Three alternatives have the following cost and annual benefit data associated wi

Question

Three alternatives have the following cost and annual benefit data associated with them Data Useful Life, Years 10 First Cost Annual Benefit Annual M&O; Costs 95,000 AnnualM&O; Gradient 2,300 Salvage Value Loan Payment Alt .3 10 $1,650,000 435,000 91,000 1,980 178,000 187,971 Alt. 1 Alt. 2 10 $1,980,000 589,000 97,000 2,100 205,000 225,565 $1,325,000 265,000 145,000 150,946 The loan payments are calculated using an interest rate of 10%, a life equal to the life of the machine and a down payment of 30%. Use a MARR of12% and determine which machine, be purc if any, should Use incremental rate of return for your analysis.

Explanation / Answer

aNSWER:

Calculation of Net present value of all the three alternatives

As the NPV of Alt. 1 is -ve, therefore it should be rejected. The remaining two alternatives should be compare based on incremental rate of return.

Incremental rate of return on Alt. 2 = Incremental NPV/Incremental Investment

= (965,503-432,693)/(1,980,000-1,650,000) = (532,810/330,000)*100 = 161.46%

As there is an incremental rate of return of 161.46% on Alt. 2 over Alt. 3, Alt. 2 should be accepted.

Particulars Alt. 1 Alt. 2 Alt. 3 Annual Benefit 265,000 589,000 435,000 Less: Annual M&O costs (95,000) (97,000) (91,000) Less: Annual M&O gradient (2,300) (2,100) (1,980) Net Annual Benefit (a) 167,700 489,900 342,020 PVAF(10 yrs,12%) (b) 5.650 5.650 5.650 Present value of annual banefit (c = a*b) 947,505 2,767,935 1,932,413 Present value of salvage value (Salvage value*PVF(10 yrs,12%) (d) (145,000*0.322) = 46,690 (205,000*0.322) = 66,010 (178,000*0.322) = 57,316 Present value of loan payments (e) (150,946*5.65) = 852,845 (225,565*5.65) = 1,274,442 (187,971*5.65) = 1,062,036 Down payments (30% of cost) (f) 397,500 594,000 495,000 Net Present Value (c+d-e-f) (256,150) 965,503 432,693

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