cost-benefit analysis notes - carlos grandet

8/3/2019 Cost-Benefit Analysis Notes - Carlos Grandet

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Annotations on a class of Cost-Benefit Analysis

Carlos Grandet

December 2011

1. Introduction

We live in a world of scarce resources. This force us to always try to get the most outof the things we have or the activities we do. However, accomplishing this is not an easytask. You never take a course in school on decision-making and most people in collegewill probably go out without taking a class that will be give them a greater orientation inthis topic. So, in the end, people are left with their very own intuition to decide what arethe actions that will benefit them the most. -It is rather natural - some people will saywhen asked on how is their internal decision proccess made. However, it does not mean,that is flawless. Most people are unaware of the costs that an action implies or tendto overestimate the benefits. In the end, this lack of analysis will probably turn againstthem. One or two individuals might not do any damage to the society, but now imaginea government simply doing an inappropiate evaluation of their projects. The current

economical crisis has put in evidence the need of governments to wisely choose theirpolicies and the terrible consequences of not doing so. These events pose an interestingchallente to all people that wish to properly evaluate a project. In this summary, I willdescribe the most important things I learned to be able to analyze and evaluate differenttypes of projects.

2. Project Profile

When it came to the creation of a project profile I think that there are three conceptsthat really caught my attention. The first is a simple one, but I had not stop to think

about it. The first question you have to ask is who are you doing the profile for. It isnot the same thing to analyze a house mortgage from the bank perspective than fromthe household one. The bank will see the money borrowed as a cost and the interestsreceived as a benefit. On that basis, it will take a decision on wheter to give the mortgageor not. However, the household will have greater costs because they will have to put someadditional money besides the loan one. On the benefits, it is not as clear what are thebenefits because unless they are selling the house, it is hard to estimate how is anyone

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benefiting from buying a house for themselves. All we can presume, is that if the personbuys the house, it is because their benefits are greater than their costs. The problem canbecome more complex if we include the societys perspective. The existence of externalitieson a house purchase also makes this point relevant. A tax on housing, for instance, couldbe a benefit in terms of wealth redistribution; a subsidy on the purchase of this house,is a cost to them. In the end, the same project can have completely different approachesdepending on which is your viewpoint. Will the household get the house? If so, will thesociety be affected or benefited? Which of the two benefit is more important? All thesequestions arise from simply understanding that there different perspectives at which youcan look at something.

The second concept I learned was more of a practical way of doing a financial analysis.I was thought in my other course to take the net present value of a project to zero. Therewas not a profound reasoning on the why, I guess is just the way they do it in books and

the people do not stop to think in the consequences. However, I learned that a simpleranalysis is to take all the flows to the period in which you start receiving benefits (supposeit is time t). By doing this, you turn the Net Present Value a monotonically decliningfunction of R (the rate of discount) that is easier to interpret. This is because, as Rincreases, the NP Vt will always decrease. On the contrary, when you take all the flows tothe time t = 0 then the N P V0 will have a parabola-like behavior, which will make NP V0to first decrease and the start to increase as R increases.

Graph 1. NPV on time t versus NPV on time 0

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The third concept was on the use of the IRR. The common idea of always taking theproject with the highest internal rate of return can have exceptions. This is because, youalso have to consider the scale of the project. A profile can yield a high IRR but when itcomes to real benefits they might low, because the cost is equally low. This is an example:

Project T=0 T=1 IRRA -1 2 100 %B -100 140 40 %

There were two other concepts I learned when creating a profile of a project. Anex-ante analysis of a project implies uncertainty in the flows estimation. For instance in

the case of a cashflow that depends on the price of a volatile commodity. The commonstatistical figures to deal with this are the mode, median and mean. A common mistakewhen dealing with this is to ignore the expected value and price outliers. A better approachis to try to incorporate the expected value by assuming a specific distribution functionand running Montecarlo experiments. An easier approach is simply to include differentscenearios based on fundamented price speculations about that specific market.

Another interesting concept is how to deal with a change in the discount rate across theproject implementation. Sometimes, the scarcity of funds might cause that the long-runinterest rate be lower than the short-run one. In order to include this into your analysisall that is needed is to assume different interest rates across time.

(1) NP V0 =F1

(1 + R1)+

F2(1 + R1)(1 + R2)

+F3

(1 + R1)(1 + R2)(1 + R3)

3. Inflation, scale, timing and replacement

The issues covered in this section were all new to me. They gave me a broader pers-pective of the cost-benefit analyisis I have learned which had always revolved around theflow discount and NPV value calculation but never went deeper than that or asked moreinteresting questions such as: How do you include price uncertainity? What is the rightscale of a project? when should a project be postponed? In the end, the greatest benefit I

get from these concepts is the ability to create an analysis that models with more accuracythe real world.

3.1. Scale of a project

The problem of the size that a project should have is a common one and the answerthe bigger the better clearly does not apply in this case. The most important principle

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when choosing the scale of a project is that each incremental change in its size shouldbe treated as a project by itself. This means, that the decision of changing the scaleof a project should be accompanied by an analysis of the present value of the marginalbenefits compared to the marginal costs. The goal when choosing scale is to have thatone which has the biggest NPV. Therefore it become an analysis of choosing the projectthat maximizes it. You could see NPV as a function of the scale and therefore you willchoose that point in which the incremental marginal NPV is zero.

