Three alternatives have the following cost and annual benefit data associated wi

Question

Three alternatives have the following cost and annual benefit data associated with them: Data Useful Life, Years First Cost Alt. 1 10 $1,325,000 265,000 Alt.3 Alt. 2 10 $1,980,000 589.000 97,000 2,100 205,000 225,565 $1,650,000 435,000 91,000 1,980 178,000 Annual Benefit Annual M&O; Costs 95,000 Annual M&O; Gradient 2,300 Salvage Value 145,000 150,946 Loan Payment 187,971 The loan and a down be purcha ments are calculated usin payment of g an interest rte of 10%, a life equal to the life of the machine se a MARR of 12% and determine which machine, if any, should pay 30%. U se incremental rate o

Explanation / Answer

Answer : in given there are 3 alternatives for compare. we shall compare 2 machine at a time

A. . Alt. 3 compard with Alt. 1 (becouse of Alt 2 has higher cost)

Year

Cash Flows

PVF @12% for 10 Years

PV of Cash Flows

Incremental Cost of Machine (Alt. 3)

0

-325000

1

-325000

Incremental Annual Benefit

1-10 years

170000

5.65

960500

Incremental Annual M&O Cost

1-10 years

4000

5.65

22600

Incremental Annual M&O Gradient

1-10 years

320

5.65

1808

Incremental Loan Repayment

1-10 years

-37025

5.65

-209191.25

IncrementalSolvage Value

10th year

33000

0.322

10626

Incremental NPV

461342.75

Alt 3 . has positive Incremental NPV as compared to Alt. 1 hence in that case we will select Alt. 3

B. Alt 2 compared with Alt. 3

Year

Cash Flows

PVF @12% for 10 Years

PV of Cash Flows

Increamental Cost of Machine (Alt. 2)

0

-330000

1

-330000

Increamental Annual Benefit

1-10 years

154000

5.65

870100

Increamental Annual M&O Cost

1-10 years

-6000

5.65

-33900

Increamental Annual M&O Gradient

1-10 years

-120

5.65

-678

Increamental Loan Repayment

1-10 years

-37594

5.65

-212406.1

IncreamentalSolvage Value

10th year

27000

0.322

8694

Increamental NPV

301809.9

Alt 2 has positive Incremental NPV as compared to Alt. 3 hence we select Alt.3 .

Machine 2 should be purchase by company.

Working:

PV calculation

1-10 years

2

Cumulative Pv @12% for 10 years

[1-(1+r)^n/10]

5.65

PV for 10th year

1/(1.12)^10

0.322

Year

Cash Flows

PVF @12% for 10 Years

PV of Cash Flows

Incremental Cost of Machine (Alt. 3)

0

-325000

1

-325000

Incremental Annual Benefit

1-10 years

170000

5.65

960500

Incremental Annual M&O Cost

1-10 years

4000

5.65

22600

Incremental Annual M&O Gradient

1-10 years

320

5.65

1808

Incremental Loan Repayment

1-10 years

-37025

5.65

-209191.25

IncrementalSolvage Value

10th year

33000

0.322

10626

Incremental NPV

461342.75

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