Question

In: Economics

A company is considering buying a CNC machine. In​ today's dollars, it is estimated that the...

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

​$30,000​,

​$32,000​,

​$34,000​,

​$36,000​,

and

​$38,000

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

​( f ​)

is estimated to be

7​%

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

​$_______

thousand.

Solutions

Expert Solution

Present value of maintenance expenses is computed as under:

Years Cash Flows Inflation @7% Nominal Cashflow Discount factor @15% Present Value
1 30000 1.07000 32100.00 0.86957 27913.20
2 32000 1.14490 36636.80 0.75614 27702.55
3 34000 1.22504 41651.36 0.65752 27386.60
4 36000 1.31080 47188.80 0.57175 26980.20
5 38000 1.40255 53296.90 0.49718 26498.15
Total 170000 6.15329 210873.86 3.35216 136480.70

Thus, Present value of maintenance costs = $136480.70

If it is repayable in equal annual installments, let it be A, then sum of their present value is computed as under:

A/1.15 + 1/1.15^2 + ...... + A/1.15^5 = $136480.70

We can see it's a GP series, So:

A/0.15 (1-1/1.15^5) = $136480.70

A/0.15 (1- 0.49718) = $136480.70

(1- 0.49718) A = $136480.70*0.15

(0.50282) A = $20472.105

A = $20472.105/0.50282

A = $40714.58

Therefore, the amount of the​ company's payments is $40714.58


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