Question

A state highway department is considering improvements to an existing highway in order to reduce the frequency of accidents on the highway. The type and frequency of accidents on the highway, studied over several years, showed that there were into three classes of accidents: fatal accidents, non-fatal injury accidents, and property damage accidents. On the average, there were 35 non-fatal accidents and 240 property damage accidents for each fatal accident. The calculated costs of such accidents embrace lost wages, medical expenses, and physical damage. Assuming that the average present cost of these three classes of accidents is found to be:

            Fatality, per person                                           $900,000

            Non-fatal injury, per accident                              $10,000

            Property damage, per accident                               $1,800

The death rate on the highway in question has been 8 deaths per 100,000,000 vehicle miles. A proposal to add a median barrier is under consideration. It is estimated that the cost per mile will be $1,500,000, the service life of the improvement will be 30 years, and the annual maintenance cost will be 3% of the capital (first) cost. The traffic density on the highway is 10,000 vehicles per day and the interest rate is 7%. It is estimated that the death rate will decrease to 4 deaths per 100,000,000 vehicle miles. Although other benefits will results from the project, it is argued that the reduction in accidents is sufficient to justify the expenditure. Using benefit-cost analysis, determine whether the median should be constructed. (Hint: find the benefit per mile and assume ratio of the different types of accidents remain the same when the median is constructed)

Answer 1