Chapter 06 - Making Investment Decisions with the Net ...



CHAPTER 6Making Investment Decisions withThe Net Present Value RuleAnswers to Problem Sets1.a, b, d, g, h.?2.Real cash flow = 100,000/1.04 = $96,154; real discount rate = 1.08/1.04 - 1 = .03846PV = 3.a. Falseb. Falsec. Falsed. False?4.The longer the recovery period, the less the -present value of depreciation tax shields. This is true regardless of the discount rate. If r = .10, then 35% of the 5-year schedule’s PV is .271. The same calculation for the 7-year schedule yields .252.?20102011201220132014Working capital50,000230,000305,000250,0000Cash flows+50,000+180,00+75,000-55,000-250,0005. ?paring present values can be misleading when projects have different economic lives and the projects are part of an ongoing business. For example, a machine that costs $100,000 per year to buy and lasts 5 years is not necessarily more expensive than a machine that costs $75,000 per year to buy but lasts only 3 years. Calculating the machines’ equivalent annual costs allows an unbiased comparison.?7.PV cost = 1.5 + .2 X 14.09 = $4.319 million. Equivalent annual cost = 4.319/14.09 = .306, or $306,000.?8.a.NPVA = $100,000; NPVB = $180,000b.Equivalent cash flow of A = 100,000/1.736 5 $57,604; equivalent cash flow of B = 180,000/2.487 = $72,376c.Machine B.?9.Replace at end of 5 years ($80,000 > $72,376).10.See the table below. We begin with the cash flows given in the text, Table 6.6, line 8, and utilize the following relationship from Chapter 3:Real cash flow = nominal cash flow/(1 + inflation rate)tHere, the nominal rate is 20%, the expected inflation rate is 10%, and the real rate is given by the following:(1 + rnominal) = (1 + rreal) (1 + inflation rate)1.20 = (1 + rreal) (1.10)rreal = 0.0909 = 9.09%As can be seen in the table, the NPV is unchanged (to within a rounding error).Year 0Year 1Year 2Year 3Year 4Year 5Year 6Year 7Net Cash Flows (Nominal)-12,600-1,4842,9476,32310,5349,9855,7573,269Net Cash Flows (Real)-12,600-1,3492,4364,7517,1956,2003,2501,678NPV of Real Cash Flows (at 9.09%) = $3,804The following spreadsheet calculates a NPV of -$147,510 (in nominal terms):Nominal CalculationYEAR?012345Capital Investment500,000?????Accumulated Depreciation?100,000200,000300,000400,000500,000Year-End Book Value500,000400,000300,000200,000100,0000Working capital40,00044,00048,40053,24058,5640Total Book Value540,000444,000348,400253,240158,5640???????Revenues?200,000220,000242,000266,200292,820Costs?100,000110,000121,000133,100146,410Depreciation?100,000100,000100,000100,000100,000Pretax Profit?010,00021,00033,10046,410Taxes at 35%?03,5007,35011,58516,244Profit after tax?06,50013,65021,51530,167???????Revenues?200,000220,000242,000266,200292,820Costs?100,000110,000121,000133,100146,410Tax on operations?03,5007,35011,58516,244Cash Flow from Operations?100,000106,500113,650121,515130,167Change in working capital-40,000-4,000-4,400-4,840-5,32458,564Capital Investment-500,000?????Net Cash Flows-540,00096,000102,100108,810116,191188,731Discount Factor @ 15%1.0000.8700.7560.6580.5720.497Present Value-540,00083,47877,20271,54466,43393,832???????NPV-147,510?????Since the nominal rate is 15% and the expected inflation rate is 10%, the real rate is given by the following:(1 + rnominal) = (1 + rreal) (1 + inflation rate)1.15 = (1 + rreal) (1.10)rreal = 0.04545 = 4.545%Adjusting the cash flows to real dollars and using this real rate gives us the same result for NPV (with a slight rounding error).YEAR?012345Net Cash Flows (Nominal)-540,00096,000102,100108,810116,191188,731Adjustment Factor for Real CF10.9090.8260.7510.6830.621Net Cash Flows (Real)-540,00087,27384,38081,75179,360117,187Discount Factor @ 4.545%1.0000.9570.9150.8750.8370.801Present Value-540,00083,47977,20371,54566,43493,834???????NPV-147,505?????No, this is not the correct procedure. The opportunity cost of the land is its value in