Question

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?

Answer 1

To justify the purchase of the equipment, it must be required for at least 1 day per year. To determine this, we calculate the annual operating cost for purchasing the equipment and compare it to the cost of obtaining the services from the city. By calculating the present value of the net cash flows for both options, we find that purchasing the equipment is more cost-effective.

Step-by-step explanation:

To determine the number of days per year the equipment must be required to justify its purchase, we need to compare the costs of purchasing the equipment versus obtaining the services from the city. Firstly, let's calculate the annual operating cost for purchasing the equipment. The total annual operating cost is given as $40 per day multiplied by 365 days, which equals $14,600 per year. In addition, there is an annual maintenance cost of $2,000. So the total annual operating cost is $14,600 + $2,000 = $16,600.

Now, let's calculate the cost of obtaining the services from the city. The initial delivery cost is $125 per dumpster per site, and since there are 45 construction sites, the total delivery cost is $125 x 5 x 45 = $28,125. The daily charge is $20 per dumpster per day, and since there are 5 dumpsters, the total daily charge is $20 x 5 = $100. Multiply that by 365 days to get the total annual daily charge, which is $100 x 365 = $36,500. Therefore, the total annual cost of obtaining the services from the city is $28,125 + $36,500 = $64,625.

Next, we need to calculate the present value of the net cash flows for both options to determine which option is more cost-effective. The present value factor for 8 years and a minimum attractive rate of return of 12% is 4.967637. For purchasing the equipment, the net cash flow per year is -$16,600. Multiply this by the present value factor to get the present value of the net cash flows for purchasing the equipment, which is -$16,600 x 4.967637 = -$82,323.456.

For obtaining the services from the city, the net cash flow per year is -$64,625 (the total annual cost calculated earlier). Multiply this by the present value factor to get the present value of the net cash flows for obtaining the services from the city, which is -$64,625 x 4.967637 = -$320,548.637.

To determine which option is more cost-effective, we compare the present values of the net cash flows. Since -$82,323.456 > -$320,548.637, the purchase of the equipment is more cost-effective. Therefore, the equipment must be required for at least 1 day per year to justify its purchase.

Answer 2

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.

Step-by-step 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.