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Chapter 10

FIN300 Ross Westerfield Corporate Finance Solutions Chapter 10 (8th Edition).pdf

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Department
Finance
Course
FIN 300
Professor
John Currie
Semester
Winter

Description
CHAPTER 10 Making Capital Investment Decisions Learning Objectives LO1 How to determine relevant cash flows for a proposed project. LO2 How to project cash flows and determine if a project is acceptable. LO3 How to calculate operating cash flow using alternative methods. LO4 How to calculate the present value of a tax shield on CCA. LO5 How to evaluate cost-cutting proposals. LO6 How to analyze replacement decisions. LO7 How to evaluate the equivalent annual cost of a project. LO8 How to set a bid price for a project. Answers to Concepts Review and Critical Thinking Questions 1. (LO1) An opportunity cost is the most valuable alternative that is foregone if a particular project is undertaken. The relevant opportunity cost is what the asset or input is actually worth today, not, for example, what it cost to acquire. 2. (LO1) It’s probably only a mild over-simplification. Current liabilities will all be paid presumably. The cash portion of current assets will be retrieved. Some receivables won’t be collected, and some inventory will not be sold, of course. Counterbalancing these losses is the fact that inventory sold above cost (and not replaced at the end of the project’s life) acts to increase working capital. These effects tend to offset. 3. (LO7) The EAC approach is appropriate when comparing mutually exclusive projects with different lives that will be replaced when they wear out. This type of analysis is necessary so that the projects have a common life span over which they can be compared; in effect, each project is assumed to exist over an infinite horizon of N- year repeating projects. Assuming that this type of analysis is valid implies that the project cash flows remain the same forever, thus ignoring the possible effects of, among other things: (1) inflation, (2) changing economic conditions, (3) the increasing unreliability of cash flow estimates that occur far into the future, and (4) the possible effects of future technology improvement that could alter the project cash flows. 4. (LO1) Depreciation is a non-cash expense, but it is tax-deductible on the income statement. Thus depreciation causes taxes paid, an actual cash outflow, to be reduced by an amount equal to the depreciation tax shield t D. c A reduction in taxes that would otherwise be paid is the same thing as a cash inflow, so the effects of the depreciation tax shield must be included to get the total incremental aftertax cash flows. 5. (LO1) There are two particularly important considerations. The first is erosion. Will the essentialized book simply displace copies of the existing book that would have otherwise been sold? This is of special concern given the lower price. The second consideration is competition. Will other publishers step in and produce such a product? If so, then any erosion is much less relevant. A particular concern to book publishers (and producers of a variety of other product types) is that the publisher only makes money from the sale of new books. Thus, it is important to examine whether the new book would displace sales of used books (good from the publisher’s perspective) or new books (not good). The concern arises any time there is an active market for used product. 6. (LO1) This market was heating up rapidly, and a number of other competitors were planning on entering. Any erosion of existing services would be offset by an overall increase in market demand. 7. (LO1) Pistachio should have realized that abnormally large profits would dwindle as more supply of services came into the market and competition became more intense. 