Question

A firm expects to install smog control equipment on the exhaust of a gasoline engine. The local smog control district has agreed to pay to the firm a lump sum of money to provide for the first cost of the equipment and maintenance during its 10-year useful life. At the end of 10 years the equipment, which initially cost $10,000, is valueless. The firm and the smog control district have agreed that the following are reasonable estimates of the end-of-year maintenance costs:

Year 1 $75 Year 6 $200
2 225 7 250
3 275 8 300
4 100 9 125
5 150 10 175

Assuming interest at 6% per year, how much should the smog control district pay to the firm now to provide for the first cost of the equipment and its maintenance for 10 years?

Answer 1

$11,292 must be paid by the smog control district to the firm now to provide for the first cost of the equipment and its maintenance for 10 years.

Step-by-step explanation:

Data Given:

Let's Sort out the data given.

Year 1 $75 Year 6 $200

2 100 7 225

3 125 8 250

4 150 9 275

5 175 10 300

This is correct sequence of the data given with the increment of 25 each year. In our question, data is randomly arranged, which is not correct.

The first cost of the equipment is $10000 and the maintenance costs are paid annually where we see that the maintenance cost is $75 for the first year and rises by $25 each subsequent year.

The rate of interest is 6% and time period is 10 years.

We need to find the amount of money that is sufficient to pay now for reimbursing this entire cost structure.

PW = 10000 + 75(P/A, 6%, 10) + 25(P/G, 6%, 10)

= 10000 + 75*7.3601 + 25*29.6023

PW = $11,292 (approximately)

This is the required amount to be paid now.