its best use, so Mr. North should consider the $45,000 value of the land as an outlay in his NPV analysis of the funeral home.Investment in net working capital arises as a forecasting issue only because accrual accounting recognizes sales when made, not when cash is received (and costs when incurred, not when cash payment is made). If cash flow forecasts recognize the exact timing of the cash flows, then there is no need to also include investment in net working capital.If the $50,000 is expensed at the end of year 1, the value of the tax shield is:If the $50,000 expenditure is capitalized and then depreciated using a five-year MACRS depreciation schedule, the value of the tax shield is:If the cost can be expensed, then the tax shield is larger, so that the after-tax cost is smaller.Note: This answer assumes that the $3 million initial research costs are sunk and excludes this from the NPV calculation. It also assumes that working capital needs begin to accrue in year 0. The following spreadsheet calculates a project NPV of -$465,000.Figures in 000'sYEAR?012345Capital Investment6,000????-500Accumulated Depreciation?1,2002,4003,6004,8006,000Year-End Book Value6,0004,8003,6002,4001,2000Working capital2002404004002400Total Book Value6,2005,0404,0002,8001,4400???????Unit Sales?5006001,0001,000600Revenues?2,0002,4004,0004,0002,400Costs?7509001,5001,500900Depreciation?1,2001,2001,2001,2001,200Pretax Profit (includes salage in yr 5)?503001,3001,300800Taxes at 35%?18105455455280Profit after tax?33195845845520???????Revenues?2,0002,4004,0004,0002,400Costs?7509001,5001,500900Tax on operations?18105455455280Cash Flow from Operations?1,2331,3952,0452,0451,220Change in working capital-200-40-1600160240Capital Investment-6,000?????Net Cash Flows-6,2001,1931,2352,0452,2051,460Discount Factor @ 12%1.0000.8930.7970.7120.6360.567Present Value-6,2001,0659851,4561,401828???????NPV-465?????16. a.NPVB = –Investment + PV(after-tax cash flow) + PV(depreciation tax shield)NPVB = –$4,127Another, perhaps more intuitive, way to do the Company B analysis is to first calculate the cash flows at each point in time, and then compute the present value of these cash flows:t = 0t = 1t = 2t = 3t = 4t = 5t = 6Investment100,000Cash Inflow26,00026,00026,00026,00026,000Depreciation20,00032,00019,20011,52011,5205,760Taxable Income6,000-6,0006,80014,48014,480-5,760Tax (at 35%)2,100-2,1002,3805,0685,068-2,016Cash Flow-100,00023,90028,10023,62020,93220,9322,016NPV (at 8%) = -$4,127b.IRRA = 9.43%IRRB = 6.39%Effective tax rate = 17.a.TABLE 6.5 Tax payments on IM&C’s guano project ($thousands)No. of years depreciation7Tax rate (percent)35Period01234567MACRS %14.2924.4917.4912.498.938.9213.38Tax depreciation1,4292,4491,7491,2498938921,338(MACRS% x depreciable investment)1.Sales052312,88732,61048,90135,83419,71702.Cost of goods sold08377,72919,55229,34521,49211,83003.Other costs4,0002,2001,2101,3311,4641,6111,77204.Tax depreciation01,4292,4491,7491,2498938921,3385.Pretax profits-4,000-3,9431,4999,97816,84311,8385,2236116.Tax-1,400-1,3805253,4925,8954,1431,828214TABLE 6.6 IM&C’s guano project – revised cash flow analysis with MACRS depreciation ($thousands)Period012345671.Sales052312,88732,61048,90135,83419,71702.Cost of goods sold08377,72919,55229,34521,49211,83003.Other costs4,0002,2001,2101,3311,4641,6111,77204.Tax-1,400-1,3805253,4925,8954,1431,8282145.Cash flow from operations-2,600-1,1343,4238,23512,1978,5884,287-2146.Change in working capital-550-739-1,972-1,6291,3071,5812,0027.Capital investment and disposal-10,0000000001, cash flow (5+6+7)-12,600-1,6842,6846,26310,5689,8955,8683,7379.Present value-12,600-1,4031,8643,6245,0963,9771,9651,043Net present value =3,566Cost of capital (percent)20b.TABLE 6.1 IM&C’s guano project – projections ($thousands)reflecting inflation and straight line depreciationPeriod012345671.Capital investment15,000-1,9492.Accumulated