Light Guard system B-C Analysis Outline
Suppose Turlock is thinking about installing a “Light Guard system” that would light up the crosswalk when people press the crosswalk button at an intersection where pedestrian safety has been a concern. The system would cost $125,000 to install and $1,000 a year to maintain (which must be paid at the end of each year). About 1,000 people cross at this intersection twice a day Monday through Friday. The reduction in risk to life and limb to each is estimated to be small, about 1 in a million each time they cross. The interest rate is 10 percent.
a) Over the course of 1 year approximately how many lives would be saved by this project? Using a conservative estimate of the value of a “statistical life” as $3 million, what is the approximate present value of the project’s life saving benefits? Are there any other benefits you would want gather data on to consider in evaluating a project of this nature?
If 1000 people cross 2 x 5 days x 50 weeks that would be about 500,000 crossings per year.
If the risk reduction is 1 in a million then the expected number of lives saved per year would be about .5.
If each statistical life is worth $3 million then this expected benefit would be about .5 x $3 million or about $1.5 million per year.
If it lasts forever the present value would be:
PV life saving benefits = $1.5 mil/.10 = $15 million
It seems likely there would be many other benefits, such as reduced injuries, aggravation, damage to cars and other property, less time dealing with problems from accidents, etc.
b) What is the approximate present value of the project’s costs? What is the approximate net present value of the project based on the data you have? Is the project admissible?
PV Costs = $125,000 + 1,000/.10 = $125,000 + 10,000 = $135,000
NPV = PV Benefits – PV Costs = $15,000,000 - $135,000 = $14,865,000
c) Suppose the technology cost $500,000 to install and even with the maintenance after three years it would have to be scrapped. The salvage value at that point is just equal to the costs of removal. What would the approximate present value of the project’s costs?
PV Costs = $500,000 + 1,000/1.1 + 1,000/(1.1)2 + 1,000/(1.1)3 = $500,000 + 2,486.85 = $502,486.85
d) Using the original installation and maintenance information, now assume the estimates of the value of life and of costs such as installation and maintenance were estimated in current real terms, but the 10 percent interest rate had been in nominal terms. You expect 5 percent inflation. How would your estimates of the approximate present value of the project’s costs, benefits, and net present value change?
Real interest = nominal interest – expected inflation = 10 percent – 5 percent = 5 percent.
PV Costs = $125,000 + 1,000/.05 = $125,000 + 20,000 = $145,000
PV life saving benefits = $1.5 mil/.05 = $30 million
NPV = PV Benefits – PV Costs = $30,000,000 - $145,000 = $30,855,000
e) There’s another project that would benefit a different group of 1,000 people $100 each immediately at a total cost of $50,000. They argue since their project is less expensive and has a positive net present value that you should under take it. Unfortunately, due to insufficient budget you can only do one of the projects. What "distributional weight" would make you indifferent between the projects?
The second project has $100,000 in benefits and $50,000 in costs so the net pv is $50,000.
Let X be the distributional weight that would make you indifferent between the projects.
Comparing this to the original project we need to find X such that
14,865,000 = X 50,000
X = 14,865,000 / 50,000
X = 297.3