CH-7 Making Capital Investment Decisions – Corporate Finance : Book Guide

Chapter 7 Making Capital Investment Decisions 1. a. Yes, the reduction in the sales of the company’s other products, referred to as erosion or cannibalism, should be treated as an incremental cash flow. These lost sales are included because they are a cost (a revenue reduction) that the firm must bear if it chooses to produce the new product. b. Yes, expenditures on plant and equipment should be treated as incremental cash flows. These are costs of the new product line. However, if these expenditures have already occurred (and cannot be recaptured through a sale of the plant and equipment), they are sunk costs and are not included as incremental cash flows. c. No, the research and development costs should not be treated as incremental cash flows. The costs of research and development undertaken on the product during the past three years are sunk costs and should not be included in the evaluation of the project. Decisions made and costs incurred in the past cannot be changed. They should not affect the decision to accept or reject the project. d. Yes, the annual depreciation expense must be taken into account when calculating the cash flows related to a given project. While depreciation is not a cash expense that directly affects cash flow, it decreases a firm’s net income and hence, lowers its tax bill for the year. Because of this depreciation tax shield, the firm has more cash on hand at the end of the year than it would have had without expensing depreciation. e. No, dividend payments should not be treated as incremental cash flows. A firm’s decision to pay or not pay dividends is independent of the decision to accept or reject any given investment project. For this reason, dividends are not an incremental cash flow to a given project. Dividend policy is discussed in more detail in later chapters. f. Yes, the resale value of plant and equipment at the end of a project’s life should be treated as an incremental cash flow. The price at which the firm sells the equipment is a cash inflow, and any difference between the book value of the equipment and its sale price will create accounting gains or losses that result in either a tax credit or liability. g. Yes, salary and medical costs for production employees hired for a project should be treated as incremental cash flows. The salaries of all personnel connected to the project must be included as costs of that project. 2. In this context, an opportunity cost refers to the value of an asset or other input that will be used in a project. The relevant cost is what the asset or input is actually worth today, not, for example, what it cost to acquire. 3. Capital budgeting can easily incorporate price increases through inflation into its analysis. The key concept is consistency. If prices are rising at a high rate, you should use nominal cash flows, which include the price increases from inflation, and a nominal discount rate. A nominal discount rate also includes the effect of inflation. 4. An operating cash flow is the cash that arises directly from the operations of the firm. It does not include financing or investment costs. There are several approaches to estimating operating cash flow. A common way is presented below: Another way is called the Bottom Up approach. In this way, the analyst first estimates project net income by subtracting Taxes from EBIT. Operating cash flow is then calculated by adding depreciation to net income. A third way is called the Top Down approach, which starts off with the company’s sales figure. The fourth approach is known as the Tax Shield approach, whereby operating cash flow is viewed as having two components: a) the cash flow with no depreciation and b) the cash flow arising from the depreciation tax shield. The formula is given below: OCF = (Sales − Costs)  (1 − tc) + Depreciation  tc 5. The Equivalent Annual Cost approach compares the equivalent annual cash flows between two projects of different lives. This type of analysis is necessary so that the projects have a common life span over which they can be compared. For example, if one project has a three- year life and the other has a five-year life, then a 15-year horizon is the minimum necessary to place the two projects on an equal footing, implying that one project will be repeated five times and the other will be repeated three times. Note the shortest common life may be quite long when there are more than two alternatives and/or the individual project lives are relatively long. Assuming this type of analysis is valid implies that the project cash flows remain the same over the common life, 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. 6. In many examples of this type, the financial analyst should consider the relevant accounting standards that the firm follows. If the company was listed on a European stock exchange it would have to follow International Accounting Standards and follow the advice given by them. The relevant standard here is IAS16 Property, Plant and Equipment, and the advice is that any costs associated with implementation, installation, or delivery should be measured as a capital investment and appear on the statement of financial position. To estimate the tax savings, we must first estimate the annual depreciation charge over the five year life of the investment. The analysis is presented below: Year 1 2 3 4 5 (a) Starting Value € 37,000.00 € 29,600.00 € 23,680.00 € 18,944.00 € 15,155.20 (b) Depreciation 20% 20%*(a) € 7,400.00 € 5,920.00 € 4,736.00 € 3,788.80 € 15,155.20 OCF =EBIT + Depreciation −Taxes OCF = Sales −Costs −Taxes (c) Accumulated Dep € 7,400.00 € 13,320.00 € 18,056.00 € 21,844.80 € 37,000.00 (d) Residual Value (a)-(c) € 29,600.00 € 23,680.00 € 18,944.00 € 15,155.20 € 0.00 (e) Tax Shield 33.3% 33.3%*(b) € 2,464.20 € 1,971.36 € 1,577.09 € 1,261.67 € 5,046.68 (f) PV Tax Shield r = 5% € 2,200.18 € 1,571.56 € 1,122.54 € 801.81 € 2,863.62 The present value of the depreciation tax shield is the sum of the present values over the five year life of the project, which is €8559.71 If the installation was treated as an expense, the company would reduce profits by €8,000 and bear an immediate tax savings of 33.3%*€8,000 = €2,664. If the €8,000 is treated as a capital investment, the analysis for the machine is now: Year 1 2 3 4 5 (a) Starting Value € 29,000.00 € 23,200.00 € 18,560.00 € 14,848.00 € 11,878.40 (b) Depreciation 20% 20%*(a) € 5,800.00 € 4,640.00 € 3,712.00 € 2,969.60 € 11,878.40 (c) Accumulated Depreciation € 5,800.00 € 10,440.00 € 14,152.00 € 17,121.60 € 29,000.00 (d) Residual Value (a)-(c) € 23,200.00 € 18,560.00 € 14,848.00 € 11,878.40 € 0.00 (e) Tax Shield 33.3% 33.3%*(b) € 1,931.40 € 1,545.12 € 1,236.10 € 988.88 € 3,955.51 (f) PV Tax Shield r = 5% € 1,724.46 € 1,231.76 € 879.83 € 628.45 € 2,244.46 The sum of the present value of tax savings (including the expense charged by the installation costs) is €6,708.96. The net effect of treating the insurance as a capital cost is (€8,559.71 - €6,708.96 = ) €1,850.75, which is less than treating the installation cost as an expense. This is because the tax savings from the €8,000 has been amortised (spread out) over the five years with the investment measurement approach. If you had a choice, you would treat the installation cost as an expense. 7. We will use the bottom-up approach to calculate the operating cash flow for each year. We also must be sure to include the net working capital cash flows each year. First, we calculate the depreciation for the investment: Year 1 2 3 4 Starting Value 325,000 260,000 208,000 166,400 Depreciation 20% 65,000 52,000 41,600 33,280 Accumulated Dep 65,000 117,000 158,600 191,880 Residual Value 260,000 208,000 166,400 133,120 So, the total cash flow each year will be: 0 1 2 3 4 Year 1 Year 2 Year 3 Year 4 Sales £105,000 £105,000 £105,000 £105,000 Costs 20,000 20,000 20,000 20,000 Depreciation 65,000 52,000 41,600 33,280 EBT £20,000 £33,000 £43,400 £51,720 Tax £5,000 £8,250 £10,850 £12,930 Net income £15,000 £24,750 £32,550 £38,790 0 1 2 3 4 Year 1 Year 2 Year 3 Year 4 Sales €105,000 €105,000 €105,000 €105,000 Costs 20,000 20,000 20,000 20,000 Depreciation 65,000 52,000 41,600 33,280 EBT €20,000 €33,000 €43,400 €51,720 Tax €5,000 €8,250 €10,850 €12,930 Net income €15,000 €24,750 €32,550 €38,790 OCF 0 €80,000 €76,750 €74,150 €72,070 Capital spending -325,000 0 0 0 133120 NWC -€ 10,000.00 -€ 2,000.00 -€ 3,000.00 € 4,000.00 € 11,000.00 Incremental cash flow -€ 335,000.00 € 78,000.00 € 73,750.00 € 78,150.00 € 216,190.00 a. NPV = –€335,000 + €78,000 / 1.12 + €73,750 / 1.122 + €78,150/ 1.123 + €216,190 / 1.124 NPV = -€13,545.81 8. In this example follow the same process as before. The worksheet is given below: Year 1 2 3 4 Starting Value € 325,000.00 € 260,000.00 € 208,000.00 € 166,400.00 Depreciation 20% € 65,000.00 € 52,000.00 € 41,600.00 € 165,400.00 Accumulated Dep € 65,000.00 € 117,000.00 € 158,600.00 € 324,000.00 Residual Value € 260,000.00 € 208,000.00 € 166,400.00 € 1,000.00 Year 1 Year 2 Year 3 Year 4 Sales € 105,000.00 € 105,000.00 € 105,000.00 € 105,000.00 Costs € 20,000.00 € 20,000.00 € 20,000.00 € 20,000.00 Depreciation € 65,000.00 € 52,000.00 € 41,600.00 € 165,400.00 EBT € 20,000.00 € 33,000.00 € 43,400.00 -€ 80,400.00 Tax € 5,000.00 € 8,250.00 € 10,850.00 -€ 20,100.00 Net income € 15,000.00 € 24,750.00 € 32,550.00 -€ 60,300.00 OCF € 0.00 € 80,000.00 € 76,750.00 € 74,150.00 € 105,100.00 Capital spending -€ 325,000.00 € 0.00 € 0.00 € 0.00 € 1,000.00 NWC -€ 2,000.00 -€ 2,000.00 -€ 3,000.00 -€ 4,000.00 € 11,000.00 Incremental cash flow -€ 327,000.00 € 78,000.00 € 73,750.00 € 70,150.00 € 117,100.00 PV(CF) -€ 327,000.00 € 69,642.86 € 58,793.05 € 49,931.38 € 74,419.17 NPV -€ 74,213.54 9. The exact same process is followed as with Q7. The worksheet is below: Year 1 2 3 4 Starting Value € 325,000.00 € 243,750.00 € 182,812.50 € 137,109.38 Depreciation 25% € 81,250.00 € 60,937.50 € 45,703.13 € 136,109.38 Accumulated Dep € 81,250.00 € 142,187.50 € 187,890.63 € 324,000.00 Residual Value € 243,750.00 € 182,812.50 € 137,109.38 € 1,000.00 Year 1 Year 2 Year 3 Year 4 Sales € 105,000.00 € 105,000.00 € 105,000.00 € 105,000.00 Costs € 20,000.00 € 20,000.00 € 20,000.00 € 20,000.00 Depreciation € 81,250.00 € 60,937.50 € 45,703.13 € 136,109.38 EBT € 3,750.00 € 24,062.50 € 39,296.88 -€ 51,109.38 Tax € 937.50 € 6,015.63 € 9,824.22 -€ 12,777.34 Net income € 2,812.50 € 18,046.88 € 29,472.66 -€ 38,332.03 OCF € 0.00 € 84,062.50 € 78,984.38 € 75,175.78 € 97,777.34 Capital spending -€ 325,000.00 € 0.00 € 0.00 € 0.00 € 1,000.00 NWC -€ 2,000.00 -€ 2,000.00 -€ 3,000.00 -€ 4,000.00 € 11,000.00 Incremental cash flow -€ 327,000.00 € 82,062.50 € 75,984.38 € 71,175.78 € 109,777.34 PV(CF) @ 12% -€ 327,000.00 € 73,270.09 € 60,574.28 € 50,661.52 € 69,765.49 NPV -€ 72,728.63 10. First, we will calculate the annual depreciation of the new equipment. It will be: Year 1 2 3 4 5 (a) Starting Value £925,000 £740,000 £592,000 £473,600 £378,880 (b) Depreciation 20% 20%*(a) £185,000 £148,000 £118,400 £94,720 £288,880 (c) Accumulated Depreciation £185,000 £333,000 £451,400 £546,120 £835,000 (d) Residual Value (a)-(c) £740,000 £592,000 £473,600 £378,880 £90,000 Notice that in the last year of the project, we calculated the annual depreciation figure as £288,880. This comprises two components. The first component is the 20% depreciation charge on the year 5 starting value of £378,880, which is equal to £75,776. This leaves a residual value of £303,104. The second component is the tax loss that the company experiences from selling the system for £90,000. This is equal to £303,104 - £90,000 = £213,104. Combined, they equal £288,880. Next we calculate the operating cash flows from the project: 1 2 3 4 5 Cash Savings 360000 360000 360000 360000 360000 Depreciation £185,000 £148,000 £118,400 £94,720 £288,880 Pre-Tax Savings £175,000 £212,000 £241,600 £265,280 £71,120 Tax @ 28% £49,000 £59,360 £67,648 £74,278 £19,914 After Tax Savings £126,000 £152,640 £173,952 £191,002 £51,206 OCF £311,000 £300,640 £292,352 £285,722 £340,086 Now we can find the project IRR. There is an unusual feature that is a part of this project. Accepting this project means that we will reduce NWC. This reduction in NWC is a cash inflow at Year 0. This reduction in NWC implies that when the project ends, we will have to increase NWC. So, at the end of the project, we will have a cash outflow to restore the NWC to its level before the project. We also must include the salvage value at the end of the project (the tax effects have already been incorporated into the analysis). The cash flows arising from the project are: 0 1 2 3 4 5 Investment -£925,000 £90,000 NWC £125,000 -£125,000 OCF £311,000 £300,640 £292,352 £285,722 £340,086 Net Cash Flow -£800,000 £311,000 £300,640 £292,352 £285,722 £305,086 IRR of the project is: IRR = 25.49% 11. First, we will calculate the annual depreciation of the new equipment. It will be: Annual depreciation = €390,000/5 Annual depreciation = €78,000 Now, we calculate the aftertax salvage value. The aftertax salvage value is the market price minus (or plus) the taxes on the sale of the equipment, so: Aftertax salvage value = MV + (BV – MV)tc Very often, the book value of the equipment is zero as it is in this case. If the book value is zero, the equation for the aftertax salvage value becomes: Aftertax salvage value = MV + (0 – MV)tc Aftertax salvage value = MV(1 – tc) We will use this equation to find the aftertax salvage value since we know the book value is zero. So, the aftertax salvage value is: Aftertax salvage value = €60,000(1 – 0.34) Aftertax salvage value = €39,600 Using the tax shield approach, we find the OCF for the project is: OCF = €120,000(1 – 0.34) + 0.34(€78,000) OCF = €105,720 Now we can find the project NPV. Notice that we include the NWC in the initial cash outlay. The recovery of the NWC occurs in Year 5, along with the aftertax salvage value. NPV = –€390,000 – 28,000 + €105,720(PVIFA10%,5) + [(€39,600 + 28,000) / 1.15] NPV = €24,736.26 2 3 4 5 £311,800 £401,440 £393,152 £386,521 £405,886 0 £800,000 NPV = =− + (1+IRR) +(1+IRR) +(1+IRR) +(1+IRR) +(1+IRR) 12. To calculate salvage value, you must estimate the annual depreciation and accumulate this to the end of the project. The income from selling the investment may or may not be taxed depending on how the residual book value compares to the market value at time of sale. Year 1 2 3 4 (a) Starting Value £9,300,000 £7,440,000 £5,952,000 £4,761,600 (b) Depreciation 20% 20%*(a) £1,860,000 £1,488,000 £1,190,400 £952,320 (c) Accumulated Depreciation £1,860,000 £3,348,000 £4,538,400 £5,490,720 (d) Residual Value (a)-(c) £7,440,000 £5,952,000 £4,761,600 £3,809,280 The salvage value of the investment is £3,100,000. The asset is sold at a loss to the book value, and so won’t be taxed. If the firm has other taxable profits, it will receive a tax gain on the loss. This will be equal to (£3,809,280 - £3,100,000) *28% = £198,598. The after-tax value of the asset is £3,298,598. 13. We will begin by calculating the initial cash outlay, that is, the cash flow at Time 0. To undertake the project, we will have to purchase the equipment and increase net working capital. So, the cash outlay today for the project will be: Equipment –€2,000,000 NWC –100,000 Total –€2,100,000 We now need to calculate the depreciation schedule of the asset so that we can calculate net income. Year 1 2 3 4 (a) Starting Value €2,000,000 €1,600,000 €1,280,000 €1,024,000 (b) Depreciation 20% 20%*(a) €400,000 €320,000 €256,000 €204,800 (c) Accumulated Depreciation €400,000 €720,000 €976,000 €1,180,800 (d) Residual Value (a)-(c) €1,600,000 €1,280,000 €1,024,000 €819,200 The Income for each year is calculated as follows: 1 2 3 4 Sales €1,200,000 €1,200,000 €1,200,000 €1,200,000 Costs €300,000 €300,000 €300,000 €300,000 Depreciation €400,000 €320,000 €256,000 €204,800 EBT €500,000 €580,000 €644,000 €695,200 Tax €175,000 €203,000 €225,400 €243,320 Net Income €325,000 €377,000 €418,600 €451,880 The operating cash flow is: 1 2 3 4 Net Income £325,000 £377,000 £418,600 £451,880 Depreciation £400,000 £320,000 £256,000 £204,800 Operating Cash Flow £725,000 £697,000 £674,600 £656,680 To find the NPV of the project, we add the present value of the project cash flows. We must be sure to add back the net working capital at the end of the project life, since we are assuming the net working capital will be recovered. So, the project NPV is: 0 1 2 3 4 Investment -€2,000,000 €819,200 NWC -€100,000 €100,000 Operating Cash Flow €725,000 €697,000 €674,600 €656,680 Net Cash Flow -€2,100,000 €725,000 €697,000 €674,600 €1,575,880 PV Cash Flows r = 14% -€2,100,000 €635,965 €536,319 €455,335 €933,047 NPV = €460,667 14. We need to first calculate the NPV of each machine. Focussing on the Techron I first, the depreciation schedule of the machine is given below: Year 1 2 3 (a) Starting Value €210,000 €168,000 €134,400 (b) Depreciation 20% 20%*(a) €42,000 €33,600 €114,400 (c) Accumulated Depreciation €42,000 €75,600 €190,000 (d) Residual Value (a)-(c) €168,000 €134,400 €20,000 We now calculate the income statement for the Techron I 1 2 3 Pre-Tax Operating Costs -€ 34,000 -€ 34,000 -€ 34,000 Depreciation -€42,000 -€33,600 -€114,400 EBT -€76,000 -€67,600 -€148,400 Tax -€26,600 -€23,660 -€51,940 Net Income -€49,400 -€43,940 -€96,460 This allows us to calculate the Operating Cash Flow of the Techron I. 1 2 3 Net Income -€49,400 -€43,940 -€96,460 Depreciation €42,000 €33,600 €114,400 Operating Cash Flow -€7,400 -€10,340 €17,940 Now we can estimate the NPV of the Techron I. 0 1 2 3 Investment -€210,000 €20,000 Operating Cash Flow -€7,400 -€10,340 €17,940 Cash Flows -€210,000 -€7,400 -€10,340 €37,940 PV Cash Flows -€210,000 -€6,491 -€7,956 €25,608 The NPV of Techron I is thus -€198,839. The equivalent annual cost of the Techron I is -€198,839 = EAC(PVIFA14%,3) EAC = –€85,646 We now do the same with the Techron II. First the depreciation schedule: Year 1 2 3 4 5 (a) Starting Value €320,000 €256,000 €204,800 €163,840 €131,072 (b) Depreciation 20% 20%*(a) €64,000 €51,200 €40,960 €32,768 €111,072 (c) Accumulated Depreciation €64,000 €115,200 €156,160 €188,928 €300,000 (d) Residual Value (a)-(c) €256,000 €204,800 €163,840 €131,072 €20,000 Then the income statement: 1 2 3 4 5 Pre-Tax Operating Costs -€ 23,000 -€ 23,000 -€ 23,000 -€ 23,000 -€ 23,000 Depreciation -€64,000 -€51,200 -€40,960 -€32,768 -€111,072 EBT -€87,000 -€74,200 -€63,960 -€55,768 -€134,072 Tax -€30,450 -€25,970 -€22,386 -€19,519 -€46,925 Net Income -€56,550 -€48,230 -€41,574 -€36,249 -€87,147 Which allows us to calculate operating cash flow: 1 2 3 4 5 Net Income -€56,550 -€48,230 -€41,574 -€36,249 -€87,147 Depreciation €64,000 €51,200 €40,960 €32,768 €111,072 Operating Cash Flow €7,450 €2,970 -€614 -€3,481 €23,925 Leading to the cash flow statement: 0 1 2 3 4 5 Investment -€320,000 €20,000 Operating Cash Flow €7,450 €2,970 -€614 -€3,481 €23,925 Cash Flows -€320,000 €7,450 €2,970 -€614 -€3,481 €43,925 PV Cash Flows -€320,000 €6,535 €2,285 -€414 -€2,061 €22,813 The Net Present Value of the Techron II is -€290,842 and the equivalent annual cost is: -€290,842 = EAC(PVIFA14%,5) EAC = –€84,717 Comparing the EAC of the Techron I (€85,646) with the EAC of the Techron II (€84,717) leads us to go with the Techron II. 15. In this question, the two machines cannot be compared using the equivalent annual cost method because once one machine runs out, it will not be replaced. In addition, with this type of question, it is important to know the relative income streams arising from each conveyor belt. This is because the longer lasting conveyer belt will provide income beyond the lifetime of the conveyor belt that breaks down first. This information isn’t provided by the question and so, it is impossible to compare each machine. 16. If the conveyor belt can be replaced, we can use the EAC method. We calculate the EAC of System A by first determining its depreciation schedule. Year 1 2 3 4 (a) Starting Value Kr430,000 Kr215,000 Kr107,500 Kr53,750 (b) Depreciation 50% 50% Kr215,000 Kr107,500 Kr53,750 Kr53,750 (c) Accumulated Depreciation Kr215,000 Kr322,500 Kr376,250 Kr430,000 (d) Residual Value (a)-(c) Kr215,000 Kr107,500 Kr53,750 Kr0 We now calculate net income from System A. 1 2 3 4 Pre-Tax Operating Costs -€ 120,000 -€ 120,000 -€ 120,000 -€ 120,000 Depreciation -Kr215,000 -Kr107,500 -Kr53,750 -Kr53,750 EBT -Kr335,000 -Kr227,500 -Kr173,750 -Kr173,750 Tax 28% -Kr93,800 -Kr63,700 -Kr48,650 -Kr48,650 Net Income -Kr241,200 -Kr163,800 -Kr125,100 -Kr125,100 Operating Cash Flow is: 1 2 3 4 Net Income -Kr241,200 -Kr163,800 -Kr125,100 -Kr125,100 Depreciation Kr215,000 Kr107,500 Kr53,750 Kr53,750 Operating Cash Flow -Kr26,200 -Kr56,300 -Kr71,350 -Kr71,350 Cash Flow Statement: 0 1 2 3 4 Investment -Kr430,000 Operating Cash Flow -Kr26,200 -Kr56,300 -Kr71,350 -Kr71,350 Cash Flows -Kr430,000 -Kr26,200 -Kr56,300 -Kr71,350 -Kr71,350 PV Cash Flows -Kr430,000 -Kr21,833 -Kr39,097 -Kr41,291 -Kr34,409 The NPV of System A is -Kr532,221 and the EAC is -Kr532,221 = EAC(PVIFA20%,4) EAC = –Kr76,809 Now for System B. The same series of tables will be presented. Depreciation Schedule: Year 1 2 3 4 5 6 Starting Value Kr540,000 Kr270,000 Kr135,000 Kr67,500 Kr33,750 Kr16,875 Depreciation 20% Kr270,000 Kr135,000 Kr67,500 Kr33,750 Kr16,875 Kr16,875 Accumulated Depreciation Kr270,000 Kr405,000 Kr472,500 Kr506,250 Kr523,125 Kr540,000 Residual Value Kr270,000 Kr135,000 Kr67,500 Kr33,750 Kr16,875 Kr0 Income Statement: 1 2 3 4 5 6 Pre-Tax Operating Costs -Kr 80,000 -Kr 80,000 -Kr 80,000 -Kr 80,000 -Kr 80,000 -Kr 80,000 Depreciation -Kr270,000 -Kr135,000 -Kr67,500 -Kr33,750 -Kr16,875 -Kr16,875 EBT -Kr350,000 -Kr215,000 -Kr147,500 -Kr113,750 -Kr96,875 -Kr96,875 Tax -Kr98,000 -Kr60,200 -Kr41,300 -Kr31,850 -Kr27,125 -Kr27,125 Net Income -Kr252,000 -Kr154,800 -Kr106,200 -Kr81,900 -Kr69,750 -Kr69,750 Operating Cash Flow: 1 2 3 4 5 6 Net Income -Kr252,000 -Kr154,800 -Kr106,200 -Kr81,900 -Kr69,750 -Kr69,750 Depreciation Kr270,000 Kr135,000 Kr67,500 Kr33,750 Kr16,875 Kr16,875 Operating Cash Flow Kr18,000 -Kr19,800 -Kr38,700 -Kr48,150 -Kr52,875 -Kr52,875 Cash Flow Statement: 0 1 2 3 4 5 6 Investment -Kr540,000 Operating Cash Flow Kr18,000 -Kr19,800 -Kr38,700 -Kr48,150 -Kr52,875 -Kr52,875 Cash Flows -Kr540,000 Kr18,000 -Kr19,800 -Kr38,700 -Kr48,150 -Kr52,875 -Kr52,875 PV Cash Flows -Kr540,000 Kr15,000 -Kr13,750 -Kr22,396 -Kr23,220 -Kr21,249 -Kr17,708 The Net Present Value of System B is -Kr623,323 and the equivalent annual cost is -Kr623,323 = EAC(PVIFA20%,6) EAC = –Kr187,437 The equivalent annual cost of System A is significantly smaller than that of System B and so System A should be chosen. 17. To determine the value of a firm, we can simply find the present value of the firm’s future cash flows. No depreciation is given, so we can assume depreciation is zero. Using the tax shield approach, we would find the present value of the aftertax revenues, and the present value of the aftertax costs. However, there is no tax in Dubai and so t = 0. The required return, growth rates, price, and costs are all given in real terms. Subtracting the costs from the revenues will give us the value of the firm’s cash flows. We must calculate the present value of each separately since each is growing at a different rate. First, we will find the present value of the revenues. The revenues in year 1 will be the number of tickets sold, times the price per ticket, or: Aftertax revenue in year 1 in real terms = (10,000 × AED300)(1 – 0) Aftertax revenue in year 1 in real terms = AED3,000,000 Revenues will grow at seven percent per year in real terms forever. Apply the growing perpetuity formula, we find the present value of the revenues is: PV of revenues = C1 / (R – g) PV of revenues = £3,000,000 / (0.10 – 0.07) PV of revenues = AED27,272,727 The real costs in year 1 will be: Costs in year 1 in real terms = AED2,000,000 Costs will grow at five percent per year in real terms forever. Applying the growing perpetuity formula, we find the present value of the costs is: PV of costs = C1 / (R – g) PV of costs = AED2,000,000 / (0.10 – 0.05) PV of costs = AED15,384,615 Now we can find the value of the firm, which is: Value of the firm = PV of revenues – PV of costs Value of the firm = AED27,272,727 – 15,384,615 Value of the firm = AED11,888,112 18. To calculate the nominal cash flows, we simple increase each item in the income statement by the inflation rate, except for depreciation. Depreciation is a nominal cash flow, so it does not need to be adjusted for inflation in nominal cash flow analysis. Since the resale value is given in nominal terms as of the end of year 5, it does not need to be adjusted for inflation. Also, no inflation adjustment is needed for either the depreciation charge or the recovery of net working capital since these items are already expressed in nominal terms. Note that an increase in required net working capital is a negative cash flow whereas a decrease in required net working capital is a positive cash flow. We first need to calculate the depreciation schedule. Year 1 2 3 4 5 (a) Starting Value £250,000 £200,000 £160,000 £128,000 £102,400 (b) Depreciation 20% £50,000 £40,000 £32,000 £25,600 £72,400 (c) Accumulated Depreciation £50,000 £90,000 £122,000 £147,600 £220,000 (d) Residual Value £200,000 £160,000 £128,000 £102,400 £30,000 0 1 2 3 4 5 Sales £200,000 £206,000 £212,180 £218,545 £225,102 Expenses £50,000 £51,500 £53,045 £54,636 £56,275 Depreciation 20% £50,000 £40,000 £32,000 £25,600 £72,400 EBT £100,000 £114,500 £127,135 £138,309 £96,426 Tax £34,000 £38,930 £43,226 £47,025 £32,785 Net Income £66,000 £75,570 £83,909 £91,284 £63,641 Operating Cash Flow £116,000 £115,570 £115,909 £116,884 £136,041 Investment -£250,000 £30,000 NWC -£10,000 £10,000 Cash Flow -£260,000 £116,000 £115,570 £115,909 £116,884 £176,041 19. To calculate the EAC of an investment, first calculate the depreciation schedule. Year 1 2 3 (a) Starting Value £65,000 £52,000 £41,600 (b) Depreciation 20% 20%*(a) £13,000 £10,400 £21,600 (c) Accumulated Depreciation £13,000 £23,400 £45,000 (d) Residual Value (a)-(c) £52,000 £41,600 £20,000 Now use the depreciation schedule to estimate the operating cash flow. 1 2 3 Pre-Tax Operating Costs -€ 12,000 -€ 12,000 -€ 12,000 Depreciation -£13,000 -£10,400 -£21,600 EBT -£25,000 -£22,400 -£33,600 Tax 24% -£6,000 -£5,376 -£8,064 Net Income -£19,000 -£17,024 -£25,536 1 2 3 Net Income -£19,000 -£17,024 -£25,536 Depreciation £13,000 £10,400 £21,600 Operating Cash Flow -£6,000 -£6,624 -£3,936 The cash flows for each year are now calculated. 