depn.2,4174,8337,2509,66712,08314,50003.Year-end book value15,00012,58310,1677,7505,3332,91750004.Working capital5501,2893,2614,8903,5832,00205.Total book value (3 + 4)13,13311,45611,01110,2236,5002,50206.Sales?52312,88732,61048,90135,83419,717?7.Cost of goods sold?8377,72919,55229,34521,49211,830?8.Other costs4,0002,2001,2101,3311,4641,6111,772?9.Depreciation2,4172,4172,4172,4172,4172,417010.Pretax profit-4,000-4,9311,5319,31015,67510,3143,6981,44911.Tax-1,400-1,7265363,2595,4863,6101,29450712.Profit after tax (10 – 11)-2,600-3,2059956,05210,1896,7042,404942Notes:No. of years depreciation6Assumed salvage value in depreciation calculation500Tax rate (percent)35TABLE 6.2 IM&C’s guano project – initial cash flow analysis with straight-line depreciation ($thousands)Period012345671Sales052312,88732,61048,90135,83419,71702Cost of goods sold08377,72919,55229,34521,49211,83003Other costs4,0002,2001,2101,3311,4641,6111,77204Tax-1,400-1,7265363,2595,4863,6101,2945075Cash flow from operations-2,600-7883,4128,46812,6069,1214,821-5076Change in working capital-550-739-1,972-1,6291,3071,5812,0027Capital investment and disposal-15,0000000001,9498Net cash flow (5+6+7)-17,600-1,3382,6736,49610,97710,4286,4023,4449Present value-17,600-1,2062,1694,7507,2316,1893,4231,659Net present value =6,614Cost of capital (percent)11c.TABLE 6.1 IM&C’s guano project – projections ($thousands)reflecting inflation and straight line depreciationPeriod012345671.Capital investment15,000-1,9492.Accumulated depn.2,4174,8337,2509,66712,08314,50003.Year-end book value15,00012,58310,1677,7505,3332,91750004.Working capital6051,4183,5875,3793,9412,20205.Total book value (3 + 4)13,18811,58511,33710,7126,8582,70206.Sales?57514,17635,87153,79139,41721,689?7.Cost of goods sold?9218,50221,50732,28023,64113,013?8.Other costs4,0002,2001,2101,3311,4641,6111,772?9.Depreciation2,4172,4172,4172,4172,4172,417010.Pretax profit-4,000-4,9622,04710,61617,63111,7494,4871,44911.Tax-1,400-1,7377163,7166,1714,1121,57050712.Profit after tax (10 – 11)-2,600-3,2251,3316,90011,4607,6372,917942Notes:No. of years depreciation6Assumed salvage value in depreciation calculation500Tax rate (percent)35TABLE 6.2 IM&C’s guano project – initial cash flow analysis with straight-line depreciation ($thousands)Period012345671Sales057514,17635,87153,79139,41721,68902Cost of goods sold09218,50221,50732,28023,64113,01303Other costs4,0002,2001,2101,3311,4641,6111,77204Tax-1,400-1,7377163,7166,1714,1121,5705075Cash flow from operations-2,600-8093,7479,31713,87710,0535,333-5076Change in working capital-605-813-2,169-1,7921,4381,7392,2027Capital investment and disposal-15,0000000001,9498Net cash flow (5+6+7)-17,600-1,4142,9347,14812,08511,4917,0723,6449Present value-17,600-1,2742,3825,2277,9616,8193,7811,755Net present value =9,051Cost of capital (percent)1118.Assume the following:The firm will manufacture widgets for at least 10 years.There will be no inflation or technological change.The 15% cost of capital is appropriate for all cash flows and is a real, after-tax rate of return.All operating cash flows occur at the end of the year.We cannot ignore incremental working capital costs and recoveryNote: Since purchasing the lids can be considered a one-year ‘project,’ the two projects have a common chain life of 10 pute NPV for each project as follows:NPV(purchase) =NPV(make) =Thus, the widget manufacturer should make the lids.19.a.Capital ExpenditureIf the spare warehouse space will be used now or in the future, then the project should be credited with these benefits.Charge opportunity cost of the land and building.The salvage value at the end of the project should be included.Research and DevelopmentResearch and development is a sunk cost.Working CapitalWill additional inventories be required as volume increases?Recovery of inventories at the end of the project should be included.Is additional working capital required