Question

Find the optimum replacement interval AND the minimum EUAC for each of the scenarios below.

Please show cash flow diagram and do not use excel functions.

$225,000 is invested in equipment having a salvage value that decreases by 25% per year. O&M costs equal $45,000 the first year and increase by $30,000 per year. Consider a MARR of 10%.

n	EUAC
1
2
3
4
5
6
7
8
9
10

Based on the results obtained, what can you conclude concerning the effect of O&M costs on the optimum replacement interval?

Answer 1

For finding the EUAC we will use below formula

Here P = Purchase price

(A/P, i,n) is a factor formula =

This formula is same for EAC of capital recovery.

Now for EAC of O&M, The formula is

= First Year cost for O&M + Increase in cost *(A/G i, n)

Here (A/G, i, n) is also a factor which is given by

=

These above two formulas are sufficient to find EUAC and replacement interval.

It will be too much lengthy to calculate the EUAC, EAC for whole scenario manually so it is recommended to use Excel or other tools for calculation. I have done in excel please refer below.

N	Salvage Value	O&M	EAC of capital recovery	EAC for O&M	Total EAC	EUAC
0	225000
1	168750	45000	247500	45000	292500	36617.71
2	126562.5	75000	129642.8571	59285.71429	188928.6	29301.84
3	94921.875	105000	90475.83082	73096.67674	163572.5	23723.38
4	71191.40625	135000	70980.93083	86435.03555	157416	19497.48
5	53393.55469	165000	59354.43318	99303.77881	158658.2	16346.07
6	40045.16602	195000	51661.66058	111706.7153	163368.4	14085.09
7	30033.87451	225000	46216.23743	123648.4506	169864.7	12633.08
8	22525.40588	255000	42174.90395	135134.3578	177309.3	12077.07
9	16894.05441	285000	39069.12129	146170.5445	185239.7	12978.92
10	12670.54081	315000	36617.71385	156763.8154	193381.5	18583.46

Please note that the calculations have been done wrt above mentioned formula's only.

Replacement Interval:-

From above table we can see that Total EAC Cost is decreasing till some point (Which is good for us) and at year 5 (158658) it has increased from year 4 value (157416) and conitunue to increase after that, so for us economic life is 4 year.

If we will not be having a O&M cost in that case Total EAC will be just same as EAC of capital recovery cost (which is decreasing continuously) and economic life have been better than with O&M Cost.

With the addition of O&M Cost a point comes in the life cycle when Total EAC Cost for the equipment continues to rise and that point is said minimum economic life of the equipment.