Introduction To Transportation Economic Analysis Discounting

Importance of Highway Investment Decisions Resources for public projects are scare What else?

Development Around the west system interchange in West DSM West DSM 1930s WEST DSM 1990s West DSM 2005

Why is it important to make efficient transportation investment choices Public sector investments leverage much greater private sector investments – Transportation costs (travel time) – Locational decisions Public Sector investment impact the cost of development

Lincoln, Nebraska - Population 250K

Des Moines, IA, City Population 190,000, Urban Area Population 500,000

Equivalence For Comparison Purposes – Cash flows through time are made equivalent through the use of interest rates. Interest rates and inflation are not the same. Interest is the time value of money

Definition Constant dollars - real dollars – Constant purchasing power over time Nominal dollars – Fluctuate in purchasing power overtime Real discount rates – The time value of money with no inflation premium Nominal discount rate – The time value of money including an inflation premium Minimum time increment is one year

Definitions Interest rate used to borrow money include Time Value of Money Inflation Premium Risk Premium Profit for lender Inflation – change in purchasing power of money with time Social discount rate – the societal time value of money Opportunity Cost – the benefits forgone by using the resource on the next most efficient use

Cash Flow Comparisons – which on is preferable $10,000 $20,000 Ten Years $10,000 $1,000 $11,000

Present Worth If i = time value Suppose that the value of $100 over 1 year is $4 (no risk) – Then $100 is equivalent to $104 in 1 year or $100 in one year is equivalent to $96 today – 4% = I PW = 100/(1-i)= 96 one year in the future PW = 100/(1-i) 2 = Work problem 1

At 4%, which on is the best deal? What happens when the interest rate is increased or decreased?

Equivalence Interest rates create comparable cash flow Equivalence depends on the interest rate used

Interest Formulas Definition Simple interest - interest is accumulated on the principal but not on the interest. Suppose $100 is borrowed at 10% per year simple interest for two years – the loan is repaid in two years with = $120

Definitions Compound interest – interest is paid on the interest. Suppose you were loaned $100 at 10% per year compounded annually – at the end of two year, you would be owed * = $ *(1+i)^ N = F

Definitions Nominal versus effective interest – Nominal is the arithmetic sum of interest charged at a rate less than one year – Nominal interest rate of 18% compounded monthly is 1.5% per month. $100 at a 18% nominal rate compounded month is 100*( )^ 12 = $ – The effective rate is 19.56% per year

Formulas

Formulas Continued

Discounting problem Example: an operator of a taxi cab company has the option of purchasing two types of vehicles. On type is a cheaper model and has a shorter expected life while the other is more expensive and has a longer expected life. The required information is listed below: (project level analysis) Type 1Type II First cost = $600,000First costs = $800,000 O&M = $100,000/yearO&M = $80,000 Life = 3 yearsLife = 5 years Salvage = $40,000Salvage = $50,000

Project with dissimilar lives Present worth analysis – pick a minimum common multiple of lives Present worth analysis – end at common year and calculate residual value Estimate the annual uniform equivalent cost – and compare one year

Present worth Comparison At an interest rate of 10%, which alternative is the most cost effective? First pick a the least common multiple of years for comparison – 15 year $600,000 $100,000 $40,000 $600,000 $100,000

$80,000 $800,000 $80,000 $50,000 Work Problem 2

Sensitivity Analysis Questions At what interest rate are the present worths about the same Why did you have to change the interest rate upwards or downward to make they equivalent? Perform Sensitivity analysis on problem 2

Break Even Analysis How high does the interest rate have to go before Type I is preferred option Break even point Why do high interest rates favor the low cost option?

Redo the analysis using a uniform annual cash flow

Gradient Are Commonly Used in Transportation evaluation problems Gradient can be expressed as a percentage – Truck traffic is expected to grow at a rate of 2 percent per year on I-80 Gradient can be expressed as a fixed growth rate – Truck traffic on I-80 is expected grow by 100 vehicle per year

Percentage Gradient If the widening of I-80 is expected to save the average truck traveling from boarder to boarder 15 minute and there are an average truck per day of 12,000, how many truck minutes will be saved over the next 20 years, assume an average annual increase in truck traffic of 2 percent per year. Do problem 4

Economic Evaluation And Transportation System Development Very seldom do we develop more than an increment change to the system – Since travel is possible between most any two points, improvements simply reduce the cost of transportation – Typical benefits Reduced travel time Reduced crash morbidity and mortality Reduced environmental degradation

Example – Six lane I-80 I will cost approximately $ 3 Billion to Six lane all of rural I-80. Do the trucker travel time saving warrant the construction. – Assume a travel time cost of $30 per hour – Assume a 4 percent social discount rate Do problem 5

Transportation Benefits Direct benefits – Travel time savings – Safety saving – Trip reliability improvement – Trip quality improvement (e.g., smooth pavement, quieter, more esthetically pleasing, etc.) Indirect benefits – Economic development – Property value increases

Transportation benefits Reduced externalities Externality are costs that no one pays – Air pollution – Noise pollution – Reduced wild life

Transportation Benefits Transfers – If a fast food restaurant locates at the new interchange on I-35 have jobs just been created or are they transferred from somewhere else. – Was economic development created because of the transportation improvement or just transferred from somewhere else.

Uncertainty and the future Transportation Facility are typically long lived facilities – Great deal of uncertainty in traffic forecasts – Great deal of uncertainty in changes in technology – Great deal of uncertainty in sustainability of current patterns

Ways of dealing with uncertainty Typical discounting of future benefits and costs weights distant less heavily Evaluate several likely scenarios – Under risk – where the likelihood of an outcome can be assess (probability of an outcome), use the expected value – Under uncertainty – where the likelihood of an outcome is unknown, us a decision rule like Max- Max of Mini-Max

Expected Value Suppose you have to invest in one location and you two project alternatives to select between. High Demand p = 0.5 Benefit 1,900,000 Low Demand p= ,000,000 High Risk Location Low Risk Location High Demand P = ,000 Low Demand p = ,000

Treatment of Risk Expected Value High Risk = 0.5(1,900,000) + 0.5(-1,000,000) = $450,000 Expected Value Low Risk = 0.7(500,000) + 0.3(200,000) = $410,000 However, people and entities are know to be risk adverse. Expected value assumes that risk is linear.

Risk Adversity Certain Money Equivalent (subtracting out risk premium) p 1 0 Expected Value CME $ Expected Monetary value Certain money equivalent

Decision Under Uncertainty Maximin and Maximax Rules – Maximin rule – select an alternative on the basis of comparing the lowest possible returns of each of the alternatives and choosing that alternative which has a minimum return larger than the minimums of the others.

Decision Making under Uncertainty Maximax Rule – Select the alterative having the largest possible return. Example: Suppose there are four alternatives with four possible outcomes (e.g., high, high medium, low medium, and low demand)

Returns from alternatives Alternatives EventA0A0 A1A1 A2A2 A3A3 A4A4 E1E1 $0$5.84$6.60$6.50$5.70 E2E2 $0$7.15$6.80$6.65$6.40 E3E3 $0$7.40$7.45$7.80$7.65 E4E4 $0$9.00$8.30$8.75$9.15

Decision making under Uncertainty Maximin Decisions A 0 A 1 A 2 A 3 A 4 $0$5.84$6.60$6.50$5.70 Maximax Decisions A 0 A 1 A 2 A 3 A 4 $0$9.00$8.30$8.75$9.15