Graph 2. PV vs scale

An important observation of this graph is that it is comparing the NPV of differentscale projects that have the same rate of return and period of time. To change the rate ofreturn, you could do an analysis with the Internal Rate of Return (IRR). The basic ideais that each increment in the scale of the project has a unique IRR. If this idea holds,then the optimum scale will be the one at which the IRR for the incremental benefits andcosts equals the discount rate used to calculate the net present value of the project. Thisinternal rate of return is called the marginal internal rate of return (MIRR).

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Graph 3. MIRR and IRR

These graph shows the relationship between the IRR and the MIRR. When the MIRRis greater than the IRR, then expansions of the project will cause the IRR to increase. Onthe contrary, when the MIRR is lower than the IRR, the overall IRR will decrease. The

scale where the IRR=MIRR is always the scale at which the IRR is maximized. However,it is important to note that this is not the scale at which the net present value of theproject is likely to be maximized. The optimum scale is where MIRR=IRR

3.2. Inflation

The issue of inflation is usually ignore in a cost-benefit analysis and my previousexperience with it was not the exception. The reason for this omission is because thecommon way of controlling for inflation, the Laspeyre Index1 does not consider the relativeprices. This means for instance, that the benefits of selling a good that increased its priceover the years, or the costs of buying the same good. This is particularly important in

some economies that depend on good with a high degree in volatility such as the oil inMexico.

A solution to this problem comes with the introduction of relative prices in youranalysis. This is done through an index that divides the price of the relevant goods by a

1The Laspeyre Index is defined as PiQ0P0Q0

where Pi Q0 is the Real GDP and P0 Q0 is the nominal

one

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price index such as the CPI or the GDP deflator.2 By doing this you can control for theinflationary pressures on the nominal prices and at the same time ensure that the changesin real prices caused by the market interaction are reflected.

If we define an economy with n goods, Pt as the price index in time t, Pit as the pricefor the good i in time t and i the share of the good i in the economy then:

(2) Pt = ni iPit

where

(3) ni i = 1

By applying (2) in (1), this can be converted to

(4) ni iPit

Pt= 1

The estimation of this figure acquires a different difficulty according to the momentin which the analysis wants to be made. If it is a ex-post analysis, then each of thevariables is easy to compute because they had already been observed. However, an ex-ante analysis of a project will require an estimation, the best way to do it is to directlyestimate the equation Pit

Ptwhich are the relative prices. To estimate this ration we can use

the trends in the price of the relevant products. For instace, you can empirically observethat historically the price of a car tends to decrease with time while a computer tends toincrease. In general, a decrease the trend in the price of a good is related to the intrinsicchange in the productivity of a good or service. Therefore, the relative prices can adjustto that.

The application of this concept in an analysis of a project will have the followingstructure:

(5) Ft = Pit

PtXit Wjt

PtLjt

where Xit represents the outputs and Ljt the inputs.

2The difference between the two is that the CPI is a price index created from a consumers A basket

and the GDP is created from a producersA basket

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3.3. Replacement

So far, the basic concept required to do any analysis is the margin. The extra benefit of

choosing a project or an increase on its scale should be compared to the extra costs. Thisapproach can also be used for determining wheter an asset or good needs replacement.An example could be a familys acquisition of a new refrigerator.

The possible choices to which the family faces are:

1. Choice A) Replace the old fridge. Buying a new fridge and selling the old one.However, the residual value is a sunk cost that should not be taken account to makean economic decision.

2. Choice B) Buy a new fridge. Buy a new fridge and keeping the old one

3. Choice C) Dont do nothing. Keep the old fridgeThe payoffs would look like:

(6) P VA = PN + P V BN

(7) P VB = PNRV0 + P V BN+O

(8) P VC = RV0 + P V BO

Where RV0 is the residual value of the old fridge in time 0. The winning optionmust satisfy that P Vw > P Vi for every iw. In cases B and C, the present value ofthe residual value is subtracted because it is implicitly included in the present valueof the net benefits of the old fridge. As we already said, sunk costs are irrelevant.

For example, lets suppose that option B is the winner, then:

(9) P VB P VA > 0P VO|N > RV0

(10) P VB P VC > 0P VN|O > PN

When the marginal benefit of the new asset is greater than its cost, then it is ap-propiate to replace the good. A more complex example will include the externalitiesof getting the refrigerator into the cost.

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3.4. Timing

The decision to postpone a project is also an important idea to consider in a projectanalysis because of the possible gains obtained from it. The basic idea to determinethis is to is find the time in which the present value of the benefits not perceivedby the postponing of the project is equal to the opportunity cost of the capitalthat could have been invest. A smaller benefit lost than the capital gain in themoney not spent means that the the project should be postponed. For example, ahighway project could yield different results according to the traffic flow today andthe expected one.

Graph 4 Benefits of postponing

The analysis of timing requires that the period to which the Net Present Value isdiscounted be the same for all the scenarios. This is to guarantee that the NPVare comparable among each other. Therefore, this is a case in which the method of

taking a NPV to the point in which it start receiving benefits should not be used.

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Graph 5.Maximizing of the NPV

The modelling of the timing problem is as follows: Suppose k is the initial invest-ment or initial costs of a project, and N P Vt represents the net present value ofconstructing in period t. Then, Bt is the net benefit of the project in the year t and

NP Vt = t = 1TBtk. The best timing is where N P Vjt > NP Vjh with th for everyh. If initial costs depends on the time so that k varies in each year then the cost ofpostponing is expressed by kt kt+1Bt+1 + rkt and appropiate time would be theone that gives the minimum value to that equation t.

