Steel cable barriers in highway medians are a low-cost way to improve traffic safety without over­stressing department of transportation budgets. Cable barriers cost $44,000 per mile, compared with $72,000 per mile for guardrail and $419,000 per mile for concrete barriers. Furthermore, cable barriers tend to snag tractor-trailer rigs, keeping them from ricocheting back into same-direction traffic. The state of Ohio spent $4.97 million in­stalling 113 miles of cable barriers. Answer the following using both tabulated factors and a spreadsheet function.

Question

(a) If the cable barriers prevent accidents totaling $1.3 million per year, what rate of return does this represent over a 10-year study period?
(b) What is the rate of return for 113 miles of guardrail if accident prevention is $1.1 million per year over a 10-year study period?

Answer 1

(a) In $ million units
Factors: 0 = -4.97 + 1.3(P/A,i*,10)
(P/A,i*,10) = 3.8231
Interpolation between 22% and 24% yields i* = 22.83%

Spreadsheet: = RATE(10,1.3,-4.97) displays i* = 22.80%

(b) Cost of guardrail = 72,000(113) = $8.136 million

Factors: 0 = -8.136 + 1.1(P/A,i*,10)
(P/A,i*,10) = 7.39636

From interest tables, i* is between 5% and 6%

Spreadsheet: = RATE(10,1100000,-72000*113) displays i* = 5.9%