A bridge is to be constructed now as part of a new road. Engineers have determined that current traffic volume on the new road will justify a two-lane road and a bridge at the present time. Because of the uncertainty regarding future traffic, the time at which the additional two lanes will be required is currently being studied. Two alternatives are being considered. Alternative 1 - One-stage construction: Build a four lane bridge right now for $360,000. Alternative 2 - Two-stage construction: Start with a two-lane bridge now for $170,000 and widen to four lanes later when traffic justifies. The future cost of widening the bridge to four-lanes at that time will be $170,000 plus an extra $23,000 for every year that widening is delayed. For example, if future widening is done at the end of year 7, the cost of widening at that time will be equal to $170,000 + 7x($23,000) = $331,000. The following estimates have been made of when widening to a four-lane bridge will be required: Pessimistic estimate Most likely estimate Optimistic estimate End of year 4 End of year 7 End of year 8
A bridge is to be constructed now as part of a new road. Engineers have determined that current traffic volume on the new road will justify a two-lane road and a bridge at the present time. Because of the uncertainty regarding future traffic, the time at which the additional two lanes will be required is currently being studied. Two alternatives are being considered. Alternative 1 - One-stage construction: Build a four lane bridge right now for $360,000. Alternative 2 - Two-stage construction: Start with a two-lane bridge now for $170,000 and widen to four lanes later when traffic justifies. The future cost of widening the bridge to four-lanes at that time will be $170,000 plus an extra $23,000 for every year that widening is delayed. For example, if future widening is done at the end of year 7, the cost of widening at that time will be equal to $170,000 + 7x($23,000) = $331,000. The following estimates have been made of when widening to a four-lane bridge will be required: Pessimistic estimate Most likely estimate Optimistic estimate End of year 4 End of year 7 End of year 8
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:(a) Calculate the PW of costs for the different scenarios of Alternative 2
PW<sub>pessimistic</sub>(8%) = $ ___ thousand (Round to one decimal place.)
PW<sub>most likely</sub>(8%) = $ ___ thousand (Round to one decimal place.)
PW<sub>optimistic</sub>(8%) = $ ___ thousand (Round to one decimal place.)
(b) Calculate the expected PW costs of Alternative 2 using the "three-point estimation" technique
Expected PW = $ ___ thousand (Round to one decimal place.)
(c) Based on these estimates, which alternative is more economical?
○ A. Alternative 1
○ B. Alternative 2
Transcribed Image Text:**Bridge Construction Alternatives**
A bridge is to be constructed as part of a new road. Engineers have determined that the current traffic volume on the new road will justify a two-lane road and a bridge at present. However, due to uncertainties regarding future traffic, the timing of the need for additional lanes is being studied. Two alternatives are under consideration:
**Alternative 1 - One-stage construction:**
Build a four-lane bridge immediately at a cost of $360,000.
**Alternative 2 - Two-stage construction:**
Start with a two-lane bridge now for $170,000 and widen it to four lanes when traffic demands. The future cost of widening the bridge to four lanes will be $170,000, plus an extra $23,000 for each year the widening is postponed. For instance, if the widening occurs at the end of year 7, the additional cost will be $331,000, calculated as $170,000 + 7($23,000).
**Estimates for the need to widen to a four-lane bridge:**
- **Pessimistic estimate:** End of year 4
- **Most likely estimate:** End of year 7
- **Optimistic estimate:** End of year 8
This analysis considers the anticipated timing and costs associated with each construction alternative to aid in decision-making.
Expert Solution
Step 1: Define Present Worth:
The present worth of multiple cash flows is given as the sum of all the present worths of the individual cash flow series. Present worth is a component of the time value of money which provides us with the value of money today.
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