This method assumes the existence of increasing benefits, however, when this is notthe case, then you have to check if the NPV is greater than zero. If it is, the methodmantains its properties.

4. Distributional Weights

There are three fundamental characteristics that apply to welfare economics

a) Benefits being measured at each step by demand price (willingness to pay)

b) Cost being measured at each step by supply price (willingness to supply)

c) Aggregation of these two across individuals regardless of who is enjoying thebenefits or costs (adding up)

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However, there are social concerns with the last point because of different valuesfor different people of a certain good. If you ask anyone, who gets more utility froman incremental dollar?, they will favor the poor instead of the rich. This problemcreates the idea that a dollar has a different value according to whom it goes.

Graph 6. Marginal Utility of Income.

This situation has led to the existence of a distributional weight that measuresbenefits and costs differently according the the family or individual it affects; usuallythe poor ones. A great limitation, however, comes from the fact that people do notknow what weight to assign and it is done in a rather hollistic manner. The resultsof this approach can cause a proyect to be approved despite having a negative value.

Unweighted Avg. Weight WeightedPresent Value of Benefits 500 1.5 750Costs -1000 .5 -500Net Present Value -500 250

These creates a great efficiency problem that increases as you weighted more thebenefits of the poor people. A better illustration of the efficiency problem can beanalyzed with different weights according to income. Suppose that the dollar ofa rich family is worth .5, and for a poor family it is worth, 2. Therefore, taking

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32 dollars from the rich family and giving 8 to the poor one will be appropiatebecause they will have the same value (32x.5)=16 and 8x2=16). This creates a lostof efficiency of 75 % that is acceptable

The distributional weights approach also creates a different analysis for tax

5. Basic needs versus Distributional Weights

There appears to be the confusion that basic needs and distributional weights arejust two similar approaches to welfare distributional issues. Nevertheless, they arequite different. Distributional weights come from an individual framework in whichthe marginal utility of certain individuals has a greater value than others. Basic

need externalities refers to the benefit that people get from the improvement ofthe circumstances of others. In other words, they have a willingness to pay for thediseased to be heal, the hungry to be fed, etc. The idea of Basic Needs externalitiesis well illustrated when analyzing the in-kind and cash transfers. It has been de-mostrated that in terms of utility giving cash transfers is better than in-kind ones.However, most of the transfers given today are in-kind (food stamps, public educa-tion, a father paying for his children school rather than giving him the money to

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use it) because the donors are better-off when they know that their money is goingto be used for something.

Basic need externalities therefore become a way in which the consumption of otherpeople or the attainment of certain states enters into the utility function of donors.Therefore, this people are receiving a benefit from the improvement of others, apositive externality. The analysis followed is the same as that of other externalities.

Graph 7. Basic needs externalities approach

This approach, however, poses a great problem which is the fact of how to valuethe positive effect of an externality in the society. (The slope of the social demandcurve in graph 3.

6. Economic opportunity cost

Whenever you are evaluating a bussiness project you consider the inflows and theoutflows throughout the years and then use an interest rate which is either the costof borrowing the money or the alternative return to the investment that moneycould have in another project. Some technicalities set aside, the evaluation is fairlyeasy because the profile is clearly defined. Money coming in is a good thing andmoney going out is a bad. However when you are considering a public project, the

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profile canAt be done so easily. Calculating the benefit of a better-educated laborforce or a healthier population is often difficult and inexact. To solve this issue theconcept of economic opportunity cost (or shadow prices) is useful.

A different approach to the three postulates of welfare economic can be:

a) Competititive demand price measures the benefit of each marginal unit to thedemander

b) Competitivie supply price (marginal cost) measures the opportunity cost ofeach marginal unit from the standpoint of the suppliers.

c) To measure the effect of a project to society, you take the differences betweencosts and benefits.

These ideas have made possible the analysis of the efficiency costs of a tax, theproblems of the monopoly and other contributions such as the Ramsey rule foroptimal taxation. Altough they have met with criticism that they donAt controlfor multiple equilibria and the fact that they do not follow a similar result if theorder of the policy is changed. Nevertheless, if you take them as only postulatesinstead of absolute truth then you can do interesting analysis

One of the analysis that is supported by this ideas is that of the social opportunitycosts in a market setting. The general concept is this: when a new demand for agood or service is generated, there are only two sources from which that demandcan be satisfied - increase in total supply and the displacemente of other demanders.The welfare postulates indicate us that the increased supply should be evaluated atthe supply price and the increased demand at the demand price

In a market equilibrum without distorsions, both prices are the same and thereforemarginal costs equal social costs. However, in the presence of distorsions such as atax, these two prices are differen and the social opportunity cost has to become aweighted average of them. In this context the following equations hold:

If pd is the demand price, ps is the supply price and D is the distorsion we can saythat:

(11) pd = ps + D

and, because the social opportunity cost of one unit is a weighted average

(12) f1pd + f2ps

(1) can be expressed as

(13) (f1 + f2)ps f1Di

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However, because f1 is just the measure of displaced demand, it can be expressedas

(14) ps + DiXi

Another way of looking at this is through an example with specific taxes. Assumingwe have two taxes tc a capital income tax and tp a personal income tax, we willhave three rates of return. p, the gros return to investment, i = p tc, the marketrate of interest and r = i tp the after-tax return on investment received by savers.In this market for capital, the money raised fo a project will come from displacedinvestment, with an opportunity cost of p and from stimulated saving, with anopportunity cost of r.

