BC Ratio should come out to 0.79, but I am not sure how. Please assist. A state

Question

BC Ratio should come out to 0.79, but I am not sure how. Please assist.

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: $900,000 $10,000 $1,800 Fatality, per person Non-fatal injury, per accident Property damage, per accident The death rate on the highway in question has been S 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 wil be S1,500,000, 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)

Explanation / Answer

Hi, there are two ways to look at this.

One is calculating the future benefits and costs and discounting it to present and then calculating BC ratio. Let's look at the calculations below:

For 100,000,000 vehicle miles, there are 8 accidents. Your benefit is 4 accidents per 100,000,000 vehicle miles. and for every 1 accident 35 non-fatal and 240 property damage accidents. total benefit calculations below:

Here total benefits have been multiplied by 365 and divided by 10,000 because there are 10,000 vehicles. for 30 years we have these benefits discounted at 7% (interest rate).

Under costs we have 3% annual maintenance cost (every year) and an initial outlay of 1,500,000. Discounting these back to present value should give you what you require here.

Fatality 3600000 Non-fatal 1400000 Property damage 1728000 Benefit / mile per year 2,45,572

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