Answer:
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.