This means that the social opportunity cost of capital will come from the expression:

(15) f1p + f2r

which can also be expressed

(16) f1(i + tc) + f2(i tp)

given that,

(17) f1 + f2 = 1

This is equal to

(18) i + f1tc f2tp

That is, a market rate of interest adjusted for distorsions.

A graphical analysis of the project shows the following:

Graph 9 Economic Opportunity Cost

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The analysis advantage is that it can be applied to the changes in more than onegood in the demand and supply side. In the case of the market for foreign exchange,we will have Em as the market exchange rate for the dollar. Then, the demand pricewill be Em + Tj where Tj is the tax on exports j. The supply price will be Em + Skwhere Sk is the subsidy on imports k. The end result is an expression for the socialopportunity cost on foreign exchange:

(19) jfj(Em + Tj) + kfk(Em + Sk)

which can be converted with (8) to

(20) Em + jfj Tj ) + kfkSk

which is equal to the market rate adjusted by the distorsion.

An example

Assume we have the following tax composition:

Rate Adjusted Property Tax Corporate Tax MarketCorporate Investment 14 % 2 % 6 % Non-corporate Investment 8 % 2 % Housing Investment 6 % 2 % 2 % (home subsidy)

A graphical representation:

Graph 10. Opportunity Cost of Investment

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In this case, the opportunity cost of capital is given by the following fcpc+fnpn+fhphwhere the weights are given by fc = ,30, fn = ,10 and fh = ,35. Then,

(21) ,3(,14) + ,1(,08) + ,35(,06) = 7,1 %

On the savings side, the interest rate is given by r = i(1 tp) In here we can assumethat the rich households have an interest of 50 %, the middle ones of 33 % and notax for the poor ones.

A graphical representation:

Graph 11. Opportunity Cost of Saving

In the case of the same 6 % market interest rate, the interest rate for the rich is,06(1 ,5) = ,03 and for the middle is ,06(1 ,33) = ,04, assuming a weight of 10 %for the rich, 10 % for the middle and 5 % for the poor, then

(22) ,1(,03) + ,1(,04) + ,05(,06) = 1%

This means that the opportunity cost comes from both the savings and the invest-ment and is 7,1 % + 1 % = 8,1

The analysis of the open economy creates a different result, because it allow us to includethe capital funds from abroad. Now, the economic social cost also includes the marginalcost of foreign funds (MCf) making the equation;: f1p + f2r + f3MCf

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The marginal cost becomes the economic opportunity cost of social capital because of tworeasons:

a) The capital market for international funds is not perfect. This means that thecountry can draw funds from abroad but not at the same price. The supplycurve is not infinitely elastic but with an upward slope

Graph 12. Capital International Market

b) The upward slope of any supply curve means that the marginal cost (of get-ting an extra unit as one moves along that supply curve) is higher than thesupply price. Another way of analyzing it is by assuming that the country hasmonopsony power for the funds destined to that country therefore:

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Graph 13. A monopsony case for the borrowing of funds

This can be further demostrated with the following equations

(23) (pq) = pq + qp

(24) (pq)/dq = p + q(p/q)

(25) (pq)/dq = p(1 + 1/

Then, marginal cost = average cost (1 + 1

)

Since the supply is upward sloping then the marginal cost is greater than theaverage cost.

An appropiate estimation of the economic cost of foreign funds needs to recognize thatthey have a behavior that is not as straightforward as the domestic. This is because thesupply of foreign savings is more volatile than the domestic one. The estimation shouldtherefore consider both equity and debt financing and should be expressed in real terms.s

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7. Applications of economic opportunity cost in fo-

reign exchange and labor markets

The same analysis can apply to other markets rather than the capital market. For instance,foreign exchange. Suppose Mexico has an import tariff of 20 % and an exchange rate of10 pesos per dollars. New demand for dollars will come from displaced imports and newlyestimulated exports caused by the increase in the price of the foreign money. We havea project that buys $100 dollars from which $60 come from displaced imports and $40from stimulated exports. Then, the project will pay 1000 pesos for the 100 dollars bought.However, these do not consider the lost of 120 pesos from import tariffs caused by the 60dollars of displaced income (60 10 ,20). Therefore, the economic cost of the project is1120 pesos and of a dollar is 11.20 pesos. This extra cost becomes an externality of the

project. Similarly, any selling of foreign exchange will bring a benefit of 11.20 pesos. Inthe end, a foreign exchange premium is created of 12 %

Labor in cost-benefit analysis has always been subject of errors derived from consideringjob creation as a benefit. However, they fail to see that such as capital or material, laboris a cost to a project. The false idea of job creation is brought down by the fact that theproject should not be measured against nothing but rather the second best alternative.It is therefore important to analyze labor just as the previous markets. In such case, anadded demand for labor will displace the demand and stimulate the supply.

In order to do a proper analysis of the economic cost of labor we must consider certainprinciples

a) People have a different supply price according to where they work

b) The opportunity cost is the supply price after taxes and deductions have beenmade.

c) When answering the question of where jobs come, one should analyze an withand without project scenario to determine wheter the supply comes from other

jobs or from newly stimulated entrants.

