Question

A company is considering buying a CNC machine. In​ today's dollars, it is estimated that the maintenance costs for the machine​ (paid at the end of each​ year) will be

​$31,000​,

​$32,000​,

​$35,000​,

​$36,000​,

and

​$38,000

for years 1 to​ 5, respectively. The general inflation rate

​( f ​)

is estimated to be

6​%

per​ year, and the company will receive

15​%

return​ (interest) per year on its invested funds during the inflationary period. The company wants to pay for maintenance expenses in equivalent equal payments​ (in actual​ dollars) at the end of each of the five years. Find the amount of the​ company's payments.

The amount of the​ company's payments is

​$40102

Answer 1

In this problem company is going to purchase a machine. It has a life of 5 years. Maintenance cost at current moey value are metioned in the problem. This cost is not uniform. Also inflation is 6% per year. Required an uniform maintenance cost payable in each year.Steps are as follows:

Step 1 First consider yearly given maintenance expenses. Increase them on the basis of inflation factor. Then calculate their present value using discount rate of 15%. Add them to get total present value of maintenance expenses required. It has been calculated in the table below.

Year	Cash flow	Inflation	Nominal	Discount	Present
		factor	cash flow	factor	value
1	31000	1.06	32860	0.88496	29079.786
2	32000	1.1236	35955.2	0.78315	28098.989
3	35000	1.19102	41685.7	0.69305	28890.274
4	36000	1.26248	45499.28	0.61332	27905.618
5	38000	1.33823	50851.6	0.54276	27600.214
Total	175100	5.97532	206851.78	3.51723	141574.881

Step 2: So $141574.881 is the present value of total maintenace cost of the project. If it is repayable in equal annual instalments of $A then sum of their present value will be exactly this figure. So-

As it is a GP series, summation formula of GP series is applied.

Answer: Company will pay $42234 per year as maintenace cost

There is slight difference from your answer, maybe due to decimal value significance

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