A granary has two options for a conveyor used in the manufacture of grain for tr
ID: 2724774 • Letter: A
Question
A granary has two options for a conveyor used in the manufacture of grain for transporting, filling, or emptying. One conveyor can be purchased and installed for $100,000 with $3,500 salvage value after 16 years. The other can be purchased and installed for $105,000 with $5,000 salvage value after 16 years. Operation and maintenance for each is expected to be $17,000 and $15,500 per year, respectively. The granary uses MACRS-GDS depreciation, has a marginal tax rate of 40%, and has a MARR of 9% after taxes.
Determine which alternative is less costly, based upon comparison of after-tax annual worth.
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Explanation / Answer
Year Initial Cost(A) Maintenance Cost(B) Depriciation(%) Tax shield on depriciation=Initial Cost*Rdepriciation*Tax Rate© Salvage Value(D) Net Cash flow=A+B-C-D PV@9% Initial Cost(A) Maintenance Cost(B) Depriciation Tax shield on depriciation=Initial Cost*Rdepriciation*Tax Rate© Salvage Value(D) Net Cash flow=A+B-C-D PV@9% 0 100000 100000 100000.0 105000 105000 105000.0 1 17000 5 2000 15000 13761.5 15500 5 2100 13400 12293.6 2 17000 9.5 3800 13200 11110.2 15500 9.5 3990 11510 9687.7 3 17000 8.55 3420 13580 10486.3 15500 8.55 3591 11909 9195.9 4 17000 7.7 3080 13920 9861.3 15500 7.7 3234 12266 8689.5 5 17000 6.93 2772 14228 9247.2 15500 6.93 2910.6 12589.4 8182.2 6 17000 6.23 2492 14508 8650.6 15500 6.23 2616.6 12883.4 7682.0 7 17000 5.9 2360 14640 8008.6 15500 5.9 2478 13022 7123.5 8 17000 5.9 2360 14640 7347.3 15500 5.9 2478 13022 6535.3 9 17000 5.91 2364 14636 6738.8 15500 5.91 2482.2 13017.8 5993.8 10 17000 5.9 2360 14640 6184.1 15500 5.9 2478 13022 5500.6 11 17000 5.91 2364 14636 5671.9 15500 5.91 2482.2 13017.8 5044.8 12 17000 5.9 2360 14640 5205.0 15500 5.9 2478 13022 4629.8 13 17000 5.91 2364 14636 4774.0 15500 5.91 2482.2 13017.8 4246.1 14 17000 5.9 2360 14640 4381.0 15500 5.9 2478 13022 3896.8 15 17000 5.91 2364 14636 4018.1 15500 5.91 2482.2 13017.8 3573.9 16 17000 2.95 1180 3500 12320 3103.0 15500 2.95 1239 5000 9261 2332.6 218548.9 209608.1 Option A Annual cost=218548.9/PVA(i=9%,n=16)=218548.9/8.313= 26290.02 Option B Annual cost=209608.1/PVA(i=9%,n=16)=209608.1/8.313= 25214.5 So alternate-B is less costly.