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Graph 14. Opportunity Cost in Labor Market

One way of approaching the economic opportunity cost of labor is through the comparisonof the same job in different places

Chicago Alaska HawaiiMarket Wage 50 200 30Incom Tax 5 50 0 %Sourcing Fractions (.8,.1,.1) (.4,.5,.1) (.3,.1,.6)

This means that the economic opportunity cost of labor is different in each city andis given by the available income of a worker in a city, plus the loss in taxes that thedisplacement of other workers caused. Chicago

(26) 50 5 + (,8x5 + ,1.x50 + ,1x0 = 54

Alaska

(27) 200 50 + (,4x5 + ,5x50 + ,1x0) = 177

Hawaii

(28) 30 0 + (,3x5 + ,1x50) + ,6x0 = 36,5

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8. Using the economic cost of capital as discount rate

In the public projects evaluation there is a debate of which is the appropiate discountrate that should be used. There is a division between the ones that one to use the socialopportunity cost of capital mentioned before (w = f1p + f2r) and those who say that themarginal rate of time preference (r) should be the proper discount rate. The intuitivelyreasoning is that the second discount rate does not consider the distorsions existing inthe market which also affect the marginal productivity of capital in the private sector (p).However, the reality is that a correct estimation using any of these methods will yield thesame result:

Assuming we have a project that requires 1000 dollars, has the values p = ,12, i = ,06and r = ,04 and the weights of f1 = ,75 and f2 = ,25, then we will have the followingflows

Period 0 1 2 3 4 ...Stimulated Savings 750 90 90 90 90 ...Replaced Investments 250 10 10 10 10 ...Total 1000 100 100 100 100 ...

In this case the discount rate is ,12(,75)+ ,04(,25) = ,1 = 10 % which is also the minimumreturn rate for this project to have a cost equal to its benefit.

When you are doing, the second approach you will only consider the r = ,04 rate, howeveryou will use a way for compensating for the distorsions. This method is called shadowprice and it consists on a lower bound for economic success of a project.

When you are using the second type of discount rate you will take the perpetuity of theannual payment for both the investment and the savings:

(29)90

,04= 2250

(30)

10

,04 = 250

Therefore, the present value is 2500, which causes the shadow price to be 2.5 because itrepresents how many times should the 1000 borrowed needs to multiply itself overtime tohave costs equal to benefits.

Despite both procedures being able to control for distorsions, the first method is preferredfor three reasons:

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a) The second method is harder to communicate because the shadow price appearsto be randomly generated. On the other hand, w is easier to sell to the audience

b)

c) It is easy to consider different rates for r when using the first method. This isbecause it can also be interpreted as jfj(Em + Tj) + kfk(Em + Sk). On thecontrary, because the justification for r comes from intertemporal consumptiondecision, varying across different groups of consumers will mean that that thebenefits of a group should be measured at their own rate. This causes problemsof evaluation because if you outweight the costs of a two different projectsin two different neighborhoods against their benefits, different results can beobtained depending on the discounting period even though both projects havethe same benefits. The group with the lower discount rate will have a biggerNPV than the the group with the higher one, but if you take the future value,the contrary will occur.

9. Labor Market Issues

Graph 15. Dual Labor Market

In this graph we see the effect of a dual labor market, which is a common situation whenthere is a big enterprise that will be paying a higher salary than the one existing in the

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market. As you can observe, this causes two different supply curves, the one of the peoplebeing hired by the enterprise and the workers left.

Graph 15a Distribution of protected workers

The justification of this new supply curve of people left comes from the fact that the bigenterprise does not distinguish between the different reserve price of the supply, so theychoose anyone in the supply curve which has different wage ranges. Therefore, it causespeople in every of the wage ranges to be left and the ones that had a higher supply pricewill not be willing to work in the regular market.

Graph 15b The existence of quasi-voluntarily unemployed.

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The labor market will distinguish between two people, the ones that got a job at themarket wage Lf and the ones that are not wanting to work because they want the higherwage. The second type of people will be called quasi-voluntarily unemployed Vqu. In theend, this will cause two economic opportunity costs:

The cost for the regular workforce

(31) EOCLf = wf

The cost for the big enterprise workforce

(32)Lf

Lf + Vquwf +

VquLf + Vqu

wf + wp2

A common problem experienced in employment policies is to try to reduce it by tellingenterprises to produce more jobs or having a decree saying they should increase theirworkers by a certain percentage. However, this often ends up creating more unemploymentbecause the increase in jobs displaces people that werent in the workforce. An increase inthe job demand will increase the wage and bring more people to the city to work. In theend, this will cause an increase in the supply of labor that will move the total amount ofpeople working but preserve the unemployment rate and the expected earnings.

Employed Unemployed Full Employment Expected EarningsInitial Equilibrum 800 200 1000 4With 100 jobs moreShort Run Response 900 100 1000 4.5

Long Run Response 900 225 1125 4

The application of the theory in actual projects helped me to connect the concepts andhave a better understanding of them.

10. Transportation: Highway Projects

The first step is to analyze the profile of the project. Therefore, the appropiate questionis why and for whom are we doing the project? An important concept is that a highwayproject is not usually the construction from scratch of a project but the improvement of

a road. THe objective is to reduce the transaction costs of the people that were using acertain path or road. However, if the cost reduction is the only criterion use to evaluatethe project, then all highway projects should be approved because they will decrease tosome degree the costs of someone. The correct approach is to analyze if the improvementis justified. This is determined, for example, through the growth of traffic; if this growthis high enough that the transaction costs of the users is higher than the cost of the projectthen it should be implemented.

