A bridge is to be constructed now as part of a new road. An analysis has shown that traffic density on the new road will justify a two-lane bridge at the present time. Because of uncertainty regarding future use of the road, the time at which an extra two lanes will be required is currently being studied. The estimated probabilities of having to widen the bridge to four lanes at various times in the future are as follows. The present estimated cost of the two-lane bridge is $2,000,000. If constructed now, the four-lane bridge will cost $3,450,000. The future cost of widening a two-lane bridge will be an extra $2,000,000 plus $250,000 for every year that widening is delayed. If money can earn 12% per year, perform an analysis to determine how sensitive the choice of a four-lane bridge built now versus a four-lane bridge that is constructed in two stages is to the interest rate. At what interest rate would constructing the two-lane bridge now be preferred?

widen bridge in 3 yrs, probability 0.1

widen bridge in 4 yrs, probability 0.2

widen bridge in 5 yrs, probability 0.3

widen bridge in 6 yrs, probability 0.4