Two investments involving a virtual mold apparatus for producing dental crowns q

Question

Two investments involving a virtual mold apparatus for producing dental crowns qualify for different property classes. Investment A has a cost of $58,500.00, lasts 9 years with no salvage value, and costs $150,000 per year in operating expenses. It is in the 3-year property class. Investment B has a cost of $86,500.00, lasts 9 years with no salvage value, and costs $125,000 per year. Investment B, however, is in the 7-year property class. The company marginal tax rate is 40%, and MARR is an after-tax 10%. Based upon the use of MACRS-GDS depreciation, compare the AW of each alternative.

AWA = $

AWB = $

What must be Investment B's cost of operating expenses for these two investments to be equivalent?

Explanation / Answer

Lets find out the Annual worth of each option at MARR 10% - Cash flows for the 1st system = Initial cash flow = 5850000 Annual expenses = 150000 Year Cost Depreciation rate Depreciation tax savings Net cost = Cost - Tax savings PV Factor @ 10% PV of net cost 0 5850000 0 0 5850000 1 5850000 1 150000 33.33 779922 -629922 0.909091 -572656 2 150000 44.45 1040130 -890130 0.826446 -735645 3 150000 14.81 346554 -196554 0.751315 -147674 4 150000 7.41 173394 -23394 0.683013 -15978.4 5 150000 0 150000 0.620921 93138.2 6 150000 0 150000 0.564474 84671.09 7 150000 0 150000 0.513158 76973.72 8 150000 0 150000 0.466507 69976.11 9 150000 0 150000 0.424098 63614.64 5.759024 4766420 Except for year 0 Depreciation tax savings = Cost x depreciation rate x Tax rate AW = 4766420/5.759024 = 827643.81 Cash flows for the 2nd system = Initial cash flow = 8650000 Annual expenses = 125000 Year Cost Depreciation rate Depreciation tax savings Net cost = Cost - Tax savings PV Factor @ 10% PV of net cost 0 8650000 0 0 8650000 1 8650000 1 125000 14.29 494434 -369434 0.909091 -335849 2 125000 24.29 840434 -715434 0.826446 -591268 3 125000 17.49 605154 -480154 0.751315 -360747 4 125000 12.49 432154 -307154 0.683013 -209790 5 125000 8.93 308978 -183978 0.620921 -114236 6 125000 8.92 308632 -183632 0.564474 -103655 7 125000 8.93 308978 -183978 0.513158 -94409.8 8 125000 4.46 154316 -29316 0.466507 -13676.1 9 125000 0 125000 0.424098 53012.2 5.759024 6879381 Except for year 0 Depreciation tax savings = Cost x depreciation rate x Tax rate AW = 6879381/5.759024 = 1194539.42

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