A tunnel through a mountain is being considered as a replacement for an existing

Question

A tunnel through a mountain is being considered as a replacement for an existing stretch of highway in south-eastern Kentucky. The existing road is a steep, narrow, winding two-lane highway that has been the site of numerous fatal accidents, with an average of 2.05 fatalities and 3.35 “serious injuries” per year. It has been projected that the tunnel will significantly reduce the frequency of accidents, with estimates of not more than 0.15 fatalities and 0.35 “serious injuries” per year. Initial capital investment requirements, including land acquisition, tunnel excavation, lighting, roadbed preparation, etc., have been estimated to be $60,000,000. Annualized upkeep costs for the tunnel will be significantly less than for the existing highway, resulting in an annual savings of $105,000. For purposes of this analysis, a “value per life saved” of $1,000,000 will be applied, along with an estimate of $750,000 for medical costs, disability, etc., per “serious injury”. Assuming that the cost per “serious injury” is unchanged, determine the “value per life saved” at which the tunnel project is marginally justified (i.e., B-C = 1.0)

Apply the benefit-cost-ratio method, with an anticipated life of the tunnel project of 50 yr and an interest rate of 8% per year
a. $1,340,526.32
b. $1,715,045.47
c. $680,230
d. $706,053
e. $1,721,045.10

Explanation / Answer

Initial capital investment         = $60,000,000 Determine the “value per life saved” at which the tunnel project is marginally justified PV annuity factor @8% for 50 years = 12.23 Savings from medicle cost etc…(3.35-.35)*7500000 = $ 2250000 Let Value per life saved = Z Project will be justified at PV of all savings = Initial capital investment 12.23*(105000+(2.05-0.15)*Z+2250000) = 60000000 2355000+1.90Z = 4904571.49 Z = 1341879.731 Since the Option a. 1,340,526.32 is approximate to the answer Therefore, Option a. $1,340,526.32 is correct option

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