0 1 2 3 Investment -£65,000 £20,000 Operating Cash Flow -£6,000 -£6,624 -£3,936 Cash Flows -£65,000 -£6,000 -£6,624 £16,064 PV Cash Flows -£65,000 -£5,455 -£5,474 £12,069 The Net Present Value is -£63,860 and the Equivalent Annual Cost is -£63,860 = EAC(PVIFA10%,3) EAC = £25,678.97 20. Replacement decision analysis is the same as the analysis of two competing projects, in this case, keep the current equipment, or purchase the new equipment. We will consider the purchase of the new machine first. Purchase new machine: The initial cash outlay for the new machine is the cost of the new machine, plus the increased net working capital. So, the initial cash outlay will be: Purchase new machine –£32,000,000 Net working capital –500,000 Total –£32,500,000 Next, we can calculate the operating cash flow created if the company purchases the new machine. The saved operating expense is an incremental cash flow. Additionally, the reduced operating expense is a cash inflow, so it should be treated as such in the income statement. Since we have not been told how the machine is to be depreciated, we will assume that depreciation is straight line (£32,000,000/4 years). The pro forma income statement, and adding depreciation to net income, the operating cash flow created by purchasing the new machine each year will be: Operating expense £8,000,000 Depreciation 8,000,000 EBT £0,000,000 Taxes – Net income £0 OCF £8,000,000 So, the NPV of purchasing the new machine, including the recovery of the net working capital, is: NPV = –£32,500,000 + £8,000,000(PVIFA18%,4) + £500,000 / 1.184 NPV = –£10,721,611 And the IRR is: 0 = –£32,500,000 + £8,00,000(PVIFAIRR,4) + £500,000 / (1 + IRR)4 Using a spreadsheet or financial calculator, we find the IRR is: IRR = 0% Now we can calculate the decision to keep the old machine: Keep old machine: The initial cash outlay for the old machine is the market value of the old machine, including any potential tax consequence. The decision to keep the old machine has an opportunity cost, namely, the company could sell the old machine. Also, if the company sells the old machine at its current value, it will incur taxes. Both of these cash flows need to be included in the analysis. So, the initial cash flow of keeping the old machine will be: Keep machine –£9,000,000 Taxes 39% of (9,000,000-1,000,000) 3,120,000 Total –£5,880,000 Next, we can calculate the operating cash flow created if the company keeps the old machine. There are no incremental cash flows from keeping the old machine, but we need to account for the cash flow effects of depreciation. The income statement, adding depreciation to net income to calculate the operating cash flow will be: Depreciation (£1,000,000/4) £250,000 EBT –£8,000,000 Taxes –3,217,500 Net income –£4,782,500 OCF -£4,532,500 So, the NPV of the decision to keep the old machine will be: NPV = –£5,880,000 - £4,532,500(PVIFA18%,4) NPV = –£6,131,803 And the IRR is: 0 = –£5,880,000 - £4,532,500(PVIFAIRR,4) Since the project never pays pay back, there is no IRR. The company should not purchase the new machine since it has a lower NPV. b. The purchase of a new machine can have a positive NPV because of the depreciation tax shield. Without the depreciation tax shield, the new machine would have a negative NPV since the saved expenses from the machine do not exceed the cost of the machine when we consider the time value of money. 21. Here we have a project in which the quantity sold each year increases. As in all capital budgeting problems we need to first determine the depreciation schedule of the investment. Year 1 2 3 4 5 (a) Starting Value £60,000 £48,000 £38,400 £30,720 £24,576 (b) Depreciation 20% £12,000 £9,600 £7,680 £6,144 £24,576 (c) Accumulated Depreciation £12,000 £21,600 £29,280 £35,424 £60,000 (d) Residual Value £48,000 £38,400 £30,720 £24,576 £0 The next stage is to calculate the operating cash flows: First, we need to calculate the quantity sold each year by increasing the current year’s quantity by the growth rate. So, the quantity sold each year will be: Year 1 quantity = 5,000 Year 2 quantity = 5,000(1 + .15) = 5,750 Year 3 quantity = 5,750(1 + .15) = 6,613 Year 4 quantity = 6,613(1 + .15) = 7,604 Year 5 quantity = 7,604(1 + .15) = 8,745 Now we can calculate the sales revenue and variable costs each year. The pro forma income statements and operating cash flow each year will be: 1 2 3 4 5 Sales of lamps g = 15% 5000 5750 6613 7,604 8,745 Revenues £225,000 £258,750 £297,563 £342,197 £393,526 Variable costs £100,000 £115,000 £132,250 £152,088 £174,901 Fixed Costs £75,000 £75,000 £75,000 £75,000 £75,000 Depreciation 20% £12,000 £9,600 £7,680 £6,144 £24,576 EBT £38,000 £59,150 £82,633 £108,965 £119,050 Tax £10,640 £16,562 £23,137 £30,510 £33,334 Net Income £27,360 £42,588 £59,495 £78,455 £85,716 Operating Cash Flow £39,360 £52,188 £67,175 £84,599 £110,292 The cash flows for the project are thus: 0 1 2 3 4 5 Investment -£60,000 Net Working Capital -£28,000 £28,000 Net Cash Flow -£88,000 £39,361 £52,190 £67,178 £84,603 £138,297 PV Cash Flow -88000 £31,489 £33,402 £34,395 £34,653 £45,317 NPV £91,256 22. Replacement decision analysis is the same as the analysis of two competing projects, in this case, keep the current equipment, or purchase the new equipment. We will consider the purchase of the new machine first. Purchase new machine: As with any capital budgeting analysis, we must first determine the depreciation schedule. Year 1 2 3 4 5 (a) Starting Value £5,000,000 £4,000,000 £3,200,000 £2,560,000 £2,048,000 (b) Depreciation 20% £1,000,000 £800,000 £640,000 £512,000 £1,048,000 (c) Accumulated Depreciation £1,000,000 £1,800,000 £2,440,000 £2,952,000 £4,000,000 (d) Residual Value £4,000,000 £3,200,000 £2,560,000 £2,048,000 £1,000,000 We now calculate the operating cash flows from the new machine. 0 1 2 3 4 5 Maintenance Costs £100,000 £100,000 £100,000 £100,000 £100,000 Depreciation 20% £1,000,000 £800,000 £640,000 £512,000 £1,048,000 EBT -£1,100,000 -£900,000 -£740,000 -£612,000 -£1,148,000 Tax -£264,000 -£216,000 -£177,600 -£146,880 -£275,520 Net Income -£836,000 -£684,000 -£562,400 -£465,120 -£872,480 Operating Cash Flow £164,000 £116,000 £77,600 £46,880 £175,520 Notice the taxes are negative, implying a tax credit. We can now present the cash flow analysis. 0 1 2 3 4 5 Investment -£5,000,000 £1,000,000 Operating Cash Flows £164,000 £116,000 £77,600 £46,880 £175,520 Net Cash Flow -5000000 164000 116000 77600 46880 1175520 PV Cash Flows @ 12% -£5,000,000 146,429 92,474 55,234 29,793 667,021 The NPV of purchasing the new machine is : NPV = -£4,009,048 Notice the NPV is negative. This does not necessarily mean we should not purchase the new machine. In this analysis, we are only dealing with costs, so we would expect a negative NPV. The revenue is not included in the analysis since it is not incremental to the machine. Similar to an EAC analysis, we will use the machine with the least negative NPV. Now we can calculate the decision to keep the old machine: Keep old machine: The decision to keep the old machine has an opportunity cost, namely, the company could sell the old machine. Also, if the company sells the old machine at its current value, it will incur taxes. Both of these cash flows need to be included in the analysis. So, the initial cash flow of keeping the old machine will be: Keep machine –£3,000,000 Taxes -£240,000 Total –£3,240,000 The Tax rebate is £240,000 because a loss of £1,000,000 will be made on the sale. Next, we can calculate the operating cash flow created if the company keeps the old machine. First of all, we need to determine the depreciation schedule of the old machine. Year 1 2 3 4 5 (a) Starting Value £4,000,000 £3,200,000 £2,560,000 £2,048,000 £1,638,400 (b) Depreciation 20% £800,000 £640,000 £512,000 £409,600 £1,538,400 (c) Accumulated Depreciation £800,000 £1,440,000 £1,952,000 £2,361,600 £3,900,000 (d) Residual Value £3,200,000 £2,560,000 £2,048,000 £1,638,400 £100,000 Operating Cash Flow: 1 2 3 4 5 Maintenance Costs £300,000 £300,000 £300,000 £300,000 £300,000 Depreciation 20% £800,000 £640,000 £512,000 £409,600 £1,538,400 EBT -£1,100,000 -£940,000 -£812,000 -£709,600 -£1,838,400 Tax -£374,000 -£319,600 -£276,080 -£241,264 -£625,056 Net Income -£726,000 -£620,400 -£535,920 -£468,336 -£1,213,344 Operating Cash Flow £74,000 £19,600 -£23,920 -£58,736 £325,056 Now the cash flow analysis. 