Question

Calculate the present worth of all costs for a newly acquired machine with an initial cost of $28,000, no trade-in value, a life of 14 years, and an annual operating cost of $17,000 for the first 5 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

Present worth of an investment = A0/(1+i)^0+A1/(1+i)^1+A2/(1+i)^2....An/(1+i)^n

Time	Cash Flow	Discounting Factor	PV of cash flow
0	28000	1	28000
1	17000	0.909090909	15454.54545
2	17000	0.826446281	14049.58678
3	17000	0.751314801	12772.35162
4	17000	0.683013455	11611.22874
5	17000	0.620921323	10555.66249
6	18700	0.56447393	10555.66249
7	20570	0.513158118	10555.66249
8	22627	0.46650738	10555.66249
9	24889.7	0.424097618	10555.66249
10	27378.67	0.385543289	10555.66249
11	30116.54	0.350493899	10555.66249
12	33128.19	0.318630818	10555.66249
13	36441.01	0.28966438	10555.66249
14	40085.11	0.263331254	10555.66249
			187444.3375

Present worth = $187444.33

Showing formulas in excel:

Time	Cash Flow	Discounting Factor	PV of cash flow
0	28000	=1/(1.1)^A2	=B2*C2
1	17000	=1/(1.1)^A3	=B3*C3
2	17000	=1/(1.1)^A4	=B4*C4
3	17000	=1/(1.1)^A5	=B5*C5
4	17000	=1/(1.1)^A6	=B6*C6
5	17000	=1/(1.1)^A7	=B7*C7
6	=B7*1.1	=1/(1.1)^A8	=B8*C8
7	=B8*1.1	=1/(1.1)^A9	=B9*C9
8	=B9*1.1	=1/(1.1)^A10	=B10*C10
9	=B10*1.1	=1/(1.1)^A11	=B11*C11
10	=B11*1.1	=1/(1.1)^A12	=B12*C12
11	=B12*1.1	=1/(1.1)^A13	=B13*C13
12	=B13*1.1	=1/(1.1)^A14	=B14*C14
13	=B14*1.1	=1/(1.1)^A15	=B15*C15
14	=B15*1.1	=1/(1.1)^A16	=B16*C16
			=SUM(D2:D16)