A plant engineer wishes to know which of two types of lightbulbs should be used
ID: 2814134 • Letter: A
Question
A plant engineer wishes to know which of two types of lightbulbs should be used to light a warehouse. The bulbs that are currently used cost $43.40 per bulb and last 14,400 hours before burning out. The new bulb (at $59.1 per bulb) provides the same amount of light and consumes the same amount of energy, but it lasts twice as long. The labor cost to change a bulb is $18.00. The lights are on 19 hours a day, 365 days a year. (Assume that the firm's marginal tax rate is 40%.) If the firm's MARR is 15%, what is the maximum price (per bulb) the engineer should be willing to pay to switch to the new bulb? Round the service life of the old bulb to the nearest whole number. Click the icon to view the interest factors for discrete compounding when ,-15% per year. The maximum price per new bulb the engineer should be willing to pay is (Round to one decimal place.)Explanation / Answer
Annual usage of one bulb = 19 hrs./day * 365 = 6935 hrs.
Life of a new bulb = 14400 * 2 = 28800 hours = 29000 hours
A new bulb will last 29000/6935 = 4.18 years
The current bulb will last 14400/6935 = 2.08 years = 2 years ( round off)
Annual cost of the current bulb = 43.4 / 2.08 = $ 20.86
Annual cost of new bulb = (59.1 + 18)/4.18 = $ 18.44
Difference of two costs = 20.86 - 18.44 = $ 2.42
Usage of new bulb will result in after tax profit of 2.42 * (1 - .4) = $ 1.45
Annual Return on investment in new bulb = 1.452 / 18.44 = 7.87 %
For a MARR of 15%, the minimum annual return should be 15% of 18.44 = $ 2.8
Pre-tax saving should be 2.8 / (1 - .4) = $ 4.7
Annual cost of new bulb should be 20.86 - 4.7 = $ 16.16
Life cycle cost cost of new bulb should be 16.16 * 4.7 = $ 75.952
Therefore, maximum cost of a new bulb should be 75.95 - 18 = $ 57.95
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