A consulting engineering firm can lease a computer system for $1,000 per month or purchase one $15,000. The leased system will have no monthly maintenance cost, but the purchased one will cost $40 per month. How many months must the system be used in order to break-even?
17 months
To calculate the break-even point, we need to find out when the total cost of leasing the system will be equal to the total cost of purchasing and maintaining the system.
Let's first calculate the total cost of leasing the system over a certain number of months:
Total cost of leasing = $1,000/month x Number of months
Now let's calculate the total cost of purchasing and maintaining the system over the same number of months:
Total cost of purchasing and maintaining = $15,000 + $40/month x Number of months
We want to find out when these two costs will be equal, so we can set them equal to each other and solve for the number of months:
$1,000/month x Number of months = $15,000 + $40/month x Number of months
Subtracting $40/month x Number of months from both sides, we get:
$1,000/month x Number of months - $40/month x Number of months = $15,000
Simplifying, we have:
$960/month x Number of months = $15,000
Dividing both sides by $960/month, we get:
Number of months = $15,000/$960/month
Number of months = 15.625
Rounding up to the nearest whole number, we get:
Number of months = 17
Therefore, the system must be used for 17 months in order to break-even.
To determine the number of months required to break-even between leasing and purchasing the computer system, we need to compare the costs of both options over time.
For the leased system:
Cost per month = $1,000
Maintenance cost per month = $0
For the purchased system:
Cost of purchase = $15,000
Maintenance cost per month = $40
Let's assume the number of months required to break-even is X.
For the leased system, the total cost over X months = X * $1,000
For the purchased system, the total cost over X months = $15,000 + $40 * X
To find the break-even point, we set the costs equal to each other:
X * $1,000 = $15,000 + $40 * X
Now, let's solve for X:
X * $1,000 - $40 * X = $15,000
$1,000X - $40X = $15,000
$960X = $15,000
X = $15,000 / $960
Calculating this value gives us:
X ≈ 15.63
Since we cannot have a fraction of a month, we round up to the nearest whole number.
So, the system must be used for at least 16 months to break-even.