0 1 2 3 4 5 Investment -£3,240,000 £100,000 Operating Cash Flows £74,000 £19,600 -£23,920 -£58,736 £325,056 Net Cash Flow - £3,240,000 £74,000 £19,600 -£23,920 -£58,736 £425,056 PV Cash Flows @ 12% - £3,240,000 £66,071 £15,625 -£17,026 -£37,328 £241,188 So, the NPV of the decision to keep the old machine will be -£2,971,469. The company should not purchase the new machine since it has a lower NPV. 23. As in any investment analysis, one must first determine the depreciation schedule of the asset. (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 1 £150,000 £30,000 £30,000 £120,000 2 £120,000 £24,000 £54,000 £96,000 3 £96,000 £19,200 £73,200 £76,800 4 £76,800 £15,360 £88,560 £61,440 5 £61,440 £12,288 £100,848 £49,152 6 £49,152 £9,830 £110,678 £39,322 7 £39,322 £7,864 £118,543 £31,457 8 £31,457 £6,291 £124,834 £25,166 9 £25,166 £5,033 £129,867 £20,133 10 £20,133 £20,133 £150,000 £0 We now calculate the operating cash flows for each year. Year Sales Incremental Cost Savings Depreciation 20% EBT Tax Net Income Operating Cash Flow 1 200,000 £100,000 £30,000 £70,000 £19,600 £50,400 £80,400 2 200,000 £104,000 £24,000 £80,000 £22,400 £57,600 £81,600 3 200,000 £108,160 £19,200 £88,960 £24,909 £64,051 £83,251 4 200,000 £112,486 £15,360 £97,126 £27,195 £69,931 £85,291 5 200,000 £116,986 £12,288 £104,698 £29,315 £75,382 £87,670 6 200,000 £121,665 £9,830 £111,835 £31,314 £80,521 £90,352 7 200,000 £126,532 £7,864 £118,668 £33,227 £85,441 £93,305 8 200,000 £131,593 £6,291 £125,302 £35,084 £90,217 £96,509 9 200,000 £136,857 £5,033 £131,824 £36,911 £94,913 £99,946 10 200,000 £142,331 £20,133 £122,199 £34,216 £87,983 £108,116 This allows us to calculate the cash flows for the NPV analysis. Year Investment Operating Cash Flows Net Working Capital Net Cash Flows PV Cash Flows @15% 0 -£150,000 -£30,000 -£180,000 -£180,000 1 £80,400 £80,400 £69,913 2 £81,600 £81,600 £61,701 3 £83,251 £83,251 £54,739 4 £85,291 £85,291 £48,765 5 £87,670 £87,670 £43,588 6 £90,352 £90,352 £39,061 7 £93,305 £93,305 £35,078 8 £96,509 £96,509 £31,549 9 £99,946 £99,946 £28,411 10 £108,116 £30,000 £138,116 £34,140 The NPV is equal to £266,945. You should undertake the analysis. 24. As in any investment analysis, we determine the depreciation schedule first. Year 1 2 3 4 5 (a) Starting Value £400,000 £320,000 £256,000 £204,800 £163,840 (b) Depreciation 20% £80,000 £64,000 £51,200 £40,960 £163,840 (c) Accumulated Depreciation £80,000 £144,000 £195,200 £236,160 £400,000 (d) Residual Value £320,000 £256,000 £204,800 £163,840 £0 Now estimate the operating cash flows. 1 2 3 4 5 Sales 10,000 10,000 10,000 10,000 10,000 Revenues g = 5% £400,000 £420,000 £441,000 £463,050 £486,203 Variable Costs g = 10% £200,000 £220,000 £242,000 £266,200 £292,820 Fixed Costs £50,000 £50,000 £50,000 £50,000 £50,000 Depreciation 20% £80,000 £64,000 £51,200 £40,960 £163,840 EBT £70,000 £86,000 £97,800 £105,890 -£20,458 Tax £19,600 £24,080 £27,384 £29,649 -£5,728 Net Income £50,400 £61,920 £70,416 £76,241 -£14,729 Operating Cash Flow £130,400 £125,920 £121,616 £117,201 £149,111 The cash flow analysis is now presented below: 0 1 2 3 4 5 Investment -400000 Operating Cash Flows £130,400 £125,920 £121,616 £117,201 £149,111 Net Working Capital -£25,000 £25,000 Net Cash Flow -£425,000 £130,400 £125,920 £121,616 £117,201 £174,111 PV Cash Flows @ 15% -£425,000 £113,391 £95,214 £79,964 £67,010 £86,564 The Net Present Value is equal to £17,143, so you should accept the project. 25. This is an in-depth capital budgeting problem. Probably the easiest OCF calculation for this problem is the bottom up approach, so we will construct an income statement for each year. Beginning with the initial cash flow at time zero, the project will require an investment in equipment. To start off, we determine the depreciation schedule. The salvage value is 20% of the installed cost, which is 20%*€21,000,000 = €4,200,000. Year 1 2 3 4 5 (a) Starting Value £21,000,000 £16,800,000 £13,440,000 £10,752,000 £8,601,600 (b) Depreciation 20% £4,200,000 £3,360,000 £2,688,000 £2,150,400 £4,401,600 (c) Accumulated Depreciation £4,200,000 £7,560,000 £10,248,000 £12,398,400 £16,800,000 (d) Residual Value £16,800,000 £13,440,000 £10,752,000 £8,601,600 £4,200,000 The Income Statement is next in line. 1 2 3 4 5 Sales 85,000 98,000 106,000 114,000 93,000 Revenues €27,625,000 €31,850,000 €34,450,000 €37,050,000 €30,225,000 Variable Costs €20,400,000 €23,520,000 €25,440,000 €27,360,000 €22,320,000 Fixed Costs €900,000 €900,000 €900,000 €900,000 €900,000 Depreciation 20% €4,200,000 €3,360,000 €2,688,000 €2,150,400 €4,401,600 EBT €2,125,000 €4,070,000 €5,422,000 €6,639,600 €2,603,400 Tax €743,750 €1,424,500 €1,897,700 €2,323,860 €911,190 Net Income €1,381,250 €2,645,500 €3,524,300 €4,315,740 €1,692,210 Operating Cash Flow €5,581,250 €6,005,500 €6,212,300 €6,466,140 €6,093,810 Net Working Capital is a function of next year’s sales and so we can now calculate how much net working capital is required each year. 0 1 2 3 4 5 Revenues €27,625,000 €31,850,000 €34,450,000 €37,050,000 €30,225,000 Net Working Capital €5,643,750 €4,777,500 €5,167,500 €5,557,500 €4,533,750 €0 The Cash Flow analysis can now be carried out. 0 1 2 3 4 5 Investment -€21,000,000 €4,200,000 Operating Cash Flows €5,581,250 €6,005,500 €6,212,300 €6,466,140 €6,093,810 Change in NWC -€5,643,750 €866,250 -€390,000 -€390,000 €1,023,750 €6,033,750 Net Cash Flow -€26,643,750 €6,447,500 €5,615,500 €5,822,300 €7,489,890 €16,327,560 PV Cash Flows @ 18% -€26,643,750 5,463,983 4,032,965 €3,543,632 €3,863,202 €7,136,926 The NPV of the investment is -€2,603,042. Using a spreadsheet, solver or trial and error, the IRR is 14.24% 26. As with every capital budgeting decision that involves reducing balance depreciation, the schedule must first be estimated. Year 1 2 3 4 5 (a) Starting Value £360,000 £288,000 £230,400 £184,320 £147,456 (b) Depreciation 20% £72,000 £57,600 £46,080 £36,864 £87,456 (c) Accumulated Depreciation £72,000 £129,600 £175,680 £212,544 £300,000 (d) Residual Value £288,000 £230,400 £184,320 £147,456 £60,000 Then the income statement is calculated. In this type of problem, you need to calculate the break-even cost savings. For an analyst, the best approach is to use a spreadsheet and then trial and error or Solver. Using this technique, a cost savings of £103,208 leads to a net present value of zero. 0 1 2 3 4 5 Pre-Tax Cost Savings £103,208 £103,208 £103,208 £103,208 £103,208 Depreciation 20% £72,000 £57,600 £46,080 £36,864 £87,456 EBT £31,208 £45,608 £57,128 £66,344 £15,752 Tax £7,490 £10,946 £13,711 £15,923 £3,781 Net Income £23,718 £34,662 £43,418 £50,422 £11,972 Operating Cash Flow £95,718 £92,262 £89,498 £87,286 £99,428 0 1 2 3 4 5 Investment -£360,000 £60,000 Operating Cash Flows £95,718 £92,262 £89,498 £87,286 £99,428 Net Working Capital -£20,000 £20,000 Net Cash Flow -£380,000 £95,718 £92,262 £89,498 £87,286 £179,428 PV Cash Flows @ 15% -£380,000 £85,463 £73,551 £63,703 £55,472 £101,812 NPV 0 IRR 12.00% 27. For this project, you will need to use a spreadsheet and trial and error or solver. Solver is an exceptionally useful add-on in Excel that allows you to quickly solve these types of problems. The approach in this question is similar to all capital budgeting decisions. First, determine the depreciation schedule, then estimate the operating cash flows, and finally undertake the cash flow analysis. 1. Determine the depreciation schedule of the investment asset. Year 1 2 3 4 5 (a) Starting Value €780,000 €624,000 €499,200 €399,360 €319,488 (b) Depreciation 20% €156,000 €124,800 €99,840 €79,872 €269,488 (c) Accumulated Depreciation €156,000 €280,800 €380,640 €460,512 €730,000 (d) Residual Value €624,000 €499,200 €399,360 €319,488 €50,000 2. Estimate the operating cash flows and carry out the cash flow analysis. Using Solver, the minimum bid price that is found to make the project feasible is €12.08. The spreadsheet with cash flows pertaining to this amount is presented below. Notice that the IRR is 16.00%, which would be expected given that the discount rate is 16%. 0 1 2 3 4 5 Sales 150,000 150,000 150,000 150,000 150,000 Revenues €1,812,526 €1,812,526 €1,812,526 €1,812,526 €1,812,526 Variable Costs €1,275,000 €1,275,000 €1,275,000 €1,275,000 €1,275,000 Fixed Costs €240,000 €240,000 €240,000 €240,000 €240,000 Depreciation 20% €156,000 €124,800 €99,840 €79,872 €269,488 EBT €141,526 €172,726 €197,686 €217,654 €28,038 Tax €49,534 €60,454 €69,190 €76,179 €9,813 Net Income €91,992 €112,272 €128,496 €141,475 €18,225 Operating Cash Flow €247,992 €237,072 €228,336 €221,347 €287,713 0 1 2 3 4 5 Operating Cash Flow €247,992 €237,072 €228,336 €221,347 €287,713 Net Working Capital -€75,000 €75,000 Investment -€780,000 €50,000 Net Cash Flow -€855,000 €247,992 €237,072 €228,336 €221,347 €412,713 PV Cash Flows @ 16% -€855,000 €213,786 €176,183 €146,285 €122,248 €196,498 NPV €0 IRR 16.00% 28. For these types of problems, Solver is a definite asset and can make your analyses quite simple. a. When the bid price is €13, the NPV of the project is €292,585, with in IRR of 29.20%. Obviously, with a higher bid price, your company will make more money. The spreadsheet of the analysis is presented below: Year 1 2 3 4 5 (a) Starting Value €780,000 €624,000 €499,200 €399,360 €319,488 (b) Depreciation 20% €156,000 €124,800 €99,840 €79,872 €269,488 (c) Accumulated Depreciation €156,000 €280,800 €380,640 €460,512 €730,000 (d) Residual Value €624,000 €499,200 €399,360 €319,488 €50,000 1 2 3 4 5 Sales 150,000 150,000 150,000 150,000 150,000 Revenues €1,950,000 €1,950,000 €1,950,000 €1,950,000 €1,950,000 Variable Costs €1,275,000 €1,275,000 €1,275,000 €1,275,000 €1,275,000 Fixed Costs €240,000 €240,000 €240,000 €240,000 €240,000 Depreciation 20% €156,000 €124,800 €99,840 €79,872 €269,488 EBT €279,000 €310,200 €335,160 €355,128 €165,512 Tax €97,650 €108,570 €117,306 €124,295 €57,929 Net Income €181,350 €201,630 €217,854 €230,833 €107,583 Operating Cash Flow €337,350 €326,430 €317,694 €310,705 €377,071 0 1 2 3 4 5 Operating Cash Flow €337,350 €326,430 €317,694 €310,705 €377,071 Net Working Capital -€75,000 €75,000 Investment -€780,000 €50,000 Net Cash Flow -€855,000 €337,350 €326,430 €317,694 €310,705 €502,071 PV Cash Flows @ 16% -€855,000 €290,819 €242,591 €203,533 €171,600 €239,042 NPV €292,585 IRR 29.20% b. When the bid price is €13, the NPV is positive. To bring the NPV back down to zero, you would need to reduce the number of cartons on sale. Using solver, the requisite number of cartons is 119,450. The spreadsheet is given below: Year 1 2 3 4 5 (a) Starting Value €780,000 €624,000 €499,200 €399,360 €319,488 (b) Depreciation 20% €156,000 €124,800 €99,840 €79,872 €269,488 (c) Accumulated Depreciation €156,000 €280,800 €380,640 €460,512 €730,000 (d) Residual Value €624,000 €499,200 €399,360 €319,488 €50,000 1 2 3 4 5 Sales 119,450 119,450 119,450 119,450 119,450 Revenues €1,552,853 €1,552,853 €1,552,853 €1,552,853 €1,552,853 Variable Costs €1,015,327 €1,015,327 €1,015,327 €1,015,327 €1,015,327 Fixed Costs €240,000 €240,000 €240,000 €240,000 €240,000 Depreciation 20% €156,000 €124,800 €99,840 €79,872 €269,488 EBT €141,526 €172,726 €197,686 €217,654 €28,038 Tax €49,534 €60,454 €69,190 €76,179 €9,813 Net Income €91,992 €112,272 €128,496 €141,475 €18,225 Operating Cash Flow €247,992 €237,072 €228,336 €221,347 €287,713 0 1 2 3 4 5 Operating Cash Flow €247,992 €237,072 €228,336 €221,347 €287,713 Net Working Capital -€75,000 €75,000 Investment -€780,000 €50,000 Net Cash Flow -€855,000 €247,992 €237,072 €228,336 €221,347 €412,713 PV Cash Flows @ 16% -€855,000 €213,786 €176,183 €146,285 €122,248 €196,498 NPV €0 IRR 16.00% c. If the bid price is €13 and the number of cartons 150,000, the NPV of the project will be positive. This means that fixed costs must increase to bring the NPV down. Using solver, the requisite fixed costs that will bring the NPV down to zero is €377,474. The spreadsheet is given below. Year 1 2 3 4 5 Starting Value €780,000 €624,000 €499,200 €399,360 €319,488 Depreciation 20% €156,000 €124,800 €99,840 €79,872 €269,488 Accumulated Depreciation €156,000 €280,800 €380,640 €460,512 €730,000 Residual Value €624,000 €499,200 €399,360 €319,488 €50,000 0 1 2 3 4 5 Sales 150,000 150,000 150,000 150,000 150,000 Revenues €1,950,000 €1,950,000 €1,950,000 €1,950,000 €1,950,000 Variable Costs €1,275,000 €1,275,000 €1,275,000 €1,275,000 €1,275,000 Fixed Costs €377,474 €377,474 €377,474 €377,474 €377,474 Depreciation 20% €156,000 €124,800 €99,840 €79,872 €269,488 EBT €141,526 €172,726 €197,686 €217,654 €28,038 Tax €49,534 €60,454 €69,190 €76,179 €9,813 Net Income €91,992 €112,272 €128,496 €141,475 €18,225 Operating Cash Flow €247,992 €237,072 €228,336 €221,347 €287,713 0 1 2 3 4 5 Operating Cash Flow €247,992 €237,072 €228,336 €221,347 €287,713 Net Working Capital -€75,000 €75,000 Investment -€780,000 €50,000 Net Cash Flow -€855,000 €247,992 €237,072 €228,336 €221,347 €412,713 PV Cash Flows @ 16% -€855,000 €213,786 €176,183 €146,285 €122,248 €196,498 NPV €0 IRR 16.00% 29. We start our analysis by first determining the depreciation schedule of the investment. Year 1 2 3 4 (a) Starting Value £2,400,000 £1,800,000 £1,350,000 £1,012,500 (b) Depreciation 25% £600,000 £450,000 £337,500 £812,500 (c) Accumulated Depreciation £600,000 £1,050,000 £1,387,500 £2,200,000 (d) Residual Value £1,800,000 £1,350,000 £1,012,500 £200,000 There are two parts to this analysis. The first part is the original contract for 10,000 units. From the spreadsheet below, it can be seen that the investment on its own would be worthwhile if the bid price was set at £275. 0 1 2 3 4 Sales 10,000 10,000 10,000 10,000 Revenues £2,750,000 £2,750,000 £2,750,000 £2,750,000 Variable Costs £1,650,000 £1,650,000 £1,650,000 £1,650,000 Fixed Costs £500,000 £500,000 £500,000 £500,000 Depreciation 25% £600,000 £450,000 £337,500 £812,500 EBT £0 £150,000 £262,500 -£212,500 Tax £0 £36,000 £63,000 -£51,000 Net Income £0 £114,000 £199,500 -£161,500 Operating Cash Flow £600,000 £564,000 £537,000 £651,000 0 1 2 3 4 Operating Cash Flow £600,000 £564,000 £537,000 £651,000 Net Working Capital -£75,000 £75,000 Investment -£2,400,000 £200,000 Net Cash Flow -£2,475,000 £600,000 £564,000 £537,000 £926,000 PV Cash Flows @ 13% -£2,475,000 £530,973 £441,695 £372,168 £567,933 NPV £702,177 Your company feels that it can also sell additional units to other countries at £275 per unit. Since these cash flows are additional to the core cash flows, fixed costs and depreciation become irrelevant cash flows. The Cash Flow Analysis for this expansion is given below: 0 1 2 3 4 Sales 3,000 6,000 8,000 5,000 Revenues £825,000 £1,650,000 £2,200,000 £1,375,000 Variable Costs £495,000 £990,000 £1,320,000 £825,000 EBT £330,000 £660,000 £880,000 £550,000 Tax £79,200 £158,400 £211,200 £132,000 Net Income £250,800 £501,600 £668,800 £418,000 Operating Cash Flow £250,800 £501,600 £668,800 £418,000 0 1 2 3 4 Operating Cash Flow £250,800 £501,600 £668,800 £418,000 Net Cash Flow £0 £250,800 £501,600 £668,800 £418,000 PV Cash Flows @ 13% £0 £221,947 £392,826 £463,512 £256,367 NPV £1,334,652 Since the NPV of this expansion is positive at £1,334,652, we can add this to the original analysis and arrive at a bid price that gives the project an NPV of £100,000. This can be done easily in Solver and the spreadsheet is presented below. The bid price that gives a £100,000 NPV is equal to £232.18. 30. To answer this question, we need to compute the NPV of all three alternatives, specifically, continue to rent the building, Project A, or Project B. We would choose the project with the highest NPV. If all three of the projects have a positive NPV, the project that is more favorable is the one with the highest NPV There are several important cash flows we should not consider in the incremental cash flow analysis. The remaining fraction of the value of the building and depreciation are not incremental and should not be included in the analysis of the two alternatives. The £225,000 purchase price of the building is a sunk cost and should be ignored. In effect, what we are doing is finding the NPV of the future cash flows of each option, so the only cash flow today would be the building modifications needed for Project A and Project B. If we did include these costs, the effect would be to lower the NPV of all three options by the same amount, thereby leading to the same conclusion. The cash flows from renting the building after year 15 are also irrelevant. No matter what the company chooses today, it will rent the building after year 15, so these cash flows are not incremental to any project. We will begin by calculating the NPV of the decision of continuing to rent the building first. Continue to rent: Rent £12,000 Taxes £3,360 Net Income £8,640 Since there is no incremental depreciation, the operating cash flow is simply the net income. So, the NPV of the decision to continue to rent is: NPV = £8,640(PVIFA12%,15) NPV = £58,845.87 Product A: Next, we will calculate the NPV of the decision to modify the building to produce Product A.. The cash flow at time zero will be the cost of the equipment, and the cost of the initial building modifications, both of which are depreciable on a 20 percent reducing balance basis. So, the depreciation schedule for product A is: Initial cash outlay: Building modifications –£36,000 Equipment –144,000 Total cash flow –£180,000 (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 1 £180,000 £36,000 £36,000 £144,000 2 £144,000 £28,800 £64,800 £115,200 3 £115,200 £23,040 £87,840 £92,160 4 £92,160 £18,432 £106,272 £73,728 5 £73,728 £14,746 £121,018 £58,982 6 £58,982 £11,796 £132,814 £47,186 7 £47,186 £9,437 £142,251 £37,749 8 £37,749 £7,550 £149,801 £30,199 9 £30,199 £6,040 £155,841 £24,159 10 £24,159 £4,832 £160,673 £19,327 11 £19,327 £3,865 £164,538 £15,462 12 £15,462 £3,092 £167,630 £12,370 13 £12,370 £2,474 £170,104 £9,896 14 £9,896 £1,979 £172,084 £7,916 15 £7,916 £1,583 £173,667 £6,333 So, the operating cash flows from project A are: Year Sales Expenditures Depreciation 20% Restoration Cost EBT Tax Net Income Operating Cash Flow 28% 1 £105,000 £60,000 £36,000 £9,000 £2,520 £6,480 £42,480 2 £105,000 £60,000 £28,800 £16,200 £4,536 £11,664 £40,464 3 £105,000 £60,000 £23,040 £21,960 £6,149 £15,811 £38,851 4 £105,000 £60,000 £18,432 £26,568 £7,439 £19,129 £37,561 5 £105,000 £60,000 £14,746 £30,254 £8,471 £21,783 £36,529 6 £105,000 £60,000 £11,796 £33,204 £9,297 £23,907 £35,703 7 £105,000 £60,000 £9,437 £35,563 £9,958 £25,605 £35,042 8 £105,000 £60,000 £7,550 £37,450 £10,486 £26,964 £34,514 9 £105,000 £60,000 £6,040 £38,960 £10,909 £28,051 £34,091 10 £105,000 £60,000 £4,832 £40,168 £11,247 £28,921 £33,753 11 £105,000 £60,000 £3,865 £41,135 £11,518 £29,617 £33,482 12 £105,000 £60,000 £3,092 £41,908 £11,734 £30,173 £33,266 13 £105,000 £60,000 £2,474 £42,526 £11,907 £30,619 £33,093 14 £105,000 £60,000 £1,979 £43,021 £12,046 £30,975 £32,954 15 £105,000 £60,000 £1,583 £3,750 £39,667 £11,107 £28,560 £30,143 The OCF for each year is net income plus depreciation. So, the NPV for modifying the building to manufacture Product A is: Year Investment Operating Cash Flow Net Cash Flow PV Cash Flows @ 12% 0 -£180,000 -£180,000 -£180,000 1 £42,480 £42,480 £37,929 2 £40,464 £40,464 £32,258 3 £38,851 £38,851 £27,654 4 £37,561 £37,561 £23,871 5 £36,529 £36,529 £20,727 6 £35,703 £35,703 £18,088 7 £35,042 £35,042 £15,851 8 £34,514 £34,514 £13,940 9 £34,091 £34,091 £12,294 10 £33,753 £33,753 £10,868 11 £33,482 £33,482 £9,625 12 £33,266 £33,266 £8,539 13 £33,093 £33,093 £7,584 14 £32,954 £32,954 £6,743 15 £6,333 £30,143 £36,477 £6,664 NPV = £72,633 Product B: Now we will calculate the NPV of the decision to modify the building to produce Product B. The cash flow at time zero will be the cost of the equipment, and the cost of the initial building modifications, both of which are depreciable on a reducing balance basis. So, the pro forma cash flows for Product B are: Initial cash outlay: Building modifications –£54,000 Equipment –162,000 Total cash flow –£216,000 (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 1 £216,000 £43,200 £43,200 £172,800 2 £172,800 £34,560 £77,760 £138,240 3 £138,240 £27,648 £105,408 £110,592 4 £110,592 £22,118 £127,526 £88,474 5 £88,474 £17,695 £145,221 £70,779 6 £70,779 £14,156 £159,377 £56,623 7 £56,623 £11,325 £170,702 £45,298 8 £45,298 £9,060 £179,761 £36,239 9 £36,239 £7,248 £187,009 £28,991 10 £28,991 £5,798 £192,807 £23,193 11 £23,193 £4,639 £197,446 £18,554 12 £18,554 £3,711 £201,157 £14,843 13 £14,843 £2,969 £204,125 £11,875 14 £11,875 £2,375 £206,500 £9,500 15 £9,500 £1,900 £208,400 £7,600 The Operating Cash Flows from Project B are: Year Sales Expenditures Depreciation 20% Restoration Cost EBT Tax Net Income Operating Cash Flow 28% 1 £127,500 £75,000 £43,200 £9,300 £2,604 £6,696 £49,896 2 £127,500 £75,000 £34,560 £17,940 £5,023 £12,917 £47,477 3 £127,500 £75,000 £27,648 £24,852 £6,959 £17,893 £45,541 4 £127,500 £75,000 £22,118 £30,382 £8,507 £21,875 £43,993 5 £127,500 £75,000 £17,695 £34,805 £9,745 £25,060 £42,755 6 £127,500 £75,000 £14,156 £38,344 £10,736 £27,608 £41,764 7 £127,500 £75,000 £11,325 £41,175 £11,529 £29,646 £40,971 8 £127,500 £75,000 £9,060 £43,440 £12,163 £31,277 £40,337 9 £127,500 £75,000 £7,248 £45,252 £12,671 £32,582 £39,829 10 £127,500 £75,000 £5,798 £46,702 £13,077 £33,625 £39,423 11 £127,500 £75,000 £4,639 £47,861 £13,401 £34,460 £39,099 12 £127,500 £75,000 £3,711 £48,789 £13,661 £35,128 £38,839 13 £127,500 £75,000 £2,969 £49,531 £13,869 £35,663 £38,631 14 £127,500 £75,000 £2,375 £50,125 £14,035 £36,090 £38,465 15 £127,500 £75,000 £1,900 £28,125 £22,475 £6,293 £16,182 £18,082 The OCF for each year is net income plus depreciation. So, the NPV for modifying the building to manufacture Product B is: Year Investment Operating Cash Flow Net Cash Flow PV Cash Flows @ 12% 0 -£216,000 -£216,000 -£216,000 1 £49,896 £49,896 £44,550 2 £47,477 £47,477 £37,848 3 £45,541 £45,541 £32,415 4 £43,993 £43,993 £27,958 5 £42,755 £42,755 £24,260 6 £41,764 £41,764 £21,159 7 £40,971 £40,971 £18,533 8 £40,337 £40,337 £16,291 9 £39,829 £39,829 £14,363 10 £39,423 £39,423 £12,693 11 £39,099 £39,099 £11,240 12 £38,839 £38,839 £9,969 13 £38,631 £38,631 £8,853 14 £38,465 £38,465 £7,871 15 £7,600 £18,082 £25,682 £4,692 NPV = £76,697. Project B is the best option and so should be chosen. 31. The discount rate is expressed in real terms, and the cash flows are expressed in nominal terms. We can answer this question by converting all of the cash flows to real pounds. We can then use the real interest rate. The real value of each cash flow is the present value of the year 1 nominal cash flows, discounted back to the present at the inflation rate. So, the real value of the revenue and costs will be: Revenue in real terms = £150,000 / 1.06 = £141,509.43 Labour costs in real terms = £80,000 / 1.06 = £75,471.70 Other costs in real terms = £40,000 / 1.06 = £37,735.85 Lease payment in real terms = £20,000 / 1.06 = £18,867.92 Revenues, labour costs, and other costs are all growing perpetuities. Each has a different growth rate, so we must calculate the present value of each separately. Other costs are a growing perpetuity with a negative growth rate. Using the real required return, the present value of each of these is: PVRevenue = £141,509.43 / (0.10 – 0.05) = £2,830,188.68 PVLabor costs = £75,471.70 / (0.10 – 0.03) = £1,078,167.12 PVOther costs = £37,735.85 / [0.10 – (–0.01)] = £343,053.17 The lease payments are constant in nominal terms, so they are declining in real terms by the inflation rate. Therefore, the lease payments form a growing perpetuity with a negative growth rate. The real present value of the lease payments is: PVLease payments = £18,867.92 / [0.10 – (–0.06)] = £117,924.53 Now we can use the tax shield approach to calculate the net present value. Since there is no investment in equipment, there is no depreciation; therefore, no depreciation tax shield, so we will ignore this in our calculation. This means the cash flows each year are equal to net income. There is also no initial cash outlay, so the NPV is the present value of the future aftertax cash flows. The NPV of the project is: NPV = PVRevenue – PVLabor costs – PVOther costs – PVLease payments NPV = (£2,830,188.68 – 1,078,167.12 – 343,053.17 – 117,924.53)(1 – .28) NPV = £929,552 Alternatively, we could have solved this problem by expressing everything in nominal terms. This approach yields the same answer as given above. However, in this case, the computation would have been much more difficult. The reason is that we are dealing with growing perpetuities. In other problems, when calculating the NPV of nominal cash flows, we could simply calculate the nominal cash flow each year since the cash flows were finite. Because of the perpetual nature of the cash flows in this problem, we cannot calculate the nominal cash flows each year until the end of the project. When faced with two alternative approaches, where both are equally correct, always choose the simplest one. 32. We are given the real revenue and costs, and the real growth rates, so the simplest way to solve this problem is to calculate the NPV with real values. While we could calculate the NPV using nominal values, we would need to find the nominal growth rates, and convert all values to nominal terms. The real labour costs will increase at a real rate of two percent per year, and the real energy costs will increase at a real rate of three percent per year, so the real costs each year will be: Year 1 Year 2 Year 3 Year 4 Real labor cost each year $15.30 $15.61 $15.92 $16.24 Real energy cost each year $5.15 $5.30 $5.46 $5.63 Remember that the depreciation tax shield also affects a firm’s aftertax cash flows. The present value of the depreciation tax shield must be added to the present value of a firm’s revenues and expenses to find the present value of the cash flows related to the project. The depreciation the firm will recognize each year is: Annual depreciation = Investment / Economic Life Annual depreciation = $32,000,000 / 4 Annual depreciation = $8,000,000 Depreciation is a nominal cash flow, so to find the real value of depreciation each year, we discount the real depreciation amount by the inflation rate. Doing so, we find the real depreciation each year is: Year 1 real depreciation = $8,000,000 / 1.05 = $7,619,047.62 Year 2 real depreciation = $8,000,000 / 1.052 = $7,256,235.83 Year 3 real depreciation = $8,000,000 / 1.053 = $6,910,700.79 Year 4 real depreciation = $8,000,000 / 1.054 = $6,581,619.80 Now we can calculate the pro forma income statement each year in real terms. We can then add back depreciation to net income to find the operating cash flow each year. Doing so, we find the cash flow of the project each year is: Year 0 Year 1 Year 2 Year 3 Year 4 Revenues $40,000,000.0 0 $80,000,000.0 0 $80,000,000.0 0 $60,000,000.0 0 Labour cost 30,600,000.00 31,212,000.00 31,836,240.00 32,472,964.80 Energy cost 1,030,000.00 1,060,900.00 1,092,727.00 1,125,508.81 Depreciation 7,619,047.62 7,256,235.83 6,910,700.79 6,581,619.80 EBT $750,952.38 $40,470,864.1 7 $40,160,332.2 1 $19,819,906.5 9 Taxes 255,323.81 13,760,093.82 13,654,512.95 6,738,768.24 Net income $495,628.57 $26,710,770.3 5 $26,505,819.2 6 $13,081,138.3 5 OCF $8,114,676.19 $33,967,006.1 8 $33,416,520.0 5 $19,662,758.1 5 Capital spending –$32,000,000 Total cash flow –$32,000,000 $8,114,676.19 $33,967,006.1 8 $33,416,520.0 5 $19,662,758.1 5 We can use the total cash flows each year to calculate the NPV, which is: NPV = –$32,000,000 + $8,114,676.19 / 1.08 + $33,967,006.18 / 1.082 + $33,416,520.05 / 1.083 + $19,662,758.15 / 1.084 NPV = $45,614,647.30 33. Here we have the sales price and production costs in real terms. The simplest method to calculate the project cash flows is to use the real cash flows. In doing so, we must be sure to adjust the depreciation, which is in nominal terms. We could analyze the cash flows using nominal values, which would require calculating the nominal discount rate, nominal price, and nominal production costs. This method would be more complicated, so we will use the real numbers. We will first calculate the NPV of the headache only pill. Headache only: We can find the real revenue and production costs by multiplying each by the units sold. We must be sure to discount the depreciation, which is in nominal terms. We can then find the pro forma net income, and add back depreciation to find the operating cash flow. The first stage in the analysis is to determine the depreciation schedule. Year 1 2 3 (a) Starting Value £10,200,000 £8,160,000 £6,528,000 (b) Depreciation 20% £2,040,000 £1,632,000 £6,528,000 (c) Accumulated Depreciation £2,040,000 £3,672,000 £10,200,000 (d) Residual Value £8,160,000 £6,528,000 £0 Depreciation in Real Terms £1,942,857 £1,480,272 £5,639,132 Note that depreciation was discounted at the rate of inflation (5%). We can now find the operating cash flows. 