10-1 Solutions to Questions and Problems NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic 1. (LO1) The $6 million acquisition cost of the land six years ago is a sunk cost. The $6.4 million current aftertax value of the land is an opportunity cost if the land is used rather than sold off. The $14.2 million cash outlay and $890,000 grading expenses are the initial fixed asset investments needed to get the project going. Therefore, the proper year zero cash flow to use in evaluating this project is $6,400,000 + 14,200,000 + 890,000 = $21,490,000 2. (LO1) Sales due solely to the new product line are: 19,000($13,000) = $247,000,000 Increased sales of the motor home line occur because of the new product line introduction; thus: 4,500($53,000) = $238,500,000 in new sales is relevant. Erosion of luxury motor coach sales is also due to the new portable campers; thus: 900($91,000) = $81,900,000 loss in sales is relevant. The net sales figure to use in evaluating the new line is thus: $247,000,000 + 238,500,000 – 81,900,000 = $403,600,000 3. (LO1) We need to construct a basic Statement of Comprehensive Income. The Statement of Comprehensive Income is: Sales $ 830,000 Variable costs 498,000 Fixed costs 181,000 Depreciation 77,000 EBT $ 74,000 [email protected]% 25,900 Net income $ 48,100 4. (LO3) To find the OCF, we need to complete the Statement of Comprehensive Income as follows: Sales $ 824,500 Costs 538,900 Depreciation 126,500 EBIT $ 159,100 [email protected]% 54,094 Net income $ 105,006 The OCF for the company is: OCF = EBIT + Depreciation – Taxes OCF = $159,100 + 126,500 – 54,094 10-2 OCF = $231,506 The depreciation tax shield, also called the CCA tax shield, is the depreciation times the tax rate, so: Depreciation tax shield =ct Depreciation Depreciation tax shield = .34($126,500) Depreciation tax shield = $43,010 The depreciation tax shield shows us the increase in OCF by being able to expense depreciation. 5. (LO3) To calculate the OCF, we first need to calculate net income. The Statement of Comprehensive Income is: Sales $ 108,000 Variable costs 51,000 Depreciation 6,800 EBT $ 50,200 [email protected]% 17.570 Net income $ 32,630 Using the most common financial calculation for OCF, we get: OCF = EBIT + Depreciation – Taxes OCF = $50,200 + 6,800 – 17,570 OCF = $39,430 The top-down approach to calculating OCF yields: OCF = Sales – Costs – Taxes OCF = $108,000 – 51,000 – 17,570 OCF = $39,430 The tax-shield approach is: OCF = (Sales – Costs)(1 – t ) + t Depreciation C C OCF = ($108,000 – 51,000)(1 – .35) + .35(6,800) OCF = $39,430 And the bottom-up approach is: OCF = Net income + Depreciation OCF = $32,630 + 6,800 OCF = $39,430 All four methods of calculating OCF should always give the same answer. 6. (LO1) Sales $ 940,000 Variable costs 385,400 Fixed costs 147,000 CCA 104,000 EBIT $ 303,600 [email protected]% 106,260 Net income $ 197,340 10-3 7. (LO1, 2) Cash flow year 0 = -990,000 Cash flow years 1 through 5 = 460,000(1 – .40) = $276,000 PV of CCATS = 990,000(.3)(.4) x (1 + .5(.15)) .15 + .3 1 + .15 = $246,782.61 NPV = -990000 + 276,000 x PVIFA (15%, 5) + 546,782.61 = -990,000 + 276,000 x {1 – [1/1+.15] /.15} + 246,782.61 = $181,977.42 8. (LO2) Cash flow year 0 = -990,000 – 47,200 = -$1,037,200 Cash flow years 1 through 5 = 460,000(1 – .4) = $276,000 Ending cash flow = 100,000 + 47,200 = $147,200 PV of CCATS = 990,000(.3)(.4) x (1 + .5(.15)) – .15 + .3 1 + .15 100,000(.3)(.4) x 1 .15 + .3 (1.15)5 = $233,524.56 5 NPV = -1,037,200+ 276,000 x PVIFA(15%, 5) + (147,200)/(1.15) + 233,524.56 = $194,703.78 9. (LO2) The NPV will be smaller because the Capital Cost Allowances are smaller early on. PV of CCATS = 990,000(.25)(.4) x (1 + .5(.15)) – .15 + .25 1 + .15 100,000(.25)(.4) x 1 .15 + .25 (1.15)5 = $218,929.28 Therefore with a 25% CCA rate, the NPV = 194,703.79 + (218,929.28– 233,524.57) = $181,108.50 10. (LO1) Neither one is correct. What should be considered is the opportunity cost of using the land, at the very least what the land could be sold for today. 