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 $434,000.

Alternative 2 - Two-stage construction: Start with a two-lane bridge now for $210 ,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$210,000plus an extra $28 ,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 $210 ,000 + 7x($28 ,000) =$406,000

The following estimates have been made of when widening to a four-lane bridge will be required:

MARR IS 9%

Pessimistic estimate Most likely estimate Optimistic estimate End of year 3 End of year 7 End of year 9 (a) Calculate the PW of costs for the different scenarios of Alternative 2 PW pessimistic (9%) = $(thousand (Round to one decimal place.) PW most likely (9%) = $ thousand (Round to one decimal place.) PWoptimistic (9%) = $ thousand (Round to one decimal place.) (b) Calculate the expected PW costs of Alternative 2 using the "three-point estimation" technique Expected PW = $1 thousand (Round to one decimal place.) (c) Based on these estimates, which alternative is more economical? O A. Alternative 2 O B. Alternative 1 Discrete Compounding; i = 9% Single Payment Uniform Series Compound Compound Sinking Amount Present Amount Present Fund Factor Worth Factor FactorWorth Factor Factor To Find F To Find P To Find F To Find To Find A Given P Given F Given A Given A Given F FIP PIF FIA PIA AIF 1.0900 0.9174 1.0000 0.9174 1.0000 1.1881 0.8417 2.0900 1.7591 0.4785 1.2950 0.7722 3.2781 2.5313 0.3051 1.4116 0.7084 4.5731 3.2397 0.2187 1.5386 0.6499 5.9847 3.8897 0.1671 1.6771 0.5963 7.5233 4.4859 0.1329 1.8280 0.5470 9.2004 5.0330 0.1087 1.9926 0.5019 11.0285 5.5348 0.0907 2. 1719 0.4604 13.0210 5.9952 0.0768 2.3674 0.4224 15.1929 6.4177 0.0658 Capital Recovery Factor To Find A Given P AIP 1.0900 0.5685 0.3951 0.3087 0.2571 0.2229 0.1987 0.1807 0.1668 0.1558