McPeak

Lecture 14=

PPA 723

C= osts and Benefits.<= /p>

A cost is anything th= at reduces an objective and a benefit is anything that contributes to an objective.

For society as a whol= e, increasing national income is the objective. Anything that reduces national inc= ome is a cost and anything that increases it is a benefit.

Anything that realloc= ates it from one party to another is a transfer.

Compare to financial = analysis where a dollar is a dollar. T= here, we would worry about tax taking money from us to give to them. Here it is not an issue.

[return to DWL argument and= can use example of user fees in the commons]

Transfers:=

T= ax payment.

S= ubsidy.

C= redit payments.<= /p>

These don’t cre= ate or diminish national income, they just move it from= one party to another. What is don= e with the money (loan money to buy fertilizer, fertilizer is a cost increased out= put is a benefit) impacts national income, but the loan payment does not.

Real resource flows a= re critical to identify. A tax i= s a claim on a real resource flow. We are looking to identify uses of the resources.

S= teps to Cost-Benefit analysis.<= /o:p>

1)&n= bsp; Define the situation

2)&n= bsp; Identify and value the costs

3)&n= bsp; Identify and value the benefits

4)&n= bsp; Discount fu= ture cost and benefits to identify net present value

5)&n= bsp; Consider the implications of the choice made on NPV income terms for other objectives (equity for example)

6)&n= bsp; Sensitivity analysis.

7)&n= bsp; Interpret r= esults

1) Defining the situa= tion:

What is the community= whose resources are relevant to the program being evaluated?

What is the spatial e= xtent of the proposed project?

What are the current resources in this community in terms of:&n= bsp; money, property, labor, environmental amenities, and government serv= ices for the community?

What will happen if t= he project is not implemented?

Identify and value th= e costs and benefits that arise with the project and compare to the situation witho= ut the project.

This is not the same = as “before” and “after”.

I= ncremental net benefit with and without project.

Patterns:

With grows at a faste= r rate than without.

With stops a decline = that will happen without.

W= ith leads to an increase, without a decrease.

= 2)&n= bsp; Identify and value the costs

P= hysical goods. Materials that= are easy to identify. =

L= abor. <= span class=3DGramE>People working and getting paid for it.

L= and. <= span class=3DGramE>The place where the project is taking place.

Contingency allowance= s. Recognizing that there will be cha= nges in physical conditions or prices over the course of the project and putting that in.

I= ntangibles. T= raffic delays, noise… Externalities.

[= omit taxes, debt service, sunk costs]

To value these, we re= turn to the concept of economic cost.

Here we expand it som= e since we have now considered externalities.

The shadow price of a= n input reflects its value to society as a whole; the full social accounting of the marginal cost of using the input.

If there are market imperfections, it is not the same as the market price.

If the market is perf= ectly competitive and there are no externalities, then it is the same as the mark= et price (the next best alternative as reflected in the market definition).

= 3)&n= bsp; Identify and value the benefits

N= ew production or increased production from current level.

Q= uality improvement.

A= bility to access higher return markets.

Cost reduction. =

A= voided losses.

These (again in the a= bsence of externalities) can be valued through market prices.

Some benefits are dif= ficult to reflect in market prices (civic pride, reduction in pollution,…). To approximate these, we use a variety of techniques to estimate the community’s willingness to pay.

= 4)&n= bsp; Di= scount future cost and benefits to identify net present value

Many projects have benefits and costs that will be realized over time.

How do we compare these values, and arrive at a single measure of the flow of c= osts and benefits over time?

We compute a single measure of these flows as the present value. We discount future benefits and fu= ture costs to arrive at a single statement of the net present value of benefits minus costs.

Why do we discount?

Impatience. Having it now is more valuable tha= n in the future. Longer time to be= with the benefit, and also “conditional continuation probability” factors in here.

Inflation. Dollar today is not the same as a = dollar in the future.

Opportunity cost. I could have invested the money and earned returns, so this is the economic standard by which I should evaluate future returns.

General form for discounting:

r= is the discount rate, usually expressed in annual terms.

Define future value by FV, and present value by PV.

t= is a time index, and in our case is indexed in years.

If I promise to pay y= ou $100 20 years from now, and the discount rate is 6%, what is the present value?<= span style=3D'mso-spacerun:yes'> In other words, what amount = could you give me now, I invest in a sure bet 6% rate = of return bond, and have it pay off $100 in 20 years?