11. (LO4) Generally, as long as there are other assets in the class, the pool remains open and there are no tax effects from the sale. This fact does not hold here since we are told that there will be no assets left in the class in 6 years. th Beyond the first year, the UCC at the beginning of the N year is given by the formula: UCC C 1  d  d N 2where C = installed capital cost; d = CCA rate. Note that the half-year rule has N  2 been incorporated. In this case: 10-4 6-2 Uth =6$548,000 (1 – (0.2/2)) (1-0.2) = $202,014.72. This is the book value of the asset at the end of the 5 year (beginning of the sixth). The asset is sold at a (terminal) loss to book value = $202,014.72 – $105,000 = $97,014.72. The terminal loss acts as a tax shield which the company can use to reduce its taxes. The reduction in taxes is a cash inflow. The tax shield = 0.35  $97,014.72 = $33,955.15 The after tax salvage value = $105,000 + $33,955.15 = $138,955.15 . 12. (LO2) A/R fell by $6,140, and inventory increased by $5,640, so net current assets fell by $500. A/P rose by $6,930. ∆NWC = ∆(CA – CL) = –500 – 6,930 = – 7,430 Net cash flow = S – C – ∆NWC = 102,000 – 43,500 – (– 7,430) = $65,930 13. (LO3) CCA =10.3($3.9M/2) = $585,000; CCA = 0.3(2.9M – $585,000) = $994,500; CCA =30.3($3.9M – 585,000 – 994,500) = $696,150. OCF =1(S – C)(1 – t )c+ t Dc= ($2.65M – $840K)(1 – 0.35) + 0.35($585,000) = $1,381,250 OCF =2(S – C)(1 – t )c+ t Dc= ($2.65M – $840K)(1 – 0.35) + 0.35($994,500) = $1,524,575 OCF =3(S – C)(1 – t )c+ t Dc= ($2.65M – $840K)(1 – 0.35) + 0.35($696,150) = $1,420,152.50 14. (LO2) Initial Cash Flow year 0 = -$2,650,000 After-tax net revenue years 1-3 = (S – C)(1 – t C = ($2,650,000 – 840,000)(1 – 0.35) = $1,176,500 Ending cash flows (year 3) = salvage value = $1,624,350 PV of CCATS = 3,900,000(.3)(.35) x (1 + .5(.12)) – .12 + .3 1 + .12 1,624,350 (.3)(.35) x 1 .12 + .3 (1.12) 3 = $633,722.80 3 NPV = – $3.9M + $1,176,500(PVIFA 12%, 3 + $633,722.80 + $1,624,350/1.12 = $715,657.53 15. (LO1, 2) Cash Flow year 0 = -$3,900,000 – 300,000 = -$4,200,000 After-tax net revenue years 1-3 = (S – C)(1 – T c = ($2,650,000 – 840,000)(1 – 0.35) = $1,176,500 Ending cash flows (year 3) = recovery of NWC + salvage value = $300,000 + 210,000 = $510,000 PV of CCATS = 3,900,000(.3)(.35) x (1 + .5(.12)) – .12 + .3 1 + .12 210,000(.3)(.35) x 1 3 .12 + .3 (1.12) = $885,399.39 NPV = –$4.2M + $1,176,500(PVIFA 12%,3) + $885,399.39 + $510,000/1.12 = -$125,838.20 10-5 16. (LO1, 2) Initial Cash Flow year 0 = -785,000 – 140,000 = -$925,000 After-tax net revenue years 1 through 5 = (13,500,000 – 11,700,000 – 215,000)(1 – .35) = $1,030,250 Ending cash flows (year 5) = $140,000 PV of CCATS = 785,000(.25)(.35) x (1 + .5(.19)) .19 + .25 (1 + .19) = $143,645.55 NPV = -925,000 + 143,645.55 + 1,030,250 x PVIFA(19%,5) + 140,000/(1.19) 5 = $2,427,440.81 Since the NPV is positive, it is probably a good project. 17. (LO2) Assuming that all outstanding accounts receivable from the previous quarter are collected in the current quarter, the amount of cash collections in the current quarter is: $15,200 – 9,500 = $5,700 This can be seen by making collections from current quarter sales a plug number Y in the current quarter’s cash flow summary for accounts receivable: Opening balance of A/R X Current quarter sales $15,200 Collections of outstanding A/R from previous quarter –X Collections from current quarter sales –Y Closing balance of A/R $15,200 - Y This gives the equation: 15,200 – Y = X + 9,500 So the total cash collections in the current are: X + Y = $5,700 18. (LO1) Management’s discretion to set the firm’s capital structure is applicable at the firm level. Since any one particular project could be financed entirely with equity, another project could be financed with debt, and the firm’s overall capital structure remains unchanged, financing costs are not relevant in the analysis of a project’s incremental cash flows according to the stand-alone principle. 