due to changes in receivables, payables, etc.?RevenueRevenue forecasts assume prices (and quantities) will be unaffected by competition, a common and critical mistake.Operating CostsAre percentage labor costs unaffected by increase in volume in the early years?2.Wages generally increase faster than inflation. Does Reliable expect continuing productivity gains to offset this?Overhead1.Is “overhead” truly incremental?DepreciationDepreciation is not a cash flow, but the ACRS deprecation does affect tax payments.ACRS depreciation is fixed in nominal terms. The real value of the depreciation tax shield is reduced by inflation.InterestIt is bad practice to deduct interest charges (or other payments to security holders). Value the project as if it is all equity-financed.TaxSee comments on ACRS depreciation and interest.If Reliable has profits on its remaining business, the tax loss should not be carried Cash FlowSee comments on ACRS depreciation and interest.Discount rate should reflect project characteristics; in general, it is not equivalent to the company’s borrowing rate.b.1.Potential use of warehouse.Opportunity cost of building.Other working capital items.More realistic forecasts of revenues and pany’s ability to use tax shields.Opportunity cost of capital.c.The table on the next page shows a sample NPV analysis for the project. The analysis is based on the following assumptions:Inflation: 10% per year.Capital Expenditure: $8 million for machinery; $5 million for market value of factory; $2.4 million for warehouse extension (we assume that it is eventually needed or that electric motor project and surplus capacity cannot be used in the interim). We assume salvage value of $3 million in real terms less tax at 35%.Working Capital: We assume inventory in year t is 9.1% of expected revenues in year (t + 1). We also assume that receivables less payables, in year t, is equal to 5% of revenues in year t.Depreciation Tax Shield: Based on 35% tax rate and 5-year ACRS class. This is a simplifying and probably inaccurate assumption; i.e., not all the investment would fall in the 5-year class. Also, the factory is currently owned by the company and may already be partially depreciated. We assume the company can use tax shields as they arise.Revenues: Sales of 2,000 motors in 2010, 4,000 motors in 2011, and 10,000 motors thereafter. The unit price is assumed to decline from $4,000 (real) to $2,850 when competition enters in 2012. The latter is the figure at which new entrants’ investment in the project would have NPV = 0.Operating Costs: We assume direct labor costs decline progressively from $2,500 per unit in 2010, to $2,250 in 2011 and to $2,000 in real terms in 2012 and after.Other Costs: We assume true incremental costs are 10% of revenue.Tax: 35% of revenue less costs.Opportunity Cost of Capital: Assumed 20%.200920102011201220132014Capital Expenditure-15,400Changes in Working CapitalInventories-801-961-1,690-345380-418Receivables – Payables-440-528-929-190-209Depreciation Tax Shield1,0781,7251,035621621Revenues8,80019,36037,93441,72745,900Operating Costs-5,500-10,890-26,620-29,282-32,210Other costs-880-1,936-3,793-4,173-4,590Tax-847-2,287-2,632-2,895-3,185Net Cash Flow-16,2011,2503,7544,6505,4285,909201520162017201820192030Capital Expenditure5,058Changes in Working CapitalInventories-459-505-556-6126,727Receivables – Payables-229-252-278-306-3363,696Depreciation Tax Shield310Revenues50,48955,53861,09267,20273,922Operating Costs-35,431-38,974-42,872-47,159-51,875Other costs-5,049-5,554-6,109-6,720-7,392Tax-3,503-3,854-4,239-4,663-5,129Net Cash Flow6,1286,3997,0387,74220,9753,696NPV (at 20%) = $5,99120.The table below shows the real cash flows. The NPV is computed using the real rate, which is computed as follows:(1 + rnominal) = (1 + rreal) (1 + inflation rate)1.09 = (1 + rreal) (1.03)rreal = 0.0583 = 5.83%t = 0t = 1t = 2t = 3t = 