$100/(1+.06)²⁰=3D$31.18

If it is current year= , $100/(1+.06)⁰ =3D 100, since anything raised to= the zero power =3D1 by convention.

If it is a stream of payments, we sum them over time.

[For future reference: if payments are eq= ual over time, and it is over an infinite time horizon, we can use the following result.

S=3D

=3D=3D]

D= istinction between the nominal rate of interest and the real rate of interest.<= /span> <= o:p>

The nominal rate incl= udes inflation. =

The real rate is in t= erms of inflation adjusted units.

Let gamma be the infl= ation rate, and i is the real rate of interest.&= nbsp; The nominal rate of return can be stated = .

That means the real r= ate of interest is nominal rate of interest – inflation divided by 1+ rate of inflation. Roughly speaking, = we can use nominal rate minus inflation rate to get real rate if inflation is “small”.

Real present value di= scounts for both real interest rates and inflation.

If your future moneta= ry values are stated in real terms, you do not discount for inflation. They ha= ve already been discounted.

If your future moneta= ry values are stated in nominal terms, you need to discount for both inflation= and real rate of interest. <= /o:p>

Is the contract you s= igned for a $100 bill to be handed to you each year, o= r for the equivalent of $100 in today’s money to be handed to you each year= ?

The discount rate you= choose depends on whether the values you are using for costs and benefits are in r= eal or nominal terms.

Inflation rate is 5%.= Nominal rate of interest is 8%.

(1+.08) =3D (1+.05)(1+i), real interest rate is 2.9%.<= /p>

Is promise to pay $10= 0 bill next year? Then 100/(1.08), worth $92.59 today.

Is promise to pay the equivalent of $100 next year? Then 100/1.029), worth $97.18 today.=

How do we choose r? A different r may change the relat= ive evaluation.

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'> The discount rate reflects the relative value= a person places on future consumption compared to current consumption.

- L= ower values show a greater preference for future consumption.<= /p>

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>- Example: suppose I will give you $100 today or $100(1+r) next year.

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>

Today	R	Next year
$100	0%	$100
$100	2%	$102
$100	5%	$105
$100	10%	$110

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>- The point at which you become indifferent between the two choices is your discount rate.

= ;

Why the di= scount rate matters

- D= iscounting affects the value placed on future benefits and costs.

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>- Higher discount rates place less importance on future bene= fits / costs. A lower discount rate increases future values in terms of current values.

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>Recall:

<= span style=3D'font-size:18.0pt'>

- C= onsider a program with 20 years of benefits at $1/year.

&nbs= p; - PV =3D $20 with 0% discount = rate

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>- PV =3D $15.9 with 3% discount rate

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>- PV =3D $13.5 with 5% discount rate

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>- PV =3D $11.6 with 7% discount rate

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>- PV =3D $9.5 with 10% discount rate

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>

What about= using market interest rates?

Economists sometimes use the rate of return at t= he U.S. Treasury.

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>- Investors looking for a safe return invest in government securities.

DATE	3-mo	6-mo	1-yr	2-yr	3-yr	5-yr	7-yr	10-yr	20-yr	30-yr
11/0= 1/1990	7.28=	7.38=	7.32=	7.68=	7.88=	8.15=	8.42=	8.57=	8.63=	8.70=
11/0= 1/1995	5.48=	5.49=	5.46=	5.52=	5.62=	5.74=	5.86=	5.98=	6.36=	6.29=
11/0= 1/1999	5.16=	5.32=	5.47=	5.83=	5.93=	6.00=	6.23=	6.06=	6.55=	6.19=
11/0= 1/2002	1.44=	1.43=	1.42=	1.46=	1.76=	2.14=	2.92=	3.54=	4.01=	5.07=

A problem = occurs if, when comparing two options, one is riskier. Using a risk-free rate favors the riskier project.

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>Another alternative is= to consider where the funds for a project come from.

If some of= the funds come from the private sector, we should consider the opportunity cost= of using those funds.

This is a good estima= te of the opportunity cost of the capital you are using. Rate of return on capital is aroun= d 10%, so we use 10%.

<= span style=3D'mso-bidi-font-weight:bold'>

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>The Office of Manageme= nt and Budget directs agencies to use a 7% real discount rate. This rate approximates the marginal pre-tax rate of return in the private sector.

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>Might the social disco= unt rate deviate from these market rates?

Social discount rate – the interest rate at which society is willing to trade future consumption for present consumption.

= ;

Some economists argue that the opportunity cost = of foregone future consumption might differ from the opportunity cost revealed= in the markets.