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Let Ci be the private cost that an individual pays in order to use the road (gasoline, tires,etc). Then, suppose that the improvement change the cost from C0 to C1. The benefitcan be divided into the one of the the existing users, V0(C0C1), and that gained by thenew induced traffic, 1/2(V1 V0)(C0 C1).

However, asides from the costs an individual pays, there are also social costs. This is thetime that people spend on a highway. As a bigger car volume in a highway is related to alower speed, then traffic congestion in a highway also means time loss by user. The saveon time that the highway improvement will bring, should therefore be also measured inthe benefits.

Let H be the value of the vehicle-hours. Let S be the speed. Then H/S is the value ofa vehicle mile. This value means that as speed increases, a vehicle mile gets cheaper. LetT C represent the total time cost per mile. Let V be the volume. Then, we asume that

speed is a function of volume with the following values:(33) S = a bV

we can also write the Total Cost function as

(34) T C = V H

S

if we take the derivative with respect to V we have the marginal cost:

(35)T C

dV= H

a

S2

The percentage speed deficit can be defined as the percentage that the marginal socialcost, MC is above marginal private cost AC. This is,

(36)(MCAC)

AC=

(a S)

S

The externalities derived from an incremental vehicle are shown in the following graph:

Graph 16. Externalities from incremental vehicles

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To eliminate the externality, then we could introduce a toll fate that acts as a tax andequals the marginal private cost to the marginal social one.

Graph 17. Internalizing the externality.

The problem is that DPC curve is changing because the demand for traffic in the road willbe different at different hours of the day. So it is hard to find an optimal tow. However,with new technologies maybe in the future this will be a reality.

A last issue to be solved is the assigning to a value of time. By doing this you canhave a complete profile of the flows of a project. A method proposed by Thomas Lisco,took advantage of different alternatives faced by transportation consumers to estimatetheir opportunity cost, In the City of Chicago, there were two ways of getting to thedowntown from a suburb area. Using the expressway and paying to do it or taking publictransportation. There was a time save related to the first option. The ideas was thereforeto analyze the difference in costs and time spents from using each alternative.

Once you have the difference, the probability of going by car be P C, is estimated usinga regression of P C = + (timesaved) + (extracost) + (income) + u

Once you have the coefficients, the next step is to set the probability equal to 1/2 in orderto get the indifferent agents between both options. Once you do this you solve for theratio Time Saved/Extra Cost to get the value of time through different income levels.

An important lesson that I learned is that the biggest incentive to improve a route isstrictly related to the flow of traffic. If the increase i traffic does not justifies the costs,

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then there should not be a road constructed. +

11. Electricity

The evaluation of any electricity projects requires the use of the least alternative costprinciple.This principle states that one project should not be assigned benefits greater than theleast alternative cost one would have to incur by providing an equivalent benefit stream ina different way. This principle is a use given to the opportunity costs, because it considersthe alternative scenario as the benchmark to evaluate a project. If we donAt use thisprinciple then you will have an incorrect project appraisal. For instance, if we assumethat the demand for electricity rises faster than the overall generating capacity, we willconclude that it is extremely important to make the project altough there was en ever

rising price of energy. Similarly, we can conclude that the project is terrible if the price ofenergy does not rise. In the presence of this price volatility, the comparison between thecreation of a new plant and the retirement of another should be give a method to measurethe profile of a project. To keep the analysis simple, an assumption for a system managedefficiently will be made. This means that the objective is to use the most efficient plantfirst and move on from there.

As with other projects, the cost-benefit profile analysis requires a forecast to be made onhow the whole electricity system will operate in the absence of a project. From there, wewill try to estimate the cost of the different alternatives to determine the best one. Thisis a brief resemblence of some of them:

11.1. Homogeneous Thermal

This type of plants use the same thermo-energy, for example, fuel. The homogeneousthermal plan is the benchmark of the project. We measure the capacity of a plant inkilowatts (KW), which is the potential power of the plant. When the demand for energypushes beyond the actual capacity, it is necessary to have additional thermal plants

In this analysis of the project, the peak hour requires an special analysis because itrepresents an extra demand that we are not capable of supplying. Thia means an increasein the variable costs for energy, therefore, there should be a different price charged in the

peak hours. In terms of the project, we will want to spend in extra capacity if the cost issatisfied.

Example Suppose that costs are $800 per KW, the relevant discount rate is 10 %, andthat the relevant depreciation rate () for this equipment is 5 % per year. Then in order to

justify the addition of a new KW of capacity, the necessary benefit is (0,1 + 0,05)($800) =$120 per year. This comes come from the sale of energy during the peak hours at a different

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price. If the peak hours per year were 2000, then the relevant peak-time surcharge wouldbe 6 cents ($120/2000) per kwh. Note that 4 cents would be the charge in off-peak hoursand 10 cents during on-peak hours.

