orBewareThe DefenderThe ChallengerNotesCapital investment when purchased 5 years ago:$17,000Useful life:another 9 yearsReplacement of impeller and bearings =$1,750Total$5,340Present Market Value$750Estimated market value at the end of the 9 years =$200Useful life = 9 yearsTax Life:5 yearsAnnual ExpensesOperating and maintenance =$3,000Effective income tax (capital gains) rate = 40%Challenger InvestmentBefore tax cash flow is –BTMVBTCF = –750Using 6%After Tax Present Cost = –$22,669ATCF for the ChallengerConstruct the challenger cash flow independently of the defenderCapital investment = $20,000Year 1$5000$15,000$2,000Effective income tax rate = 40%Economic LifeRecall thatCapital investment = $13,000 two years ago; for the next five years, we haveYear 0$5,0001 Replacement Analysis Should we replace an asset that we own now or later? Reasons for replacing an asset • Physical Impairment • Altered Requirements • Technology The replacement of assets often represents economic opportunity for the firm. We compare the two alternatives: • The asset that we own: The Defender • The Asset that we might buy to replace it: The Challenger Factors to consider (or ignore) • Sunk Costs • Existing Asset Value and the outsider viewpoint • Income Tax Considerations • Economic Life of the challenger and the defender An asset has various types of lives • Useful Life • Tax Life • Economic Life The Economic Life of an asset is • the period of time that minimizes the net annual cost (NAC) for the investment (when it primarily consists of costs) or • the period of time that maximizes the net annual worth (NAW) for the investment (when it consists of costs and revenues) Example 1 • Investment in a machine: $15,000 • Useful life 10 years • Salvage decreasing with time like the book value using SYD method. Assume salvage after 10 years is zero • Operating cost is $500 in first year, but increases by 40% in each subsequent year • What is the economic life? The MARR is 18%2 Replacement Computation of the Economic Life Time Operating Cost Salvage Value NAC0 15000 1 500 12273 5927 2 700 9818 5669 3 980 7636 5462 4 1372 5727 5307 5 1921 4091 5207 6 2689 2727 5162 7 3765 1636 5178 8 5271 818 5256 9 7379 273 5404 10 10331 0 5627 Let A(n) = cost in year n S(n) = Salvage in year n P = Investment at time 0 PA = present worth of annual costs = A(1)(P/F, i, 1) + A(2)(P/F, i, 2) + … + A(n)(P/F, i, n) NAC = (P + PA)(A/P, i, n) – S(n)(A/F, i, n) The Economic Life Minimizes the NAC Find NAC(1), NAC(2),…, NAC(10). The economic life is the life that minimizes NAC. In this case the economic life = 6 years. Economic Life0200040006000800010000120001400016000012345678910Operating CostSalvage ValueNAC Economic Life Summary: • For many situations, the economic life and the useful life are the same. • When the economic life is different from the useful life, use the economic life when determining the advisability of an investment. • When comparing two alternatives, compute and use the economic life of each alternative in the comparison.Replacement 3 Replacement Analysis: Example 2 It is 2003. Should we buy a new car to replace the old wreck? Your minimum acceptable rate of return is 12%. Old Car: Initial cost was $4,500 in 1995. The car was supposed to last for 8 years with a trade-in value $500 at the end of 8 years. Maintenance costs next year will be $800, and are expected to go up by $400 a year in the coming years (800, 1200, 1600, . . .). The car is now a death trap, not worth more than $250. To trade it in, you're going to have to clean it up for a cost of $50. In the future, net salvage value is also expected to be $200 at any time. New car: Cost is $8,250, less trade-in allowance of $250. This car is supposed to last for 10 years with a trade-in value of $750 at the end of that time. If you sell it before the end of its useful life, you expect the trade-in value to be the same as the book value computed with straight-line depreciation. Maintenance will be $100 per year for the first three years and $300 per year thereafter. The Defender Investment Operating Costs and Revenues Salvage Value Economic Life The Challenger Investment Operating Costs and Revenues Salvage Value Economic Life4 Replacement Investment for the Defender The opportunity cost for the defender is the money that you give up by not disposing of it. You must also add any costs at time 0 to make it equivalent to the challenger. The investment consists of • the current market value for the defender, • less costs necessary for its disposal, • less taxes on the capital gain (when taxes are considered), • plus any real costs at time 0 necessary to keep the defender. Beware Don't use any defender characteristics to compute the challenger investment, costs, or salvage. Don't use any challenger characteristics to compute the defender investment, costs, or salvage. The Defender Investment: PD = $200. Operating Cost: AD(n) = $800 + $400(n-1) Salvage Value: SD(n) = $200 NACD(n) = PD(A/P, i, n) + $800 + $400(A/G, i, n) – 200(A/F, i, n) The Challenger Investment: PC = $8,250 Operating Cost: AC(n) = $100, $100, $100, $300, $300, $300, ... Salvage Value: SC(n) = $8,250 –$750n NACC(n) = PC(A/P, i, n) + 100 –SC(n)(A/F, i, n) for n = 1, 2, 3NACC(n) = PC(A/P, i, n) + 300 – 200(P/A, i, 3) (A/P, i, n) – SC(n)(A/F, i, n) for n = 4,…,10 Defender Challenger Age, n A(n) S(n) NAC Age, n A(n) S(n) NAC 0 200 0 8250 1 800 200 824 1 100 7500 1840 2 1200 200 1013 2 100 6750 1798 3 1600 200 1194 3 100 6000 1757 4 300 5250 1760 5 300 4500 1747 6 300 3750 1728 7 300 3000 1705 8 300 2250 1681 9 300 1500 1657 10 300 750 1632Replacement 5 Which do we select? • Defender cost for one more year: $824 • Challenger cost per year: $1632 Notes • All parameters of the defender and challenger are independent. • Use economic lives in the analysis. • The economic life of the defender is often one year. • The economic life of the challenger is often its useful life. • Choose the winner on the basis of minimum NAC or maximum NAW Replacement Analysis Examples • Do we replace now or later? • Case 1: When the useful lives of the defender and the challenger are known and the same. • Case 2: When the