
(a)
The joint probability of saving and useful life.

Answer to Problem 17P
The joint probability of saving and useful life is shown in the following table.
Yearly saving | Joint probability |
Explanation of Solution
Given:
The first cost is
The salvage value is zero.
The interest rate is
Calculations:
The table for joint probability of saving and useful life is given below.
Yearly saving | Probability of saving |
Useful life | Probability of useful life |
Joint probability |
Table (1).
Conclusion:
The joint probability of saving and useful life is
Yearly saving | Joint probability |
Table (2).
(b)
The present worth of optimistic, most likely and pessimistic scenario.

Answer to Problem 17P
The present worth for optimistic estimates is
The present worth for most likely estimates is
The present worth for optimistic estimates is
Explanation of Solution
Given:
The first cost is
Concept used:
The estimates which under any circumstance can give the best possible results are called as optimistic estimates. These estimates are estimated at the best future events.
The estimates which are most probable or likely to happen are called as most likely estimates. These estimates occur at normal circumstances.
The estimates which under any circumstance can give the worst possible results are called as pessimistic estimates. These estimates are estimated at the abnormal circumstances.
Write the expression for present worth.
Here, the outflow is
Calculations:
The optimistic estimates are saving of
The most likely estimates are saving of
The pessimistic estimates are saving of
Calculate the present worth for optimistic estimates.
Substitute
The present worth for optimistic estimates is
Calculate the present worth for most likely estimates.
Substitute
The present worth for most likely estimates is
Calculate the present worth for optimistic estimates.
Substitute
The present worth for optimistic estimates is
Conclusion:
Thus, the present worth for optimistic estimates is
The present worth for most likely estimates is
The present worth for optimistic estimates is
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Chapter 10 Solutions
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