does not consider the timing of cash flows during the payback period. 3. In general, the Payback Period should not be used. However, it is used from time to time because it is easy to understand, and because it favors projects that pay off quickly. This can be an important factor in some fast-paced industries where a quick return is important. The Payback Period may have some justification as a backup method, but not as the primary analytical tool. d. 1. According to the IRR method, Project A should be chosen. It returns nearly two percent more than the closest competing project. 2. Remember, that to achieve the IRR during a project’s life, the project’s cash inflows must be reinvested at the IRR rate. This may be difficult or impossible to accomplish when high IRR’s are involved. (Suppose you were Aerocomp’s financial manager, and you were getting the cash flows from Project A. What would you do with them: Pay dividends? Put them in a money market account at? You might encounter a great deal of difficulty locating an investment that would pay you back the IRR rate of 14.08%). As a matter of interest (no pun intended) if Project A’s cash flows were reinvested at 7% annually instead of the IRR rate of 14.08%, the project’s total return for the five-year period would drop to 11.84%. 3. Another disadvantage of the IRR method is that it does not give any consideration to project size. For example, the IRR method would select a project that returned $10 on a $1 investment over any of the projects in this case, even though the dollar return to the firm was only $9. This is not a problem when all projects with IRRs over the cost of capital can be selected, but when the projects are mutually exclusive, or when capital rationing is in effect (as it is in this case), the IRR method may lead the firm to make an incorrect choice. (Note: It is important to avoid confusion on this point. The IRR and NPV methods will both accept and reject the same investments, but they will not give them the same ranking. In this case, projects A, C, and D are all acceptable per IRR and NPV. However, the IRR method would choose projects A, D, and C, in that order, while the NPV method would choose C, A, and D.) 4. If the size of Aerocomp’s capital budget were not limited, the IRR method would accept projects A, C, and D. Project B, with an IRR of 7.18%, almost 3% less than the cost of capital, would be rejected. e. 1. According to the NPV method, Project C, with an NPV of over $52,000, will be chosen. It will add to the present value of the firm over $12,000 more than the next best project. Of course, under the IRR, Project A will be selected. Actually Project C is only a third place finisher under the IRR method. 2. If the size of Aerocomp’s capital budget were not limited, the NPV method would accept projects A, C, and D. Project B, with an NPV of negative $63,848, would be rejected anyway. Note that both the NPV and IRR methods rejected project B. The return is less than the cost of capital. 3. The likely selection is Project C because of its high net present value. This is partly attributable to the fact that only one project can be selected. Had there not been capital limitations, one might put more emphasis on the IRR or use a profitability index approach. Of course, some instructors might select Project A as being preferable using other criteria, and that is fine. There may be some interesting opportunities for a classroom debate or discussion on these points. f. 1. Profitability index = Project A Project B Project C Project D [39,971 + 300,000]/ 300,000 = 1.133 [- 63,848 + 700,000]/ 700,000 = 0.909 [52,192 + 800,000]/ 800,000 = 1.065 [20,609 + 510,000]/ 510,000 = 1.040 2. The profitability index suggests project A with the highest relative profitability. However, project A adds the most value to the firm. Notice that projects A and D together, at roughly the same initial investment as C, provide a higher combined NPV. Galaxy Systems, Inc. (Divisional Cost of Capital) Purpose: The case combines risk analysis with discount rate considerations. To emphasize how many multidivisional corporations operate, the case actually gets into the topic of divisional hurdle rates. The student is able to see how different divisions in a corporation might have different required rates of return based on their risk exposure. In this particular case, a key risk measure for the consideration is beta. (Only observe how they might be used). Calculations related to net present value and internal rate of return are purposely simple to emphasize more conceptual items. Emphasis can be made on how financial decisions are made in a corporate culture. This case draws on material from many of the capital budgeting chapters. Proposal A NPV Year (10% discount rate for the auto airbags production division) N = 10 Event 0 Airbag model 1-10 Revenue T = 40% r = 10% d = 20% Expected Cash Flow Aftertax Cash Flow $(3,050,000) 720,000 – 432,000  0.20 × 0.40  1 + .5 × .10  PV (CCA ) = [$3,050,000]    0.10 + 0.20  1 + .10  = [$3,050,000](.266666667 )(0.954545455) = Present Value @ 10% $(3,050,000) 2,654,453 776,363 NPV = $380,816 IRR (approximate) N = 10 Year Event 0 Airbag model 1-10 Revenue T = 40% r = 13% d = 20% Expected Cash Flow Aftertax Cash Flow $(3,050,000) 720,000 – 432,000  0.20 × 0.40  1 + .5 × .13  PV (CCA ) = [$3,050,000]    0.13 + 0.20  1 + .13  = [$3,050,000](.24242424 )(0.942477876 ) = Present Value @ 13% $(3,050,000) 2,344,137 696,862 NPV = $(9,001) Proposal B NPV (15% discount rate for the aerospace division) N = 10 T = 40% r = 15% d = 20% Event Expected Cash Flow Aftertax Cash Flow 0 Radar 1-10 Revenue $(3,100,000) 750,000 – 450,000 Year  0.20 × 0.40  1 + .5 × .15  PV (CCA ) = [$3,100,000]    0.15 + 0.20  1 + .15  = [$3,100,000](.228571429 )(0.934782609 ) = Present Value @ 15% $(3,100,000) 2,258,446 662,360 NPV = $(179,194) IRR (approximate) N = 10 T = 40% r = 13.5% d = 20% Event Expected Cash Flow Aftertax Cash Flow 0 Radar 1-10 Revenue $(3,100,000) 750,000 – 450,000 Year  0.20 × 0.40  1 + .5 × .135  PV (CCA ) = [$3,100,000]    0.135 + 0.20  1 + .135  = [$3,100,000](.23880597 )(0.940528634 ) = Present Value @ 13.5% $(3,100,000) 2,393,783 696,271 NPV = $(9,946) Proposal C NPV Year (10% discount rate for the auto airbags production division) N = 15 Event 0 Airbag model 1-15 Cost savings T = 40% r = 10% d = 20% Expected Cash Flow Aftertax Cash Flow $(225,000) 30,000 – 18,000 Present Value @ 10% $(225,000) 136,909  0.20 × 0.40  1 + .5 × .10  PV (CCA ) = [$225,000]    0.10 + 0.20  1 + .10  [225,000](.266666667 )(0.954545455) = 57,273 NPV = $(30,818) IRR (approximate) N = 10 Year Event 0 Airbag model 1-10 Revenue T = 40% r = 7% Expected Cash Flow Aftertax Cash Flow $(3,100,000) 30,000 – 18,000  0.20 × 0.40  1 + .5 × .07  PV (CCA ) = [$225,000]    0.07 + 0.20  1 + .07  = [$225,000](.296296296 )(0.966183575) = d = 20% Present Value @ 7% $(225,000) 163,942 64,486 NPV = $3,428 Proposal D NPV Year 0 1-8 (15% discount rate for the aerospace division) N=8 T = 40% r = 15% d = 20% Event Expected Cash Flow Aftertax Cash Flow Radar Revenue $(1,700,000) 500,000 – 300,000  0.20 × 0.40  1 + .5 × .15  PV (CCA ) = [$1,700,000]    0.15 + 0.20  1 + .15  = [$1,700,000](.228571429 )(0.934782609 ) = Present Value @ 15% $(1,700,000) 1,346,196 363,230 NPV = $9,426 IRR (approximate) slightly over 15% a. Proposal A should be accepted IRR > discount rate (13% > 10%) NPV is positive $380,186 Proposal B should be rejected IRR < discount rate (13.5% < 15%) NPV is negative ($179,194) Proposal C should be rejected IRR 15%) NPV is positive $9,426 b. While the decisions related to Proposals A and B appear to be straightforward, Proposals C and D require further discussion. Proposal C has a negative net present value and the internal rate of return of 7% is well below the required rate of return of 10%. Nevertheless, it calls for the development of special equipment to be used in the disposal of environmentally harmful waste material created in the manufacturing process. Given tougher environmental laws, the project may have to be accepted. We are not told whether the installation is mandatory under the law, but there probably is adequate motivation to move forward with the project. Of course, if the installment of the equipment is required by law, then Galaxy must move forward regardless of the numbers. Proposal D has a positive net present value and the internal rate of return of slightly over 15 percent above the required rate of return of 15 percent for the division. However, the proposal appears to have even greater risk than projects normally undertaken in the aerospace division. While the high required rate of return for this division is supposed to cover the risk exposure of dealing in U.S. government contracts, Project D calls for the development of a microelectric control system for fighter jets that are still in the design stage. Even if the microelectric systems are successfully developed, there may not be a need for them if the other aerospace company cannot successfully develop fighter jets. Furthermore, the target market for the jets is in underdeveloped countries, which increases the uncertainty associated with this project. In the final analysis, top management might require an anticipated return of 20 percent or more to take on this highly speculative project. c. The $300,000 that has already been spent on the initial research for Proposal B (radar surveillance equipment) is a sunk cost. The money has already been spent and should have no influence on subsequent decisions. Sometimes in the real world, egos get in the way of corporate decisions, and division heads (or other executives) push hard for the continuance of projects that they spent funds on to explore; but that is not justification to continue on. This is somewhat like buying stock in an underperforming company in the stock market. Sometimes, you just have to take your losses. Of course, even if we considered the $300,000 that had already been spent, it would raise the total cost of the project and make it even less economical. Further overall comments: Companies that use divisional required rates of return often do have difficulties in finding betas for firms that produce products comparable to a division. That is, finding a “pure play” comparison is difficult. Therefore, using the average beta for an entire industry may be the next best alternative. For example, if a division produces machine tools, its beta may be inferred from the entire machine tool industry rather than from a given firm in the industry. Solution Manual for Foundations of Financial Management Stanley B. Block, Geoffrey A. Hirt, Bartley Danielsen, Doug Short, Michael Perretta 9780071320566, 9781259268892, 9781259261015