4t = 5t = 6t = 7t = 8Investment-35,000.015,000.0Savings8,580.08,580.08,580.08,580.08,580.08,580.08,580.08,580.0Insurance-1,200.0-1,200.0-1,200.0-1,200.0-1,200.0-1,200.0-1,200.0-1,200.0Fuel1,053.01,053.01,053.01,053.01,053.01,053.01,053.01,053.0Net Cash Flow-35,000.08,433.08,433.08,433.08,433.08,433.08,433.08,433.023,433.0NPV (at 5.83%) = $27,254.221. All numbers are in thousands:t = 0t = 1t = 2t = 3t = 4t = 5t = 6t = 7t = 8Sales4,200.04,410.04,630.54,862.05,105.15,360.45,628.45,909.8Manufacturing Costs3,780.03,969.04,167.54,375.84,594.64,824.45,065.65,318.8Depreciation120.0120.0120.0120.0120.0120.0120.0120.0Rent100.0104.0108.2112.5117.0121.7126.5131.6Earnings Before Taxes200.0217.0234.8253.7273.5294.3316.3339.4Taxes70.076.082.288.895.7103.0110.7118.8Cash Flow – Operations250.0261.1272.6284.9297.8311.3325.6340.6Working Capital350.0420.0441.0463.1486.2510.5536.0562.80.0Increase in W.C.350.070.021.022.123.124.325.526.8-562.8Initial Investment1,200.0Sale of Plant400.0Tax on Sale56.0Net Cash Flow-1,550.0180.0240.1250.5261.8273.5285.8298.81,247.4NPV(at 12%) = $85.822. We can use the following spreadsheet to calculate a NPV of 6.352 billion RMB for the Ambassador China project. This calculation uses the following assumptions:1. Calculations are done on a nominal basis, converting the salvage value estimate from a real to a nominal value (638) using the 5% inflation estimate; Salvage = book value so no taxes are incurred on salvage. 2. Depreciation is calculated at 4000 – 638 (salvage) / 5 = 672.4 per year3. Cars sales occur in year 1 (there is some ambiguity here as the problem state it takes a year for the plant to become operational but also that sales will occur in the first year).4. The tax shield in year 0 can be used to offset profits from other operations.5. No working capital costs (this is unrealistic, but no figures are given)RMB; figures in millionsYEAR?012345Capital Investment4,000????-638Accumulated Depreciation?6721,3452,0172,6893,362Year-End Book Value4,0003,3282,6551,9831,311638???????Unit Sales?0.100.100.100.100.10Price / unit (growing 4%)?65,00067,60070,30473,11676,041Raw Material Cost / Unit (growing 3%)?18,00018,54019,09619,66920,259???????Revenues?6,5006,7607,0307,3127,604Raw Material Costs?1,8001,8541,9101,9672,026Labor Costs (growing 7%)?1,1001,1771,2591,3481,442Land costs (prepaid)300300300300300?Depreciation?672.4672.4672.4672.4672.4Pretax Profit-3002,6282,7572,8893,0253,464Taxes at 25%-75657689722756866Profit after tax-2251,9712,0672,1672,2692,598???????Revenues?6,5006,7607,0307,3127,604Cash costs3003,2003,3313,4693,6143,468Tax on operations?657689722756866Cash Flow from Operations-3002,6432,7402,8392,9413,270Capital Investment-4,000????638Net Cash Flows-4,3002,6432,7402,8392,9413,908Discount Factor @ 12%1.0000.8930.7970.7120.6360.567Present Value-4,3002,3602,1842,0211,8692,218???????NPV6,352?????23.[Note: Section 6.2 provides several different calculations of pre-tax profit and taxes, based on different assumptions; the solution below is based on Table 6.6 in the text.]See the table below. With full usage of the tax losses, the NPV of the tax payments is $4,779. With tax losses carried forward, the NPV of the tax payments is $5,741. Thus, with tax losses carried forward, the project’s NPV decreases by $962, so that the value to the company of using the deductions immediately is $962.t = 0t = 1t = 2t = 3t = 4t = 5t = 6t = 7Pretax Profit-4,000-4,5147489,80716,94011,5795,5391,949Full usage of tax losses immediately(Table 7.6)-1,400-1,5802623,4325,9294,0531,939682NPV (at 20%) = $4,779Tax loss carry-forward0007145,9294,0531,939682NPV (at 20%) = $5,74124.In order to solve this problem, we calculate the equivalent annual cost for each of the two alternatives. (All cash flows are in thousands.)Alternative 1 – Sell the new machine: If we sell the new machine, we receive the cash flow from the sale, pay taxes on the