Question

Alternative A has an initial acquisition cost of $10,000 and an annual average operating and maintenance cost of $1402 per down time. Alternative B has a higher acquisition cost of $20,000, but has a lower annual average operating and maintenance cost of $500 per down time. With an expected lifetime of 5 years for both alternatives, and an annual interest of 5%, determine the break even number of down times per year.

please show all work

Answer 1

For Both the alernatives, Let's assume Break-even number of downtimes per year as X.

Alternative A:

Let's assume the number of down-time be X each year. So the maintenance cost for downtime would be $1402 X.

Since this cost will be incurred for Year 1 - 5, Present value needs to be calculated.

Present value of $1 at annuity of 5%= 4.329477

Present value of Maintenance cost = 4.329477 * 1402 X = $6069.926 X

Total Present value for Alternative 1= $10,000 + $6069.926 X

Alternative B:

Let's assume the number of down-time be X each year. So the maintenance cost for downtime would be $500 X.

Since this cost will be incurred for Year 1 - 5, Present value needs to be calculated.

Present value of $1 at annuity of 5%= 4.329477

Present value of Maintenance cost = 4.329477 * 500 X= $2164.738 X

Total Present value for Alternative 2= $20,000 + $2164.738X

Since we are calculating the break even number of downtime per year, Cost would be same under both the alternatives at Break-even number of Units X

$10,000+ 6069.926X = $20,000 + 2164.738X

3905.188 X = $10,000

X = $10,000 / 3905.188

X = 2.56

Break-even number of downtimes per year is 2.56