11.2. Run on the Stream

This energy is caused by the water from a river that is sent to turbines to producemechanical energy. To evaluate the benefits of this project, we start assuming that theturbine capacity will be fully used. This is typical a graph used to evaluate a run of streamproject

Graph 18 Run of the stream

Example (Taking the same assumptions as the thermal energy). If the peak hours are2000 a year then we are left with 6760 hours of off-peak use. Now we can calculate, for

each KW of turbine capacity the revenue:

2000hrs@10cents = $200

6760hrs@4cents = $270,4

Then, the total installed capacity will generate a revenue of $470 ,4 per KW. Because of thevariable flow of the stream, turbines will not be used at full capacity always. Let assume

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it is an 80 % of capacity. The estimated benefits would then be $376,32(= 0,8$470,4) peryear per KW. In the other hand, the cost of the new capacity would be $300(= 200015%)per year per KW. The project is accepted.

11.3. Daily Reserve

A way to improve the water availability is the creation of a dam that will help accumulatewater and control the river flow. This becomes efficient becomes often you will have theriver flow running when there is not enough electricty demand and therefore it will bewasted. This will allow for the water release when electricity is needed. T he next graphshows the excess of water-capacity (green area). It that can be stored and used later atthe value of 10 cents or 4 cents. The blue area represents the water that is valued at 4cents because is used in peak hours.

Graph 19. Daily reserve

As with prior analysis, the size of the dam will be chosen according to the peak timeelectricity demand. If the peak time surcharge multiplied by the peak time hours is biggerthan the costs, then the project will be accepted. The principal cost of this project arerelated to their constraints, this are:

a) The cost of the dam

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b) If the amount of the turbine capacity is not increased, the benefit of extra peaktime energy would be limited to the amount by which the turbine capacity ofthe ROS project exceeds the stream flow.

11.4. Pump Storage

The main idea of the pump storage is the re-utilization of the water that already has beenused to generate energy. This project requires the construction of a second dam (lowerreservoir) to capture water and then pump it back to upstream. The idea is to pump itback in low demand period so the same energy is used, therefore you will a greater waterstream in a high peak period. A necessary condition for this project is the existence ofcheap off peak energy so the cost of pumping the water is not high. A concern that thisproject might cause relates on the water rights of the river, because it will mean takingwater from others downstream. The existence of this technology usually is combinedwith the nuclear energy. Both technologies work together to provide an efficient source ofelectricity. To understand how this mix works, it is necessary to understand the conceptof a load curve. This curve represents the electrical energy demanded in the whole yearfrom the most demanded hours to the least demanded hours. This means that often thebuilt capacity will be unused because there is not enough demand. For the case of thenuclear energy, for instance, they are usually never shut down. So a load curve could showus how much energy from the nuclear can be used to pump the water.

Graph 20. Pump storage

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In the previous graph, we can see that R is the energy available for pump and G is theenergy generated once the water has been pumped up. If we assume that N* is the optimalnuclear capacity, then there must be a function R = f(G) that relates the optimal storageto fulfill peak hours demand.

11.5. Seasonal Storage

Seasonal hydro dams aim at allowing extra water to be shifted from one part of the yearto another to supply a steady energy demand. Also, this works in the other way. Thismeans that it could be used in rivers that have pretty steady stream flow, but the demandof energy is highly concentrated in some seasons

11.6. Economics of Electricity: A more realistic approach

A energy decision-making in the real world usually has all of the previous technologyinstalled at the same time which leads to the need of analyzing which ones are to beactivated first based on the energy demand and the costs. The order of use will depend onhow expensive is the energy. In this case, ROS is the cheapest technology and thereforeit should be used first. The pumping technology is the most expensive one, therefore itshould be used last.

When it comes to seasonal storage plants and thermal plants, the problem can be expres-sed like this:

Graph 21. Load curve

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To solve you could have the following procedure

Example

Strategy A: 300MW turbine HA600MW TA

StrategyB400MW

TB500MW turbine HB

Difference (B-A)Uses 200MW less in TUses 200MW more in H

Assume that we already have the plants but we are wondering which plant must bebigger in order to attend the peak hours. Lets focus on the costs of these strategies. Thesaving of strategy A is 200MW in hydro but an extra 200MW in thermal. In other words,

as we move from strategy A to B, we are reducing 200MW of homogeneous thermalcapacity and adding 200MW of turbine capacity in our seasonal hydro dam. Intuitivelyit is cheaper to add 1MW of turbine capacity to an existing dam with a place alreadyprepared for additional turbines than to add 1MW of homogeneous thermal capacity whichentails building the whole plant plus its associated turbines. And second, the start-up andshutdown costs vary significantly since in a hydro dam are practically zero.

As a result we should think that strategy B is usually the winner in the stacking process.We say ausuallya because it could happen than that there is no extra room for moreturbines (if it is a old dam) in the dam, so the history is different.

12. Irrigation Projects

When thinking on irrigation projects it is fundamental to consider that they are linkedto the amount of water delivered. Once this is considered the next important step isto analyze the value of water delivered by the project. The main problem that ariseswith water in an irrigation project is that there is not a market system that leads to anequilibrum in which the marginal product is equal to the price that has to be paid. In thecase of water in agriculture, the amount of water is given by water rights over it whichare determined by the hectares of land. Aditionally, one can never know how much wateryou will get because it depends on the forces of nature for that year. Therefore, there

is no way of paying a price for a marginal unit of water or for that matter knowing themarginal productivity of water based on what farmers pay for it. In order to value water,two methods can be used:

a) Residual Value Method: The basic idea is to suppose the construction of anirrigation project that increases water availability in a farm and leave anotherfarm without a project. Then, you estimate the value of a crop with or without

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the project and also the cost of input other than land and water. You thenobtain a residual value for each of the two profiles, which is the differencebetween the inflow and the outflow. By substracting one residue value fromthe other you get the difference that can be attributed to water in the project,or the value of water. However, because this method is innacurate you canend up with a big standard deviation that keeps the value of water relativelyunknown.

b) A second approach uses the land prices as estimates of the current value ofwater rights. This is possible when water is such a scarce resource and the landis so abundant that the marginal productivity of it is close to 0. Therefore, thereason why the value of land can increase is because it entitles access to water.Therefore, people will be willing to buy land just because of the water.