gain, and pay the costs associated with keeping the old machine. The present value of this alternative is:The equivalent annual cost for the five-year period is computed as follows:PV1 = EAC1 [annuity factor, 5 time periods, 12%]–93.80 = EAC1 [3.605]EAC1 = –26.02, or an equivalent annual cost of $26,020Alternative 2 – Sell the old machine: If we sell the old machine, we receive the cash flow from the sale, pay taxes on the gain, and pay the costs associated with keeping the new machine. The present value of this alternative is:The equivalent annual cost for the ten-year period is computed as follows:PV2 = EAC2 [annuity factor, 10 time periods, 12%]–127.51 = EAC2 [5.650]EAC2 = –22.57, or an equivalent annual cost of $22,570Thus, the least expensive alternative is to sell the old machine because this alternative has the lowest equivalent annual cost.One key assumption underlying this result is that, whenever the machines have to be replaced, the replacement will be a machine that is as efficient to operate as the new machine being replaced.25. Assuming that the light bulb purchases occur at year 0 (for use during the following year or years), the cost structure and PV of each option isYEAR?0123456789PV @ 5%Low Energy3.501.601.601.601.601.601.601.601.601.6014.87Conventional0.506.60????????6.79The equivalent annual cost for the low energy bulb is computed as follows:PVLE = EACLE [annuity factor, 9 time periods, 5%]14.87 = EACLE [7.108]EACLE = $2.09, which is much cheaper than the $6.79 cost of using a conventional light bulb for the year.26.The current copiers have net cost cash flows as follows:YearBefore-TaxCash FlowAfter-Tax Cash FlowNet Cash Flow1-2,000(-2,000 .65) + (.35 .0893 20,000)-674.92-2,000(-2,000 .65) + (.35 .0892 20,000)-675.63-8,000(-8,000 .65) + (.35 .0893 20,000)-4,574.94-8,000(-8,000 .65) + (.35 .0445 20,000)-4,888.55-8,000(-8,000 .65)-5,200.06-8,000(-8,000 .65)-5,200.0These cash flows have a present value, discounted at 7%, of –$15,857. Using the annuity factor for 6 time periods at 7% (4.767), we find an equivalent annual cost of $3,326. Therefore, the copiers should be replaced only when the equivalent annual cost of the replacements is less than $3,326.When purchased, the new copiers will have net cost cash flows as follows:YearBefore-TaxCash FlowAfter-Tax Cash FlowNet Cash Flow0-25,000-25,000-25,000.01-1,000(-1,000 .65) + (.35 .1429 25,000)600.42-1,000(-1,000 .65) + (.35 .2449 25,000)1,492.93-1,000(-1,000 .65) + (.35 .1749 25,000)880.44-1,000(-1,000 .65) + (.35 .1249 25,000)442.95-1,000(-1,000 .65) + (.35 .0893 25,000)131.46-1,000(-1,000 .65) + (.35 .0892 25,000)130.57-1,000(-1,000 .65) + (.35 .0893 25,000)131.48-1,000(-1,000 .65) + (.35 .0445 25,000)-260.6These cash flows have a present value, discounted at 7%, of –$21,967. The decision to replace must also take into account the resale value of the machine, as well as the associated tax on the resulting gain (or loss).Consider three cases:The book (depreciated) value of the existing copiers is now $6,248. If the existing copiers are replaced now, then the present value of the cash flows is:–21,967 + 8,000 – [0.35 (8,000 – 6,248)] = –$14,580Using the annuity factor for 8 time periods at 7% (5.971), we find that the equivalent annual cost is $2,442.Two years from now, the book (depreciated) value of the existing copiers will be $2,678. If the existing copiers are replaced two years from now, then the present value of the cash flows is:(–674.9/1.071) + (–675.6/1.072) + (–21,967/1.072) +{3,500 – [0.35 (3,500 – 2,678)]}/1.072 = –$17,602Using the annuity factor for 10 time periods at 7% (7.024), we find that the equivalent annual cost is $2,506.Six years from now, both the book value and the resale value of the existing copiers will be zero. If the existing copiers are replaced six years from now, then the present value of the cash flows is:–15,857+ (–21,967/1.076) = –$30,495Using the annuity factor for 14 time periods at 7% (8.745), we find that the equivalent annual cost is $3,487.The copiers should be replaced immediately.27.a.Year 1Year 2Year 3Year 4Year 5Year 6Year 7Year 8Year 9Year 10Year 11MACRSPercent10.00%18.00%14.40%11.52%9.22%7.37%6.55%6.55%6.56%6.55%3.29%MACRS Depr.40.0072.0057.6046.0836.8829.4826.2026.2026.2426.2013.16Tax Shield15.6028.0822.4617.9714.3811.5010.2210.2210.2310.225.13Present Value (at 7%) = $114.57 millionThe equivalent annual cost of the depreciation tax shield is computed by dividing the present value of the tax shield by the annuity factor for 25 years at 7%:Equivalent annual cost = $114.57 million/11.654 = $9.83 millionThe equivalent annual cost of the capital investment is:$34.3 million – $9.83 million = $24.47 millionThe extra cost per gallon (after tax) is: $24.47 million/900 million gallons = $0.0272 per gallonThe pre-tax charge = $0.0272/0.65 = $0.0418 per gallon28.a.PVA = $66,730 (Note that this is a cost.)PVB = $77,721 (Note that this is a cost.)Equivalent annual cost (EAC) is found by:PVA =EACA [annuity factor, 6%, 3 time periods]66,730 =EACA 2.673EACA =$24,964 per year rentalPVB =EACB [annuity factor, 6%, 4 time periods]77,721 =EACB 3.465EACB =$22,430 per year rentalb.Annual rental is $24,964 for Machine A and $22,430 for Machine B. Borstal should buy Machine B.The payments would increase by 8% per year. For example, for Machine A, rent for the first year would be $24,964; rent for the second year would be ($24,964 1.08) = $26,961; etc.29.Because the cost of a new machine now decreases by 10% per year, the rent on such a machine also decreases by 10% per year. Therefore:PVA = $61,820 (Note that this is a cost.)PVB = $71,614 (Note that this is a cost.)Equivalent annual cost (EAC) is found as follows:PVA =EACA [annuity factor, 6%, 3 time periods]61,820 =EACA 2.673EACA =$23,128, a reduction of 7.35%PVB =EACB [annuity factor, 6%, 4 time periods]71,614 =EACB 3.465EACB =$20,668, a reduction of 7.86%30.With a 6-year life, the equivalent annual cost (at 8%) of a new jet is:$1,100,000/4.623 = $237,941If the jet is replaced at the end of year 3 rather than year 4, the company will incur an incremental cost of $237,941 in year 4. The present value of this cost is:$237,941/1.084 = $174,894The present value of the savings is:The president should allow wider use of the present jet because the present value of the savings is greater than the present value of the cost.31.a.Year 0Year 1Year 2Year 3Year 4Year 5Year 6Year 7Pre-Tax Flows-14,000-3,0643,2099,75516,46314,0387,6963,951IRR = 33.5%Post-Tax Flows-12,600-1,6302,3816,20510,68510,1366,1103,444IRR = 26.8%Effective Tax Rate = 20.0%b.If the depreciation rate is accelerated, this has no effect on the pretax IRR, but it increases the after-tax IRR. Therefore, the numerator decreases and the effective tax rate decreases.If the inflation rate increases, we would expect pretax cash flows to increase at the inflation rate, while after-tax cash flows increase at a slower rate. After-tax cash flows increase at a slower rate than the inflation rate because depreciation expense does not increase with inflation. Therefore, the numerator of TE becomes proportionately larger than the denominator and the effective tax rate increases.c.Hence, if the up-front investment is deductible for tax purposes, then the effective tax rate is equal to the statutory tax rate.32.a.With a real rate of 6% and an inflation rate of 5%, the nominal rate, r, is determined as follows:(1 + r) =(1 + 0.06) (1 + 0.05)r =0.113 = 11.3%For a three-year annuity at 11.3%, the annuity factor is: 2.4310For a two-year annuity, the annuity factor is: 1.7057For a three-year annuity with a present value of $28.37, the nominal annuity is: ($28.37/2.4310) = $11.67For a two-year annuity with a present value of $21.00, the nominal annuity is: ($21.00/1.7057) = $12.31These nominal annuities are not realistic estimates of equivalent annual costs because the appropriate rental cost (i.e., the equivalent annual cost) must take into account the effects of inflation.b.With a real rate of 6% and an inflation rate of 25%, the nominal rate, r, is determined as follows: (1 + r) =(1 + 0.06) (1 + 0.25)r =0.325 = 32.5%For a three-year annuity at 32.5%, the annuity factor is: 1.7542For a two-year annuity, the annuity factor is: 1.3243For a three-year annuity with a present value of $28.37, the nominal annuity is: ($28.37/1.7542) = $16.17For a two-year annuity with a present value of $21.00, the nominal annuity is: ($21.00/1.3243) = $15.86With an inflation rate of 5%, Machine A has the lower nominal annual cost ($11.67 compared to $12.31). With inflation at 25%, Machine?B has the lower nominal annual cost ($15.86 compared to $16.17). Thus it is clear that inflation has a significant impact on the calculation of equivalent annual cost, and hence, the warning in the text to do these calculations in real terms. The rankings change because, at the higher inflation rate, the machine with the longer life (here, Machine A) is affected more.33.a.The spreadsheet on the next two pages indicates that the NPV for the Mid-American wind farm investment is: -$87,271,675By eliminating the tax in the spreadsheet, we find that the NPV is still negative: -$7,692,376NPV becomes positive with a tax subsidy of approximately 3.5%.b.Using the same spreadsheet, we can show that a capacity factor of 30% reduces NPV to: -$138,249,182ESTIMATED NPV OF MIDAMERICAN ENERGY'S WINDFARM PROJECT IN THE ABSENCE OF ANY TAX BREAKSPROJECT DATA?Capacity (megawatts)360.5Load factor35%Year 1 electricity price $/mWh55.00Year 1 maintenance & other costs ($)18,900,000Inflation3.00%Total capital cost ($)386,000,000MACRS years20Cost of capital12.0%Year0123456Capital cost386,000,000Revenues60,791,11562,614,84864,493,29466,428,09368,420,93670,473,564Maintenance & other costs18,900,00019,467,00020,051,01020,652,54021,272,11721,910,280MACRS depreciation14,475,00027,869,20025,784,80023,854,80022,040,60020,380,800Pretax profit27,416,11515,278,64818,657,48421,920,75225,108,21928,182,484Tax9,595,6405,347,5276,530,1197,672,2638,787,8779,863,869Cash flow-386,000,00032,295,47537,800,32137,912,16538,103,28938,360,94238,699,414PV-386,000,00028,835,24530,134,18526,985,13024,215,32921,767,02919,606,328NPV-87,271,675MACRS depreciation (%)3.757.226.686.185.715.28Year7891011121314Capital costRevenues72,587,77074,765,40477,008,36679,318,61781,698,17584,149,12086,673,59489,273,802Maintenance & other costs22,567,58823,244,61623,941,95524,660,21325,400,02026,162,02026,946,88127,755,287MACRS depreciation18,875,40017,447,20017,215,60017,215,60017,215,60017,215,60017,215,60017,215,600Pretax profit31,144,78234,073,58835,850,81137,442,80339,082,55640,771,50042,511,11344,302,915Tax10,900,67411,925,75612,547,78413,104,98113,678,89414,270,02514,878,89015,506,020Cash flow39,119,50839,595,03240,518,62741,553,42242,619,26143,717,07544,847,82446,012,495PV17,695,67915,991,76914,611,42313,379,09012,252,01911,221,08410,277,9649,415,068NPVMACRS depreciation (%)4.894.524.464.464.464.464.464.46Year15161718192021Capital costRevenues91,952,01694,710,57697,551,894100,478,450103,492,804106,597,5880Maintenance & other costs28,587,94629,445,58430,328,95231,238,82032,175,98533,141,2640MACRS depreciation17,215,60017,215,60017,215,60017,215,60017,215,60017,215,6008,607,800Pretax profit46,148,47048,049,39250,007,34252,024,03054,101,21956,240,724-8,607,800Tax16,151,96516,817,28717,502,57018,208,41118,935,42719,684,253-3,012,730Cash flow47,212,10648,447,70549,720,37251,031,22052,381,39253,772,0703,012,730PV8,625,4757,902,8707,241,4916,636,0796,081,8355,574,377278,857NPVMACRS depreciation (%)4.464.464.464.464.464.462.23 ................
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