FIGURE 4. Annual operating costs for machine B.
Calculation Procedure:
- Compute the annual cost of machine A
By using the capital-recovery factor, A = $6800(0.21632) + $1240 = $2711.
- Construct a money-time diagram for machine B
Figure 4 shows the annual operating costs for machine B.
- Convert the operating costs for machine B to an equivalent
uniform series
The value S of these costs as of the end of the tenth year is S = $800(USCA, n = 4)(SPCA,
TI = 6) + $1200(USCA, n = 3)(SPCA, n = 3) + $1500(USCA, n = 3), or S = $800(4.506)
(1.587) + $1200(3.246)(1.260) + $1500(3.246) = $15,498. Now apply the relationship R
= S(SFP, n = 10), where R = annual payment of a uniform series that is equivalent to the
actual operating costs. Then R = $15,498(0.06903) = $1070. This is the equivalent uni-
form annual operating cost for machine B.
- Compute the annual cost of machine B, and compare the
two machines
Using the capital-recovery factor, we find A = ($12,000 - $100O)(0.14903) + $1000(0.08)
- $1070 = $2789. Machine A has a lower annual cost, and so it is more economical.
Related Calculations: As an alternative method in step 3, compute the value P'
of the operating costs as of the purchase date. Then P' = $800(USPW, n = 4) +
$1200(USPW, n = 3)(SPPW, n = 4) + $1500(USPW, n = 3)(SPPW, n = 7), or P' =
$800(3.312) + $1200(2.577)(0.7350) + $1500(2.577)(0.583) = $7176. Now apply the re-
lationship R = /"(CR, TI = 10), or R = $7176(0.14903) = $1069. Note that the arithmetic
mean of the annual operating costs for machine B is $1130. However, since the costs in-
crease with time and the earlier payments in a series have a more pronounced effect than
the later payments, the equivalent annual operating cost is less than $1130.
ECONOMICS OF EQUIPMENT
REPLACEMENT
A machine having an installed cost of $10,000 was used for 5 years. During that time its
trade-in value and operating costs changed as follows:
Operating cost,
End of year Salvage value, $ $/year
1 600 0 230 0
2 400 0 250 0
3 320 0 330 0
4 250 0 480 0
5 200 0 680 0
Year