0 1 2 3 Sales 5,000,000 5,000,000 5,000,000 Revenues £20,000,000 £20,000,000 £20,000,000 Variable Costs £7,500,000 £7,500,000 £7,500,000 Depreciation in Real Terms £1,942,857 £1,480,272 £5,639,132 EBT £10,557,143 £11,019,728 £6,860,868 Tax £2,956,000 £3,085,524 £1,921,043 Net Income £7,601,143 £7,934,204 £4,939,825 Operating Cash Flow £9,544,000 £9,414,476 £10,578,957 0 1 2 3 Operating Cash Flow £9,544,000 £9,414,476 £10,578,957 Investment -£10,200,000 Net Cash Flow -£10,200,000 £9,544,000 £9,414,476 £10,578,957 PV Cash Flows @ 13% -£10,200,000 £8,446,018 £7,372,916 £7,331,748 The NPV is equal to £12,950,681. Headache and arthritis: For the headache and arthritis pill project, the equipment has a salvage value. We will now determine the depreciation schedule of the equipment. Year 1 2 3 (a) Starting Value £12,000,000 £9,600,000 £7,680,000 (b) Depreciation 20% £2,400,000 £1,920,000 £6,680,000 (c) Accumulated Depreciation £2,400,000 £4,320,000 £11,000,000 (d) Residual Value £9,600,000 £7,680,000 £1,000,000 Depreciation in Real Terms £2,285,714 £1,741,497 £5,770,435 Using the same method as the headache only pill, the cash flows each year for the headache and arthritis pill will be: 0 1 2 3 Sales 10,000,000 10,000,000 10,000,000 Revenues £40,000,000 £40,000,000 £40,000,000 Variable Costs £17,000,000 £17,000,000 £17,000,000 Depreciation in Real Terms £2,285,714 £1,741,497 £5,770,435 EBT £20,714,286 £21,258,503 £17,229,565 Tax £5,800,000 £5,952,381 £4,824,278 Net Income £14,914,286 £15,306,122 £12,405,287 Operating Cash Flow £17,200,000 £17,047,619 £18,175,722 0 1 2 3 Operating Cash Flow £17,200,000 £17,047,619 £18,175,722 Investment -£12,000,000 £1,000,000 Net Cash Flow -£12,000,000 £17,200,000 £17,047,619 £19,175,722 PV Cash Flows @ 13% -£12,000,000 £15,221,239 £13,350,786 £13,289,737 The NPV of the broader remedy is £29,861,762. The company should manufacture the broader headache and arthritis remedy since the project has a higher NPV. 34. This is an in-depth capital budgeting problem. Since the project requires an initial investment in inventory as a percentage of sales, we will calculate the sales figures for each year first. The incremental sales will include the sales of the new table, but we also need to include the lost sales of the existing model. This is an erosion cost of the new table. The lost sales of the existing table are constant for every year, but the sales of the new table change every year. So, the total incremental sales figure for the five years of the project will be: Year 1 Year 2 Year 3 Year 4 Year 5 New €7,280,000 €7,420,000 €7,700,000 €8,120,000 €7,392,000 Lost sales –900,000 –900,000 –900,000 –900,000 –900,000 Total €6,380,000 €6,520,000 €6,800,000 €7,220,000 €6,492,000 Now we will calculate the initial cash outlay that will occur today. The company has the necessary production capacity to manufacture the new table without adding equipment today. So, the equipment will not be purchased today, but rather in two years. The reason is that the existing capacity is not being used. If the existing capacity were being used, the new equipment would be required, so it would be a cash flow today. The old equipment would have an opportunity cost if it could be sold. As there is no discussion that the existing equipment could be sold, we must assume it cannot be sold. The only initial cash flow is the cost of the inventory. The company will have to spend money for inventory in the new table, but will be able to reduce inventory of the existing table. So, the initial cash flow today is: New table –€728,000 Old table 90,000 Total –€638,000 In year 2, the company will have a cash outflow to pay for the cost of the new equipment. Since the equipment will be purchased in two years rather than now, the equipment will have a higher salvage value. The book value of the equipment in five years will be the initial cost, minus the accumulated depreciation. We must therefore determine the depreciation schedule first. Year 3 4 5 (a) Starting Value €10,500,000 €8,400,000 €6,720,000 (b) Depreciation 20% €2,100,000 €1,680,000 €1,344,000 (c) Accumulated Depreciation €2,100,000 €3,780,000 €5,124,000 (d) Residual Value €8,400,000 €6,720,000 €5,376,000 Book value = €5,376,000 The taxes on the salvage value will be: Taxes on salvage = (€5,376,000 – 6,100,000)(.38) Taxes on salvage = –€275,120 So, the aftertax salvage value of the equipment in five years will be: Sell equipment €6,100,000 Taxes –275,120 Salvage value €5,824,880 Next, we need to calculate the variable costs each year. The variable costs of the lost sales are included as a variable cost savings, so the variable costs will be: Year 1 Year 2 Year 3 Year 4 Year 5 New €3,276,000 €3,339,000 €3,465,000 €3,654,000 €3,326,400 Lost sales –360,000 –360,000 –360,000 –360,000 –360,000 Variable costs €2,916,000 €2,979,000 €3,105,000 €3,294,000 €2,966,400 Now we can prepare the rest of the pro forma income statements for each year. The project will have no incremental depreciation for the first two years as the equipment is not purchased for two years. Adding back depreciation to net income to calculate the operating cash flow, we get: Year 1 Year 2 Year 3 Year 4 Year 5 Sales €6,380,000 €6,520,000 €6,800,000 €7,220,000 €6,492,000 VC €2,916,000 €2,979,000 €3,105,000 €3,294,000 €2,966,400 Fixed costs €1,700,000 €1,700,000 €1,700,000 €1,700,000 €1,700,000 Dep. €0 €0 €2,100,000 €1,680,000 €1,344,000 EBT €1,764,000 €1,841,000 -€105,000 €546,000 €481,600 Tax €670,320 €699,580 -€39,900 €207,480 €183,008 NI €1,093,680 €1,141,420 -€65,100 €338,520 €298,592 Dep. - - €2,100,000 €1,680,000 €1,344,000 OCF €1,093,680 €1,141,420 €2,034,900 €2,018,520 €1,642,592 Next, we need to account for the changes in inventory each year. The inventory is a percentage of sales. The way we will calculate the change in inventory is the beginning of period inventory minus the end of period inventory. The sign of this calculation will tell us whether the inventory change is a cash inflow, or a cash outflow. The inventory each year, and the inventory change, will be: Year 1 Year 2 Year 3 Year 4 Year 5 Beginning €728,000 €742,000 €770,000 €812,000 €739,200 Ending €742,000 €770,000 €812,000 €739,200 €0 Change –€14,000 –€28,000 –€42,000 €72,800 €739,200 Notice that we recover the remaining inventory at the end of the project. The total cash flows for the project will be the sum of the operating cash flow, the capital spending, and the inventory cash flows, so: Year 1 Year 2 Year 3 Year 4 Year 5 OCF €1,093,680 €1,141,420 €2,034,900 €2,018,520 €1,642,592 Equipment €0 -€10,500,000 €0 €0 €5,496,660 Inventory -€14,000 -€28,000 -€42,000 €72,800 €739,200 Total €1,079,680 -€9,386,580 €1,992,900 €2,091,320 €7,878,452 The NPV of the project, including the inventory cash flow at the beginning of the project, will be: 0 1 2 3 4 5 Cash Flows -€638,000 €1,079,680 -€9,386,580 €1,992,900 €2,091,320 €7,878,452 PV Cash Flows -€638,000 €947,088 -€7,222,669 €1,345,151 €1,238,229 €4,091,821 NPV = -€238,380 The company should not go ahead with the new table. b. You can perform an IRR analysis, and would expect to find three IRRs since the cash flows change signs three times. c. The profitability index is intended as a “bang for the buck” measure; that is, it shows how much shareholder wealth is created for every euro of initial investment. In this case, the largest investment is not at the beginning of the project, but later in its life. However, since the future negative cash flow is discounted, the profitability index will still measure the amount of shareholder wealth created for every euro spent today. Solution Manual for Corporate Finance David Hillier, Stephen Ross, Randolph Westerfield, Jeffrey Jaffe, Bradford Jordan 9780077139148