ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
Question
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Chapter 6, Problem 51P
To determine

The machine should be chosen.

Expert Solution & Answer
Check Mark

Answer to Problem 51P

The machine B is the best choice.

Explanation of Solution

Given:

Cost & Details Machine A Machine B
Initial cost of machine $15000 $25000
Annual maintenance cost $1600 $400
Annual benefits $8000 $13000
Salvage value $3000 $6000
Life 6 10

Calculation:

Calculate the EUAC for Machine A.

EUAC=[P(AP,i,n)Operatingandmaintenancecost+Annualbenefits+F(AF,i,n)] ...... (I)

Here, present worth is P, future value is F, rate is i, year is n, and annual cost is A.

Calculate the factor (AP,i,n).

(AP,i,n)=[i(1+i)n(1+i)n1] ...... (II)

Substitute 12% for interest and 6years in Equation (II).

(AP,i,n)=[0.12( 1+0.12)6( 1+0.12)61]=0.2432

Calculate the factor (AF,i,n).

(AF,i,n)=[i(1+i)n1] ...... (III).

Substitute 12% for interest and 6years in Equation (III).

(AF,i,n)=[0.12( 1+0.12)61]=0.1232

Substitute $15000 for P, $3000 for F, $1600 for operation and maintenance cost, $8000 for annual benefits, 0.2432 for (AP,i,n), and 0.1232 for (AF,i,n) in Equation (I).

EUAC=[($15000×0.2432)$1600+$8000+($3000×0.1232)]=$3121.6

Calculate the EUAC for Machine B.

EUAC=[P(AP,i,n)Operatingandmaintenancecost+Annualbenefits+F(AF,i,n)] ...... (IV)

Here, present worth is P, future value is F, rate is i, year is n, and annual cost is A.

Calculate the factor (AP,i,n).

(AP,i,n)=[i(1+i)n(1+i)n1] ...... (V)

Substitute 12% for interest and 10years in Equation (V).

(AP,i,n)=[0.12( 1+0.12)10( 1+0.12)101]=0.1770

Calculate the factor (AF,i,n).

(AF,i,n)=[i(1+i)n1] ...... (VI).

Substitute 12% for interest and 10years in Equation (VI).

(AF,i,n)=[0.12( 1+0.12)101]=0.0570

Substitute $25000 for P, $6000 for F, $400 for operation and maintenance cost, $13000 for annual benefits, 0.1770 for (AP,i,n), and 0.0570 for (AF,i,n) in Equation (IV).

EUAC=[($25000×0.1770)$400+$13000+($6000×0.0570)]=$8517.

Conclusion:

Therefore the machine B is the best choice.

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