
Concept explainers
i.
Cash Flow equation including B variable.

Answer to Problem 45P
Explanation of Solution
Given:
Cash- flow moment-equation.
Concept used:
Cash-flow movement equation shows equilibrium from a given pivot point.
Positive force is calculated from right side from pivot point. It is calculated by adding number of years at any pivot point.
Negative forces are discounted when calculation is done from left-side of pivot point.
In this case, year 4 has been taken as pivot point. The distance from point 4 is 0, distance from 2 is 1 and the distance from point 1 is 2. These are the points situated at right side of the pivot points. Hence, the value will be positive. These values will be compounded.
Since there exist no points at left side of the pivot points. Thus, the value will not be negative as a result there will be no discounted value.
Upside values will be added and downside values will be deducted.
Calculation:
With year 3 as the pivot point, the cash flow moment equation will be as follows
Conclusion:
Therefore, above equations will provide the equilibrium of the cash-flows at the given points.
ii.
Cash Flow equation including variable C.

Answer to Problem 45P
Explanation of Solution
Given:
Cash- flow moment-equation.
Concept used:
Cash-flow movement equation shows equilibrium from a given pivot point.
Positive force is calculated from right side from pivot point. It is calculated by adding number of years at any pivot point.
Negative forces are discounted when calculation is done from left-side of pivot point.
Calculation:
In this case, year 5 has been taken as pivot point. The distance from point is 2, distance from point 2 is 3 and distance from point 1 is 4. These are the points situated at the right side of the pivot point with upside direction Hence, the value will be positive These values will be compounded.
The distance from point 5 is -1. These are the points situated at left-side of the pivot point with downside direction. Hence, the value will be negative. These values will be discounted.
Conclusion:
Therefore, above equations will provide the equilibrium of the cash-flows at the given points.
iii.
Cash Flow equation including variable V.

Answer to Problem 45P
Explanation of Solution
Given:
Cash- flow moment-equation.
Concept used:
Cash-flow movement equation shows equilibrium from a given pivot point.
Positive force is calculated from right side from pivot point. It is calculated by adding number of years at any pivot point.
Negative forces are discounted when calculation is done from left-side of pivot point.
In this case, Year 5 has been taken as pivot point. The distance from point 3 is 2, distance from point 2 is 3 and the distance from point 1 is 4. These are the points situated at right side of the pivot point with upside direction. Hence, the value will be positive. These values will be compounded. Since there exist no points at left side of the pivot point. Thus, the value will not be negative as a result there will be no discounted value.
Calculation:
With Year 4 as the pivot point, the cash flow moment equation will be as follows:
Conclusion:
Therefore, above equations will provide the equilibrium of the cash-flows at the given points.
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Chapter 4 Solutions
Engineering Economic Analysis
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