Question

Calculate the present worth of all costs for a newly acquired machine with an initial cost of $34,000, no trade-in value, a life of 14 years, and an annual operating cost of $17,000 for the first 3 years, increasing by 10% per year thereafter. Use an interest rate of 10% per year.

The present worth of all costs for a newly acquired machine is determined to be $

Answer 1

initial investment = 34000

O&M cost = 17000 for first three years and 10% increase after that (g=10%)

useful life = 14 yrs

i = 10%

The present value of gradient series when i=g is given by formula = C*n/(i+1)

Here n =12 (14-2) becaue gradient series is from yr 3 to yr 14

we will consider gradient series from yr 3 to yr 14 and present value at the end of second of this gradient series

= -17000 * 12 / (1+0.1) = 17000 * 12 / 1.1

= -185454.54

Now present value of maintenace cost = -17000/1.1 - 17000/1.1² - 185454.54/1.1²

= -182772.347

Net present value of cost = -34000-182772.347 = -216772.34

We could have used excel and gotten the same result, using excel

Year	Investment	O&M cost	Net cash flow	discount factor	Present value
0	-34000		-34000	1.000000	-34000.00
1		-17,000.00	-17,000.00	0.909091	-15454.55
2		-17,000.00	-17,000.00	0.826446	-14049.59
3		-17,000.00	-17,000.00	0.751315	-12772.35
4		-18,700.00	-18,700.00	0.683013	-12772.35
5		-20,570.00	-20,570.00	0.620921	-12772.35
6		-22,627.00	-22,627.00	0.564474	-12772.35
7		-24,889.70	-24,889.70	0.513158	-12772.35
8		-27,378.67	-27,378.67	0.466507	-12772.35
9		-30,116.54	-30,116.54	0.424098	-12772.35
10		-33,128.19	-33,128.19	0.385543	-12772.35
11		-36,441.01	-36,441.01	0.350494	-12772.35
12		-40,085.11	-40,085.11	0.318631	-12772.35
13		-44,093.62	-44,093.62	0.289664	-12772.35
14		-48,502.98	-48,502.98	0.263331	-12772.35
			Net present value		-216772.35