In: Economics
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.
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