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

1. Annual worth Vs Present worth Analysis
To calculate the annual worth and present worth of the given two alternatives, the following steps have to be followed:

The net present value(NPV) has to be found for each alternative and further the annual worth is calculated using standard formula.

Annual worth = P[i(1+i)ⁿ / (1+i)ⁿ - 1]

where P is the present worth, I is the discount rate and n is the number of expected life of a asset.

Alternative 1:

NPV = Recurring payments + Salvage value - Initial cost of machinery

Recurring payments = Value of profit made i.e 50 additional drinks sale price of $6 = $300 minus cost of producing 50 drinks at $2 = $100. Therefore profit is $200 for 1 week. So for 52 weeks it is $10,400. From this maintenance cost of $2,000/- to be reduced. Final profit is $8,400/-

Recurring payments = 8,400[(1+.2)⁷ - 1) / .2(1+.2)⁷]

= $30,279.48/-

Salvage value = 200(1/1+.2)^{7 =} 55.8

Hence NPV = 30,279.48+55.8-6000 = $24,335.28/-

Annual worth = 24,335.28[.2(1+.2)⁷ / (1+.2)⁷-1] = 31,545 * .2774

   = $6,750.61/-

Alternative 2 :

NPV = Recurring payments + Salvage value - Initial cost of machinery

Recurring payments = present value of profit made i.e 100 additional drinks sale price of $8 = $800 minus cost of producing 100 drinks at $1 = $100. Therefore profit is $700 for 1 week. So for 52 weeks it is $36,400. From this reduce the annual maintenance cost of $1,000. Final profit is $35,400/-.

Recurring payments = 35,400[(1+.2)¹⁴ - 1) / .2(1+.2)¹⁴]

= $163,215.24/-

Salvage value = 500(1/1+.2)^{14 =} $38.95

Hence NPV = 163,215.24+38.95-10,000 = $153,254.19/-

Annual worth = 153,254.19[.2(1+.2)¹⁴ / (1+.2)¹⁴-1] = 153,254.19 * .2169

   = $33,240.83/-

Since the NPV and the annual worth are higher in alternative 2, alternative two to buy computer controlled mixing system to be opted.