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Cpst stock price today order capstone papers examples for money hillsboro reporter news august 4 this video illustrates benefit-cost analysis based on an example by Watkins so let's look at a proposed extension of highway 101 in California without the extension there'll be 18,000 passenger trips per hour with the extension increases to 24,000 the travel time drops from 50 minutes to 30 minutes the value of time in rush hour is given at $0.10 a minute or $6 an hour there also values for non rush hour their benefits of time saving for the old trips trips that would have been taken anyway that benefit is the rectangle of the consumer surplus analysis or the value of time saved multiplied by the number of trips for new or induced trips we're estimating the area of the consumer surplus triangle and then one half of the time saved multiplied by the number of new trips this is the rule of 1/2 and this gives you the hourly time benefits for the old trip sitting for the new trips and we sum that up and you get $7,000 for the rush hour period and 422 dollars for the non-rush hour trips for a given day and then we're gonna have to sum this up over all the days in discounting so multiplied across the year 260 workdays per year or so 52 times 5/6 rush hours per weekday this is California highway 101 which gives you 1560 rush hours per year and leaves you with 7,200 non-rush hours per year and you multiply those numbers that you have to get your annual time benefits safety can be monetized by looking at live save multiplied by a value of life suppose people accept an increase in the risk of death by 0.1 percent per year in return for $400 higher income per year then we can assume that project that reduces the risk of death e in a year by 0.1 percent gives a benefit to each person affected by it for $400 per year the implicit valuation of a life in this case is $400,000 thus the benefit of the reduced risk project is the expected number of live save times the implicit value of life six times four hundred thousand dollars equals 2.4 million dollars annually sum up the time savings in the reduced risk and you get the total value of benefits per year of 16 point four million dollars similarly we have cost per year how much do you have to lay out near zero you buy the right of way let's say it's a hundred million dollars construction takes four years fifty million dollars a year you don't have any construction costs from years five to twenty nine you also have maintenance costs every year it's a million dollars and then in year thirty you've got the salvage costs so the road has a 30-year life at the end of thirty years how much is the road worth if we shut it down now we might or might not close the road but the other way of thinking about this is that we're selling the right-of-way to the future at that point for a hundred million dollars and then the future can do what it wants they would have to rebuild the road at it at that point anyway or they can close it and turn it into a park so it's a hundred million dollars in the future now the key point is that a hundred million dollars in 30 years is a lot less than a hundred million dollars today because we're discounting it based on some interest rate for this example we assume that the interest rate is 2 percent so we need to compute the present value of benefits which don't start from year five but then run from year five to year twenty nine and we have to work that out so we have an equation for turning present value from taking an annual stream of money and the interest rate in the number of years and convert that into a present value and we were present value in year five and we take the present value in year five which is the future value today and have an interest rate in the number of years and turn that into a present value now this is just the compounding equation 1 plus I to the N how much money do you have this year earning 1% or any one percent on your interest if you put in a dollar one plus 0.01 to the 1 gives you a dollar in one cent next year this is the same equation it's just running them backwards and running them over many many years you can do this in a spreadsheet if you don't want to memorize the equations the only equation that you have to memorize you should be able to derive is the future value of the present value equals F which is P times 1 plus I to the N 1 plus I to the N times the present equals the future value and turning interest and everything else is just that equation in a different format so what are we doing well we are 26 years that we're getting some benefits on we're getting sixteen point three six million dollars of benefits a year at two percent interest for 26 years we've run it through this equation we get a three hundred twenty nine million dollar present value starting you your five and now we've got to take that to the present but present value and your five and turn that into a present value today and that's only worth three hundred and four million dollars that's the net value of benefits we're doing the same kind of thing for costs we have a hundred million dollars in year 30 and that's worth 50 million dollars today a two percent interest we're the present value of the annual stream of cost of construction for four years that's equal to one hundred ninety million dollars today the president value of maintenance costs of 1 million dollars a year for 26 years and that's equal to 20 million dollars and that 20 million dollars in year five we have to bring back to the present which gives us 18 point six million so again you don't need to memorize the numbers of the equations we need to do is a little bit of calculation summing up the benefits and the costs and present value terms the difference between the two is fifty million dollars the ratio of benefits to costs is 1.2 so in this example our conclusion is that we have a net present value that's positive a benefit cost ratio that's above 1 and this can try to do two percent if this is true we should do the project right but if we redo the problem at an interest rate of three percent we get a different conclusion the answer is very sensitive to the interest rate and this is really important you're financing it all if you're selling bonds today to do this not selling bonds for the benefits but you're selling bonds for the construction costs and maybe for the maintenance costs you can maybe guarantee what your interest rate is but if you're not doing that if you're paying this at a current dollar every year interest rates may go up they may go down it looked like a good project at low interest rates it's not a good project at high interest rates and so for different projects you want to consider the interest rate risk and you do a sensitivity analysis you test the answer at low interest rates and a high interest rates and if it's good at both interest rates that's great it's good at one interest rate and at the other it's a much riskier project is that something to consider when you're doing the analysis there are other considerations here the land for instance the market value of the right-of-way we paid a hundred million dollars for it we're a public agency public agencies don't pay property tax so we mentioned tax the public agency is getting a benefit from the tax but the market may have had a different use for the land which would have generated other public benefits that's something to keep in mind that there's a cost to taking property out of the market sphere if or a private road and a private firm we're doing this then the private firm would be paying property taxes on the revenue that the land generated and it wouldn't be much of an issue but because of the public structure the way we've constructed it it doesn't pay property taxes to itself and then we're losing some money to the public sector because of that physical therapy capstone projects cheap The New School.