a) A company is trying to decide between two machines for its manufacturing line

Question

a) A company is trying to decide between two machines for its manufacturing line. The Process1000 has an initial cost of $59220 and operating costs of $10 per hour. It will allow the company to produce a higher quality product, providing an annual benefit of $82874. The company will use the Process1000 10989 hours per year. The Process1000 has a useful life 3 years and an estimated salvage value of $18296 at the end of its useful life.

The Super X has an initial cost of $70921. It is a bigger machine and can process more at a time so the company will ony need to use it for 8120 hours per year. The Super X has an estimated benefit of $81393 per year. The Super X will have a useful life of 8 years and a salvage value of $33192 at the end of its useful life.

Using a MARR of 7%, what is the maximum operating cost per hour at which the Super X could run to make it equally desirable to the Process1000?

b) Tristan's Toys invested in a new manufacturing system. The initial cost was $327030. Annual costs are projected to be $193637, increasing by 14% each subsequent year. The system will require a substantial overhaul of $37722 at the end of year 7. The line is estimated to have a lifespan of 13 years.

The company projects it will sell 55928 units the first year, with the number of units sold increasing by 36562 units each subsequent year. What is the minimum price that the company must charge per unit to breakeven on the investment? Use a MARR of 4% compounded annually to make the calculation.

Explanation / Answer

(a)

First, we compute Present Worth (PW) for Process1000 as follows.

Net annual benefit ($) = Annual benefit - Operating cost = 82874 - (10 x 10989) = 82874 - 109890 = - 27016

PW ($) = - 59220 - 27016 x P/A(7%, 3) + 18296 x P/F(7%, 3) = - 59220 - 27016 x 2.6243 + 18296 x 0.8163

= - 59220 - 70898 + 14935

= - 115183

Let minimum hourly operating cost for SuperX be $C per hour.

PW for SuperX ($) = - 70921 - (C x 8120) x P/A(7%, 8) + 81393 x P/A(7%, 8) + 33192 x P/F(7%, 8)

= - 70921 - (C x 8120) x 5.9713 + 81393 x 5.9713 + 33192 x 0.582

= - 70921 - (C x 8120) x 5.9713 + 486022 + 19318

= 434419 - (C x 8120) x 5.9713

For equivalence, PW of SuperX = PW of Process1000

434419 - (C x 8120) x 5.9713 = - 115183

(C x 8120) x 5.9713 = 549602

(C x 8120) = 92041

C = $11.34

NOTE: First question is answered.

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