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 ​$41.1 per bulb and last 14600 hours before burning out. The new bulb​ (at ​$52.3 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 ​$19. The lights are on 19 hours a​ day, 365 days a year.​ (Assume that the​ firm's marginal tax rate is 25​%.) If the​ firm's MARR is 16​%, 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.

Answer 1

We have that the new bulb 's Price is P  is mathematically given as

P= $100.68

Bulb Price

Generally the Arithmetic equation for the life time of new bulb  is mathematically given as

life time = old bulb life / (usage per 24 x 365)

Therefore

L= 14,600 / (19 x 365)

L= 2.10 years

Where

old bulb=(2 x 45.9) (1 + 15/100)2.10 x 2 + 16

Old bulb=$181.11

After tax

tax = 181.11(1 - 40%)

tax= $108.66

Therefore

the new bulb 's Price is P

108.66 = P x (1.7986) x (0.6)

P= $100.68

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