In: Finance
Machine A costs $350,000 to purchase, result in electricity bills of $100,000 per year, and last for 10 years. Machine B costs $550,000 to purchase, result in electricity bills of $80,000 per year, and last for 15 years. The discount rate is 12%. What are the equivalent annual costs for two models? Which model is more cost-effective?
Machine A |
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Year |
Annual Cost (C) |
PV Factor Calculation |
PV Factor @ 12 % (F) |
PV (= C x F) |
0 |
$350,000 |
1/(1+0.12)^0 |
1 |
$350,000 |
1 |
$100,000 |
1/(1+0.12)^1 |
0.892857143 |
$89,286 |
2 |
$100,000 |
1/(1+0.12)^2 |
0.797193878 |
$79,719 |
3 |
$100,000 |
1/(1+0.12)^3 |
0.711780248 |
$71,178 |
4 |
$100,000 |
1/(1+0.12)^4 |
0.635518078 |
$63,552 |
5 |
$100,000 |
1/(1+0.12)^5 |
0.567426856 |
$56,743 |
6 |
$100,000 |
1/(1+0.12)^6 |
0.506631121 |
$50,663 |
7 |
$100,000 |
1/(1+0.12)^7 |
0.452349215 |
$45,235 |
8 |
$100,000 |
1/(1+0.12)^8 |
0.403883228 |
$40,388 |
9 |
$100,000 |
1/(1+0.12)^9 |
0.360610025 |
$36,061 |
10 |
$100,000 |
1/(1+0.12)^10 |
0.321973237 |
$32,197 |
NPV |
$915,022 |
Machine B |
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Year |
Annual Cost (C) |
PV Factor Calculation |
PV Factor @ 12 % (F) |
PV (= C x F) |
0 |
$550,000 |
1/(1+0.12)^0 |
1 |
$550,000 |
1 |
$80,000 |
1/(1+0.12)^1 |
0.892857143 |
$71,429 |
2 |
$80,000 |
1/(1+0.12)^2 |
0.797193878 |
$63,776 |
3 |
$80,000 |
1/(1+0.12)^3 |
0.711780248 |
$56,942 |
4 |
$80,000 |
1/(1+0.12)^4 |
0.635518078 |
$50,841 |
5 |
$80,000 |
1/(1+0.12)^5 |
0.567426856 |
$45,394 |
6 |
$80,000 |
1/(1+0.12)^6 |
0.506631121 |
$40,530 |
7 |
$80,000 |
1/(1+0.12)^7 |
0.452349215 |
$36,188 |
8 |
$80,000 |
1/(1+0.12)^8 |
0.403883228 |
$32,311 |
9 |
$80,000 |
1/(1+0.12)^9 |
0.360610025 |
$28,849 |
10 |
$80,000 |
1/(1+0.12)^10 |
0.321973237 |
$25,758 |
11 |
$80,000 |
1/(1+0.12)^11 |
0.287476104 |
$22,998 |
12 |
$80,000 |
1/(1+0.12)^12 |
0.256675093 |
$20,534 |
13 |
$80,000 |
1/(1+0.12)^13 |
0.22917419 |
$18,334 |
14 |
$80,000 |
1/(1+0.12)^14 |
0.204619813 |
$16,370 |
15 |
$80,000 |
1/(1+0.12)^15 |
0.182696261 |
$14,616 |
NPV |
$1,094,869 |
Equivalent Annual Cost, EAC = NPV x Discount rate/1 - (1 + Discount rate)-Number of periods
EAC for Machine A = $ 915,022 x 0.12/[1-(1+0.12)-10]
= $ 915,022 x 0.12/[1-0.321973237]
= $ 915,022 x 0.12/ 0.678026763
= $ 109,802.68/0.678026763
= $ 161,944.46
EAC for Machine B = $ 1,094,869 x 0.12/[1-(1+0.12)-15]
= $ 1,094,869 x 0.12/[1-0.182696261]
= $ 1,094,869 x 0.12/0.817303739
= $ $131,384.30/0.817303739
= $ 160,753.33
Machine B is more cost effective as EAC of Machine B is less than that of Machine A.