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(a)
The expected value of the present worth.
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Answer to Problem 29P
The expected value of the present worth is
Explanation of Solution
Given:
The present worth of optimistic projection is
The present worth of most-likely projection is
The present worth of pessimistic projection is
The probability of optimistic projection is
The probability of most-likely projection is
The probability of pessimistic projection are
Concept used:
Write the expression to calculate the probable present worth.
Here, the probable present worth is
Write the expression to calculate the expected value of the present worth.
Here, the expected value of the present worth is
Calculation:
Calculate the probable optimistic present worth.
Substitute
Calculate the probable most-likely present worth.
Substitute
Calculate the probable pessimistic present worth.
Substitute
Calculate the expected value of the present worth.
Substitute
Conclusion:
Thus, the expected value of the present worth is
(b)
The expected value of annual savings and the corresponding present worth.
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Answer to Problem 29P
The expected value of annual savings is
The present worth is
Explanation of Solution
Given information:
The saving of optimistic projection is
The saving of most-likely projection is
The saving of pessimistic projection is
The probability of optimistic projection is
The probability of most-likely projection is
The probability of pessimistic projection is
The interest rate is
The transmission line have a life of
The outflow is
Concept used:
Write the expression to calculate the probable saving.
Here, the probable saving is
Write the expression to calculate the expected value of saving & annual inflow.
Here, the expected value of saving & annual inflow is
Write the expression to calculate
Here, the interest rate is
Write the expression to calculate the present worth.
Here, the expected value of saving & annual inflow is
Calculation:
Calculate the probable optimistic saving.
Substitute
Calculate the probable most-likely saving.
Substitute
Calculate the probable pessimistic saving.
Substitute
Calculate the expected value of saving & annual inflow.
Substitute
The annual inflow is
Calculate the value of
Substitute
Calculate the present worth.
Substitute
The present worth is
Conclusion:
Thus, the expected value of annual savings is
The present worth is
(c)
If the answers (a) and (b) match.
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Answer to Problem 29P
Yes, the answer in both (a) and (b) part are same.
Explanation of Solution
In part (a) the different probable present worth has been calculated for each saving and expected present worth has been calculated.
In part (b) the different probable saving has been calculated for each probability and annual saving has been calculated. Then by annual saving and outflow the expected present worth has been calculated.
Both the parts come to the same equation. This is why the net expected value is same.
Conclusion:
Yes, the answer in both (a) and (b) part are same.
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Chapter 10 Solutions
Engineering Economic Analysis
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