19. (LO1) The $7.2 million acquisition cost of the land seven years ago is a sunk cost, and so it is not relevant. The $586,000 grading cost to make the land usable is relevant. The $962,000 current appraisal of the land is an opportunity cost if the land is used rather than sold off. If the land is sold at $962,000 there will be a capital loss of (7,200,000 – 962,000) $6,238,000 of which the company can write off 50% of it against any taxable Capital Gains. This means that at a tax rate of 30% they would be able to write off 30% x $3,119,000 and thus save $935,700 in taxes. The $25 million cash outlay is the initial fixed asset investment needed to get the project going. Therefore, the proper year zero cash flow to use in evaluating this project is = $0.962M + $25M + .586M - $.9357M= $25,612,300. 20. (LO1) Currently the firm has sales of 23,000($14,690) + (38,600) ($43,700) = $2,024,690,000. With the introduction of a new mid-sized car its sales will change by (28,500) ($33,600) + (12,500) ($14,690) – (8,200) 10-6 ($43,700) = $782,885,000. This amount is the incremental sales and is the amount that should be considered when evaluating the project. 21. (LO1, 2) Initial Cash Flow 0 = -560,000 – 29,000 = -$589,000 After-tax savings in Operating Costs years 1 through 5 = (165,000) (1 – .34) = $108,900 Ending cash flows (year 5) = $85,000 + 29,000 = $114,000 PV of CCATS = 560,000(.2)(.34) x (1 + .5(.10)) – 85,000(.2)(.34) x 1 .10 + .2 (1 + .10) .10 + .2 (1.10)5 = $109,200.55 5 NPV = -589,000 + 109,200.55+ 108,900 x PVIFA(10%, 5) + 114,000/(1.10) = $3,802.26 22. (LO1, 2) Initial cash flow net revenue year 0 = -720,000+ 110,000 = -$610,000 After-tax savings in order processing costs years 1 through 5 = (350,000)(1 – .35) = $227,500 Ending cash flows (year 5) = $280,000 – 110,000 = $170,000 PV of CCATS = $260,000 NPV = 0 = -610,000 + 260,000 + 227,500 x PVIFA(IRR%,5) + 170,000/(1+IRR) 5 NPV = 0 = -610,000 + 260,000 + 227,500 x ({1-[1/(1+IRR)] }/IRR) + 170,000/(1+IRR) 5 IRR = 61.85% 23. (LO1, 2) $300,000 cost saving case Initial Costs year 0 = -720,000+110,000 = -$610,000 After-tax savings in processing costs years 1 through 5 = (300,000)(1 – .35) = $195,000 Ending cash flows (year 5) = $280,000 – 110,000 = $170,000 PV of CCATS = $114,969.60 5 NPV = -610,000 + 114,969.60 + 195,000 x PVIFA(20%,5) + 170,000/(1+.20) = $156,458.15 Accept the project. $240,000 cost saving case Initial cash flow year 0 = -$610,000 After tax savings in order processing costs years 1 through 5 = (240,000)(1 – .35) = $156,000 Ending cash flows (year 5) = $280,000 – 110,000 = $170,000 PV of CCATS = $114,969.60 5 NPV = -610,000 + 114,969.60 + 156,000 x PVIFA(20%,5) + 170,000/(1+.20) = $39,824.28 Accept the project. Required pretax cost saving case (RCS) Initial cash flow year 0 = -$610,000 Ending cash flows (year 5) = $280,000 – 110,000 = $170,000 PV of CCATS = $114,969.60 5 NPV = 0 = -610,000 + 114,969.60 + RCS(1 – .35) x PVIFA(20%,5) + 170,000/(1+.20) Solve for RCS 10-7 RCS = Required pretax cost saving = $219,513.18. 