Question

A machine that produces a certain piece must be turned off by the operator after each piece is completed. The machine "coasts" for 15 seconds after it is turned off, thus preventing the operator from removing the piece quickly before producing the next piece. An engineer has suggested installing a brake that would reduce the coasting time to 3 seconds.
The machine produces 50,000 pieces a year. The time to produce one piece is 1 minute 45 seconds, excluding coastint time. The operator earns $10 an hour and other direct costs for operating the machine are $5 an hour. The brake will require servicing every 589 hours of operation. It will take the operator 30 minutes to perform the necessary maintenance and will require $48 in parts and material. The brake is expected to last 7,500 hours of operation (with proper maintenance) and will have no salvage value.How much could be spent for the brake if the Minimum Attractive Rate of Return is 10% compounded annually?

Answer 1

Answer:

$9197.72

Explanation:

To find the amount to be spent for the brake if the Minimum Attractive Rate of Return is 10% compounded annually, we have the following:

Cost incurred without the brake = Number of pieces * (Number of minutes for producing one product / total number of minute in an hour) * cost per peice

Where,

Number of minutes for producing a product without the brake system =

105 seconds(1 min, 45 sec) + 15 seconds(coast time) = 2 minutes or 120 seconds

Thus,

Cost incurred without break is =

$50,000* \frac{2}{60}* (10 + 5) = 25,000$

Let's find the number of minutes for installing a break

= 105 + 3 seconds = 108 seconds = 1.8 minutes

Cost incurred with break =

$50,000 * \frac{1.8}{60} * (10 + 5) = 22,500$

To find the maintainence cost, let's consider parts & material cost and labor cost for operator

$(\frac{50000 * \frac{1.8}{60}}{589}) * (\frac{30}{60} * (10+48)) = 73.85$

No. of years the brake will last

$= \frac{\frac{7500}{50000}}{1.8/60} = 5 years$

The maximum amount that can be spent on brake will be the difference in cost incurred with brake and without brake * present value of annuity factor of 5 years at 10%

= (25,000 - 22,573.85)*PVAF, 10% for 5 years = $9197.72

$9198 (rounded off)

The the amount to be spent for the brake if the Minimum Attractive Rate of Return is 10% compounded annually is $9197.72