Alfred Home Construction is considering the purchase of five dumpsters and the transport truck to store and transfer construction debris from building sites. The entire rig is estimated to have an initial cost of $125,000, a life of 8 years, a $5000 salvage value, an operating cost of $40 per day, and an annual maintenance cost of $2000. Alternatively, Alfred can obtain the same services from the city as needed at each construction site for an initial delivery cost of $125 per dumpster per site and a daily charge of $20 per day per dumpster. An estimated 45 construction sites will need debris storage throughout the average year. If the minimum attractive rate of return is 12% per year, how many days per year must the equipment be required to justify its purchase?

If the total number of days per year is 1,419 or less, then the company should obtain the services from the city. But if the total number of days per year is 1,420 or more, then the company should purchase the equipment.

Explanation:

alternative 1:

initial outlay = $125,000

useful life 8 years

depreciation per year = ($125,000 - $5,000) / 8 = $15,000

costs:

$40 per day

maintenance $2,000 per year

total annual costs = $40x + $2,000

alternative 2:

$125 x 45 sites = $5,625

$20x

total annual costs = $5,625 + $20x

how large does x need to be in order for alternative 1 to be better using a 12% discount rate

cash flows

year 0 = ($125,000)

year 1 = $40x + $2,000 - $5,625 - $20x = $20x - $3,625  

year 2 = $20x - $3,625

year 3 = $20x - $3,625

year 4 = $20x - $3,625

year 5 = $20x - $3,625

year 6 = $20x - $3,625

year 7 = $20x - $3,625

year 8 = $20x - $3,625 + $5,000 = $20x + $1,375

I used the present value of an annuity formula, to determine the value of cash flow:

the PV annuity factor for 12% and 7 periods is 4.5638, so:

24,756.20 x 4.5638 = $112,982

$29,756.20 / (1.12⁸) = $12,018

total = $125,000

$20x - $3,625 = 24,756.20

$20x = $28,381.20

x = $28,381.20 / $20 = 1,419.06 days (including all 45 sites)

That means that if the total number of days per year is 1,419 or less, then the company should obtain the services from the city. But if the total number of days per year is 1,420 or more, then the company should purchase the equipment.

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