24. (LO8) Cash flow Year PV @ 20% Capital Spending -1,300,000 0 -$1,300,000 Salvage 650,000 3 376,157.41 Additions to NWC -340,000 0 -340,000 340,000 3 196,759.26 Aftertax operating income 1 to 3 ? Tax shield on CCA* 146,791.67 NPV 0 Solving for PV of after-tax operating income we obtain: $ 920,291.67 Dividing by PVIFA(20%,3) we find that annual after-tax operating income must be $436,885.71 Consequently, sales must be $436,885.71/ (1 – .36) + 89($96,000) = $9,226,633.93 in order to break even. Therefore the selling price should be no less than $9,226,633.92 / 89 or $103,670.04 per system. *PV of CCATS = 1,300,000(.2)(.36) x (1 + .5(.2)) .2 + .2 1 + .2 – 650,000(.2)(.36) x 1 3 .2 + .2 (1.2) = $146,791.67 25. (LO3) a. EBIT = Sales – cost – depreciation = $425,000 – $96,000 – $375,000  0.2 = $254,000 b. According to the bottom-up approach: OCF = (S – C – D)(1 – T) + D = $254,000  (1 – 0.35) + $75,000 = $ 240,100 c. According to the tax shield approach: OCF = (S – C)(1 – T) + TD = ($425,000 – $96,000)  (1 – 0.35) + 0.35  $75,000 = $240,100 26. (LO3) Depreciation = $280,000/2 .25 = $35,000 According to the top down approach: OCF = (S – C) – (S – C – D)  T = ($650,000 – $490,000) – (650,000 – $490,000 – $35,000)  0.38 = $112,500 According to the tax shield approach: OCF = (S – C)(1 – T) + TD = ($650,000 – $490,000)  (1 – 0.38) + 0.38  $35,000 = $112,500 27. (LO7) Method 1: PV @ 13%(Costs) = -$6,700 – 400  PVIFA (13%, 3) = -$7,644.46 Method 2: PV @ 13%(Costs) = -$9,900 – 620  PVIFA (13%, 4) = -$11,744.17 Difference= $4,099.71 in favour of Method 1 Without replacement: On this basis we would need to know whether the benefit of 1 more year’s use is sufficient to offset the additional cost of $4,099.71. 10-8 With replacement: Method 1: EAC = -7,644.46/PVIFA(13%,3) = -$3,237.60 Method 2: EAC = -11,744.17/PVIFA(13%,4) = -$3,948.32 On this basis, Method 2 is again more expensive. 28. (LO7) Method 1: CF = 0$6,700 PVCCATS = (6,700)(.39)(.25)(1.065)/[(.13 + .25)(1.13)] = $1,620.19 PV(Costs) = -400(1 – .39)PVIFA (13%, 3) – 6,700 + 1,620.19 = -$5,655.93 EAC = -$5,655.93/PVIFA(13%, 3) = -$2,395.41 Method 2: CF = 0$9,900 PVCCATS = (9,900)(.39)(.25)(1.065)/[(.13 + .25)(1.13)] = $2,394.02 PV(Costs) = -620(1 – .39)PVIFA (13%, 4) – 9,900 + 2,394.02 = -$8,630.93 EAC = -$8,630.93/PVIFA(13%, 4) = -$2,901.67 Method 2 is more expensive. 29. (LO7) To calculate the EAC of the project, we first need the NPV of the project. Notice that we include the NWC expenditure at the beginning of the project, and recover the NWC at the end of the project. The NPV of the project is: 5 NPV = –$270,000 – 25,000 – $42,000(PVIFA 11%,5 + $25,000/1.11 = –$435,391.39 Now we can find the EAC of the project. The EAC is: EAC = –$435,391.39 / (PVIFA 11%,5 = –$117,803.98 30. (LO7) Assuming a carry-forward on taxes: Both cases: salvage value = $40,000 Techron I: After-tax operating costs = $67,000(1 – 0.35) = $43,550 PVCCATS = (290,000)(.35)(.20)(1.05)/[(.10 + .20)(1.10)] – {[(40,000)(0.20)(0.35)/[0.10 + 0.20]] (1/1.10) }= $57,578.64 3 PV(Costs) = -$290,000 – 43,550(PVIFA 10%,3 + (40,000/1.10 ) + 57,578.64 = -$310,671.17 EAC = -$310,671.17 / (PVIFA 10%,3 = -$124,925.48 Techron II: After-tax operating costs = $35,000(1 – 0.35) = $22,750 PVCCATS = (510,000)(.35)(.20)(1.05)/[(.10 + .20)(1.10)] – {[(40,000)(0.20)(0.35)/[0.10 + 0.20]] 5 (1/1.10) }= $107,795.64 5 PV(Costs) = -$510,000 – 22,750(PVIFA 10%,5 + (40,000/1.10 ) + 107,7795.64 = -$463,607.90 EAC = -$463,607.90 / (PVIFA 10%,5 = -$122,298.60 The two milling machines have unequal lives, so they can only be compared by expressing both on an equivalent annual basis which is what the EAC method does. Thus, you prefer the Techron II because it has the lower annual cost. 31. (LO7) Pre-fab segments Given: Initial cost = $6.5M; d = 4%; k = 11%; T = 35%; S = .25 x $6.5M = $1,625,000; n = 25 PVCCATS = $565,442.71 Assuming end of year costs: PV(Costs) = -$150,000x(1-.35) x PVIFA(11%, 25) = -$821,120.11 10-9 Total PV(Costs) = -$6,500,000 – $821,120.11 + $565,442.71 + $1,625,000PVIF(11%, 25) = -$6,636,064.25 EAC = -$6,636,064.25/PVIFA(11%, 25) = -$787,967.88 Carbo
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