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In: Finance

Machine A costs $350,000 to purchase, result in electricity bills of $100,000 per year, and last...

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?

Solutions

Expert Solution

Machine A

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

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.


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