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MoDOT is considering the construction of a short stretch of a four-lane highway. Because that part of town is under development, only two lanes are

MoDOT is considering the construction of a short stretch of a four-lane highway. Because that part of town is under development, only two lanes are needed for the next ten years. Thereafter, four lanes will be needed. Option A is to build a two-lane highway now for $17,825,000 that has annual maintenance cost of $125,000 and then 10 years later put in the other two lanes for $15,222,000 that require an additional $45,000 annual maintenance. Option B is to build all four lanes now for $28,995,000 that has an annual maintenance cost of $170,000. Assume interest rate of 3%. Note that after ten years, both options have the same annual maintenance. To compare the two options, we need only to analyze the time value of money in the first years. Therefore, compute present worth of the two options for the first ten years.

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