In order to do a correct evaluation for this project one should consider thereal product that the land buyers are getting. Since the amount of water isdetermined by nature, then a buyer wouldnt buy a specific amount of waterbut an expected one. Therefore, it is necessary to create a distribution of thewater quantity across a period of time and get an expected value of the wateraccording to the the probability given to each quartile of water available thatyear.

Graph 22. Distribution of water in a year

The next step is to calculte the prices of water which is given by QlPl = PII

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where l is land and I is an index created with the probability of water accordingto the distribution over the years.

To evaluate the effect of constructing a dam, we use the fact that water availa-bility will increase with the dam to create two different indexes. I1 which is theno project one and I2 which is the project one. These causes the benefit of thedam to partially be B = PI(I

2 I1). However, the benefit is not only caused

by the increase in the amount of water but also by the increase in the valueof water from the damn when compared to the water from the river. Becausewater in the damn is more readily available it is worth more. Therefore, thetotal benefit is T B = PI(I

2 I1) + d(PII) where d is the increase in the value

of the water of the dam against the river water.

13. Education

The relationship between education and future earning power has always been noted.More years of education will in average yield a greater wage. However, the interestingquestion is to determine what is the actual effect of an extra year to your increase insalary. This could allow the creation of a financial profile that could weigh the benefitsreceived by education to the costs it has. The application of financial tools such as NPVor IRR to the education effects is important for public policy to determine wheter or notshould there be a greater effort on reducing drop-out rates in a country. A methodology toestimate the NPV and IRR was given by Harberger and Peon in their paper Estimating

Private Returns to Education in Mexico. In it, they took the viewpoint from an individualdemanding education to establish the profile of the project. The objective was to determinea rate of return of finishing the four levels of education in Mexico : primary, middle school,high school and college. The benefits were given by the future earnings and the costs by theforgone earnings that studying implies. These profile creates somes bias problems causedby the existence of students that work and study at the same time or the existence ofprivate school which require additional costs. Since these two effects have opposing signsand they account for a small fraction of the costs and benefits and there the available datacouldnAt allow them to incorporate this variables into the analysis, they were omitted.

The Net Present Value of education is a function given by the discounted differencebetween the wage of a worker with an educational level n and the wage of a worker withan educational level preceding n, n-1.

NP Vn = Tt=1

Wt,n Wt,n1(1 + r)t

This analysis allows an estimation of the opportunity cost, forgone earnings. We knowthat Wt,n = 0 for the d number of years spent in schooling, therefore

dt=1

Wt,n1(1+r)t

is the

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opportunity cost of education at level n. By doing this present value, the study analyzesthe decision of passing to the next education level for each individual based on the benefitsthat going to that level will create minus the cost of doing it which is salary they willperceive with that education level if they were not studying.

In order to estimate the value of Wt, the equation used was:

In(w) =1 age +3 age2 +G +

5n=2ngn +

5n=2n(agegn) + i=1iOci + e

where W is the wage income, G is a dummy for gender, g is a dummy that is equal to 1when the worker belongs to the n level of education and O is a dummy for a specific typeof occupation.

The salary for each educational level could be estimated with the traditional earningsequation which is a function of experience and education. However, there are other va-

riables that influence the earnings profile such as the genre. The occupation is includedbecause if the educational level is related to the occupation, then the estimators will bebiased if they ommitted this variable.

A traditional approach was to estimate wages a function of education and experienceand consider the coefficient of education as the rate of return, however, this is incorrectbecause it does not consider the costs associated with education, unlike the proposedmethodology.

This analysis was applied to estimate the returns on education in the 32 states of Mexi-co. Using a survey that inquired on the wages of workers from different industries theyestimated the model using a state regression and a pooled regression They assumed an

interest rate of 5 % because it is the average return that people get from banks and isclose to the mortgag rate. Results show that there is an increasing rate of return as anindividual pursues an additional level of education. The rate of return does not favor anspecific gender as it varies in each educational level.

Genre Primary Middle School High School CollegeMasculine 2.13 % 5.86 % 11.26 % 14.27 %Femenine 5.49 % 7.28 % 10.36 % 14.39

The low rate of return that finishing primary school gives to students is interesting becauseit means that with the used discount rate it is better to be working than studying at thatage. However, the conclusion should not be so eager to determine that because there is

an increase in the earnings as people continue studying which end paying-off for thatinitial lost. Another interesting result is that the rates did not vary significantly betweenall of Mexico states, this creates a strong case for suggesting an integrated labor marketin the country. Finally, incorporating economic growth into the analysis does change theresults and creates higher IRR and NPV, the conservative estimates of a 1 % and 2& forMexico during the next years, makes this values trustworthy and important to model inthe educational project profile.

cost-benefit analysis notes - carlos grandet

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