The operation cost of a company is $500,000 this year (year 0). The company expects an...

The operation cost of a company is $500,000 this year (year 0). The company expects an annual cost of $100,000 from year 1 to year 5, and the cost decreases by 4% each year from year 6 to year 12. What's the equivalent annual worth if all the expenses occur within years 1-12 ( I=10%)

Expert Solution

operation cost in yr 0 is 500000

annual cost of 100000 from year 1 to year 5, and the cost decreases by 4% each year from year 6 to year 12.

i = 10%

t = 12yrs

We need to find the present cost and then using the annuity factor of (A/P,10%,12) convert that present value into annual series

using excel

Year	Maintenance Cost	PV Factor	Present value
0	5,00,000.00	1	5,00,000.00
1	1,00,000.00	0.909090909	90,909.09
2	1,00,000.00	0.826446281	82,644.63
3	1,00,000.00	0.751314801	75,131.48
4	1,00,000.00	0.683013455	68,301.35
5	1,00,000.00	0.620921323	62,092.13
6	96,000.00	0.56447393	54,189.50
7	92,160.00	0.513158118	47,292.65
8	88,473.60	0.46650738	41,273.59
9	84,934.66	0.424097618	36,020.59
10	81,537.27	0.385543289	31,436.15
11	78,275.78	0.350493899	27,435.18
12	75,144.75	0.318630818	23,943.43
	Total present value		11,40,669.76

Equivalent annual cost = present value * (A/P,10%,12)

= 11,40,669.76 * (A/P,10%,12)

= 11,40,669.76 * 0.146763315

= 167408.47

Showing formula in excel

Year	Maintenance Cost	PV Factor	Present value
0	500000	=1/(1+0.1)^W3	=X3*Y3
1	100000	=1/(1+0.1)^W4	=X4*Y4
2	100000	=1/(1+0.1)^W5	=X5*Y5
3	100000	=1/(1+0.1)^W6	=X6*Y6
4	100000	=1/(1+0.1)^W7	=X7*Y7
5	100000	=1/(1+0.1)^W8	=X8*Y8
6	=X8*(1-0.04)	=1/(1+0.1)^W9	=X9*Y9
7	=X9*(1-0.04)	=1/(1+0.1)^W10	=X10*Y10
8	=X10*(1-0.04)	=1/(1+0.1)^W11	=X11*Y11
9	=X11*(1-0.04)	=1/(1+0.1)^W12	=X12*Y12
10	=X12*(1-0.04)	=1/(1+0.1)^W13	=X13*Y13
11	=X13*(1-0.04)	=1/(1+0.1)^W14	=X14*Y14
12	=X14*(1-0.04)	=1/(1+0.1)^W15	=X15*Y15
	Total present value		=SUM(Z3:Z15)

Rahul Sunny answered 2 years ago

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