Question

SITUATION: Two alternatives for a margarita mixer are under consideration. One system, the Mixer-Plus has an initial cost of $6,000. The salvage value after 7 years is expected to be $200. The operating costs including operator wages, routine maintenance, overhauls, etc., is expected to be $2,000 per year. It is expected that this machine will encourage the purchase of an additional 50 drinks per week costing $2.00 apiece to produce and for which $6.00 can be charged. Alternatively, a completely computer controlled mixing system, the Master Blender, with an initial cost of $10,000 is available. The operating costs including operator wages, routine maintenance, overhauls, etc., is expected to be $1,000 per year. The salvage value at the end of 14 years is $500. If this alternative is used an additional 100 drinks per week is expected costing $1.00 apiece to produce and for which $8.00 can be charged. Assume either machine will be employed for 52 weeks per year. The minimum attractive rate of return for the business is 20% per year. REQUIREMENTS: 1. Which method should be selected based on an annual-worth analysis? Show the AW for each alternative. 2. Which method should be selected based on a present-worth analysis? Show the PW for each alternative.

Answer 1

To calculate annual worth for the two alternatives, the initial cost and the salvage value must be annualized. The revenue and operating costs are given as annual figures.

Mixer Plus
Annualized initial cost = 6000*(A/P, 20%, 7) = PMT(0.2,7,6000) = 1664.54
Annualized salvage value = 200*(A/F, 20%, 7) = PMT(0.2,7,,200) = 15.48
Annual costs = 2000
Annual profit = 50*(6-2)*52 = 10400
Annual worth = 10400+15.48-1664.54-2000 = 6750.94

Master Blender
Annualized initial cost = 10000*(A/P, 20%, 14) = PMT(0.2,14,10000) = 2168.93
Annualized salvage value = 500*(A/F, 20%, 14) = PMT(0.2,14,,500) = 8.45
Annual costs = 1000
Annual profit = 100*(8-1)*52 = 36400
Annual worth = 33239.52

Master Blender should be chosen as it has the higher AW

To calculate present worth for the two alternatives, the annual revenue, costs and salvage value must be converted to present value.

Mixer Plus
Initial cost = 6000
Annual costs = 2000
Annual profit = 50*(6-2)*52 = 10400
Annual cash-flow = 8400-2000 = 8400
PV of annual cash-flow = 8400*(P/A, 20%, 7) = PV(0.2,7,8400) = 23069.39
PV of salvage value = 200*(P/F, 20%, 7) = PV(0.2,7,,200) = 55.82
Present Worth = 23069.39+55.82-6000 = 17125.20
Annual worth = 10400+15.48-1664.54-2000 = 6750.94

Master Blender
Initial cost = 10000
Annual costs = 1000
Annual profit = 100*(8-1)*52 = 36400
Annual cash-flow = 35400
PV of annual cash-flow = 35400*(P/A, 20%, 14) = PV(0.2,14,35400) = 163214.08
PV of salvage value = 500*(P/F, 20%, 14) = PV(0.2,14,,200) = 38.94
Present worth = 153253.02

Master Blender should be chosen as it has the higher PW