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The benefit to cost ratio using present worth method, future worth method and annual worth method is the same.
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Answer to Problem 21P
The benefit to cost ratio using present worth method, future worth method and annual worth method is
Explanation of Solution
Given:
The annual benefit is
The annual disbenefit is
The first cost is
The annual cost is
The interest rate is
The time period is
Concept used:
Write the expression for present worth of benefits.
Here, the present worth is PW, annual benefit is
Write the expression for present worth of costs.
Here, first cost is
Write the expression for benefit to cost ratio using the present worth method.
Write the expression for future worth of benefits.
Here, the future worth is FW.
Write the expression for future worth of costs.
Write the expression for benefit to cost ratio using the future worth method.
Write the expression for annual worth of benefits.
Here, the annual worth is AW.
Write the expression for annual worth of costs.
Write the expression for benefit to cost ratio using the annual worth method.
Calculations:
Calculate the present worth of benefits.
Substitute
Calculate the present worth of costs.
Substitute
Calculate the benefit to cost ratio using
Substitute
The benefit to cost ratio using
Calculate the future worth of benefits.
Substitute
Calculate the future worth of costs.
Substitute
Calculate the benefit to cost ratio using
Substitute
The benefit to cost ratio using
Calculate the annual worth of benefits.
Substitute
Calculate the annual worth of costs.
Substitute
Calculate the benefit to cost ratio using
Substitute
The benefit to cost ratio using
Conclusion:
Thus, the benefit to cost ratio using present worth method, future worth method and annual worth method is
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Chapter 16 Solutions
Engineering Economic Analysis
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