ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
Question
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Chapter 9, Problem 61P
To determine

(a)

The value of X that makes the two alternatives equally desirable.

Expert Solution
Check Mark

Answer to Problem 61P

The value of X that makes the two alternatives equally desirable is 9.23years.

Explanation of Solution

Given:

B’s first cost is $1200.

Concept used:

Write the expression to calculate the equivalent uniform annual cost.

EUAC=A(A/P,i,n) ...... (I)

Here, the amount is A, rate of interest is i and time period is n.

Calculation:

Calculate the equivalent uniform annual cost for A.

Substitute, 800 for A, 12% for i and 5 for n in Equation (I).

EUAC=800(A/P,12%,5)=800(0.12(1+0.12)5(1+0.12)51)=800×0.2777=221.92

To make both the alternatives equally desirable.

(EUABEUAC)A=(EUABEUAC)B(EUABEUAC)A=(EUABA(A/P,i,n))B ...... (II)

Here, equivalent uniform annual benefit is EUAB, equivalent uniform annual cost is EUAC, amount is A, interest rate is i and time period is n.

Substitute, $230 for EUABA, $221.92 for EUACA, $230 for EUABB

12% for i and 1200 for A in Equation (II)

230221.92=2301200(A/P,12%,X)221.92=1200(0.12(1+0.12)X(1+0.12)X1)

Calculate the value of X

X=9.23years.

Conclusion:

Therefore, the value of X that makes the two alternatives equally desirable is 9.23years.

To determine

(b)

The value of X that makes the two alternatives equally desirable.

Expert Solution
Check Mark

Answer to Problem 61P

The value of X that makes the two alternatives equally desirable is 5.13years.

Explanation of Solution

Given:

B’s annual benefit is $280.

Concept used:

Write the expression to calculate the equivalent uniform annual cost

EUAC=A(A/P,i,n) ...... (I)

Here, the amount is A, rate of interest is i and time period is n.

Calculation:

Calculate the equivalent uniform annual cost for A.

Substitute, 800 for A, 12% for i and 5 for n in Equation (I)

EUAC=800(A/P,12%,5)=800(0.12(1+0.12)5(1+0.12)51)=800×0.2777=221.92

To make both the alternatives equally desirable,

(EUABEUAC)A=(EUABEUAC)B(EUABEUAC)A=(EUABA(A/P,i,n))B ...... (II)

Here, equivalent uniform annual benefit is EUAB, equivalent uniform annual cost is EUAC, amount is A, interest rate is i and time period is n.

Substitute, $230 for EUABA, $221.92 for EUACA, $280 for EUABB

12% for i and 1000 for A in Equation (II)

230221.92=2801000(A/P,12%,X)271.92=1000(0.12(1+0.12)X(1+0.12)X1)

Calculate the value of X

X=5.13years.

Conclusion:

The value of X that makes the two alternatives equally desirable is 5.13years.

To determine

(c)

The value of X that makes the two alternatives equally desirable.

Expert Solution
Check Mark

Answer to Problem 61P

The value of X that makes the two alternatives equally desirable is 6.73years.

Explanation of Solution

Given:

MARR is 10%.

Concept used:

Write the expression to calculate the equivalent uniform annual cost

EUAC=A(A/P,i,n) ...... (I)

Here, the amount is A, rate of interest is i and time period is n.

Calculation:

Calculate the equivalent uniform annual cost for A.

Substitute, 800 for A, 10% for i and 5 for n in Equation (I)

EUAC=800(A/P,12%,5)=800(0.10(1+0.10)5(1+0.10)51)=800×0.2637=211.03

To make both the alternatives equally desirable,

(EUABEUAC)A=(EUABEUAC)B(EUABEUAC)A=(EUABA(A/P,i,n))B ...... (II)

Here, equivalent uniform annual benefit is EUAB, equivalent uniform annual cost is EUAC, amount is A, interest rate is i and time period is n.

Substitute, $230 for EUABA, $211.03 for EUACA, $280 for EUABB

10% for i and 1000 for A in Equation (II)

230211.03=2301000(A/P,10%,X)211.03=1000(0.10(1+0.10)X(1+0.10)X1)

Calculate the value of X

X=6.73years.

Conclusion:

The value of X that makes the two alternatives equally desirable is 6.73years.

To determine

(d)

The value of X that makes the two alternatives equally desirable.

Expert Solution
Check Mark

Answer to Problem 61P

The value of X that makes the two alternatives equally desirable is 6.45years.

Explanation of Solution

Given:

B’s first cost is $1200

B’s annual benefit is $280

MARR is 10%.

Concept used:

Write the expression to calculate the equivalent uniform annual cost

EUAC=A(A/P,i,n) ...... (I)

Here, the amount is A, rate of interest is i and time period is n.

Calculation:

Calculate the equivalent uniform annual cost for A.

Substitute, 800 for A, 10% for i and 5 for n in Equation (I)

EUAC=800(A/P,12%,5)=800(0.10(1+0.10)5(1+0.10)51)=800×0.2637=211.03

To make both the alternatives equally desirable,

(EUABEUAC)A=(EUABEUAC)B(EUABEUAC)A=(EUABA(A/P,i,n))B ...... (II)

Here, equivalent uniform annual benefit is EUAB, equivalent uniform annual cost is EUAC, amount is A, interest rate is i and time period is n.

Substitute, $230 for EUABA, $211.03 for EUACA, $280 for EUABB

10% for i and 1200 for A in Equation (II)

230211.03=2801200(A/P,10%,X)261.03=1200(0.10(1+0.10)X(1+0.10)X1)

Calculate the value of X

X=6.45years.

Conclusion:

The value of X that makes the two alternatives equally desirable is 6.45years.

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Chapter 9 Solutions

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