Reasons social discount rates may differ from ma= rket rates

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>1) Concern for future generations

= - Private sector may save too little, because it doesn’= ;t care about future generations.

= - Thus, the government acts as an advocate for future generations, who are not represented in the marketplace.<= /p>

Estimate = by Costanza et al. (1997) of the value of the annual flo= w of goods and services from the environment.&n= bsp; 33 trillion.

&nbs= p;

Years	5% discount	10% discount<= /o:p>
1	31390571008524	29859634795187
10	20015511770517	12140021558658
100	222352250970	1498197682
200	1498197682	68018
300	10094777	3
400	68018	0
500	458	0
600	0	0

Discounting can lead to outcomes tha= t are “pretty grim” for future generations.

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>

<= span style=3D'font-size:18.0pt;mso-bidi-font-weight:bold'>2) Market inefficiency

= - Investments create knowledge, a positive externality (spillovers / leaks).

= - Thus, one can argue that firms under-invest.

= ;

Sometimes you see a 1= 0% rate by convention.

Example: Compare costs of paving a road and gravelling a road. Present Va= lue Cost computation.

Gravelling costs $28,= 000 to do now, and requires $2,000 per year upkeep for the next 10 years.

Paving costs $35,000 = to do now, and requires $1,000 per year upkeep over the next 10 years.=

Discount rate is 10%.= Say this is the nominal rate of re= turn on capital, and these values are nominal values (signing a contract).<= /o:p>

	Gravel	Pave
Now (t=3D0)	&nbs= p; 28,000	&nbs= p; 35,000
1=	2,000/(1+.1)^{1<= /sup>=3D1,818}	1,000/(1+.1)^{1<= /sup>=3D 909}
2=	2,000/(1+.1)^{2<= /sup>=3D1,653}	1,000/(1+.1)^{2<= /sup>=3D 826}
3=	2,000/(1+.1)^{3<= /sup>=3D1,503}	1,000/(1+.1)^{3<= /sup>=3D 751}
4=	2,000/(1+.1)^{4<= /sup>=3D1,366}	1,000/(1+.1)^{4<= /sup>=3D 683}
5=	2,000/(1+.1)^{5<= /sup>=3D1,242}	1,000/(1+.1)^{5<= /sup>=3D 621}
6=	2,000/(1+.1)^{6<= /sup>=3D1,129}	1,000/(1+.1)^{6<= /sup>=3D 564}
7=	2,000/(1+.1)^{7<= /sup>=3D1,026}	1,000/(1+.1)^{7<= /sup>=3D 513}
8=	2,000/(1+.1)^{8<= /sup>=3D 933}	1,000/(1+.1)^{8<= /sup>=3D 467}
9=	2,000/(1+.1)^{9<= /sup>=3D 848}	1,000/(1+.1)^{9<= /sup>=3D 424}
10	2,000/(1+.1)¹⁰⁼=3D 771	1,000/(1+.1)¹⁰⁼=3D 386

GRAVEL: $40,289

PAVING: $41,144

Gravel is less costly= than paving in PV terms.

If we add in benefits= , we can arrive at net present value.

Assume the impacted population is of size 1000. A= lso assume we did a study that indicates that the average monetary value per ye= ar the population of 1000 of an improved road is $8 if paved and $6 if gravel = (each). So the total annual benefits of the gravel road are $6000 and total annual benefits of the paved road are $8000= .

If the discount rate = =3D 6%, then NPV_paving =3D $16,520, while NPV_gravel=3D$1,440.

If the discount rate = =3D 10%, then NPV_paving =3D $8,012, while NPV_gravel=3D-$3,422.

N= ote that as the discount rate increases, future (net) benefits have less weight agai= nst the current period costs. Ch= oice of discount rate can influence which project is selected in Cost Benefit analysis (though not in this case).

Another measure is so= metimes used; the internal rate of return. What r leads to PV benefits equal to PV costs?

For the paving projec= t, just over 15% makes NPV=3D0. For t= he gravel project, it is a bit over 7%.

Solve for the r that = makes:

Also note we can cons= ider the benefit cost ratio, under the rule that if it is greater than one, the bene= fits outweigh the costs.

The ratio is 1.40 at a discount rate of 6% for the paving project.

= 5)&n= bsp; Consider other factors that weigh in the decision: Equity, impact on sub-groups, things like this.

While the average ben= efit is indeed $6 or $8 for our community members, this is highly skewed, as only 5= 00 people have vehicles. The oth= er members will not have any direct benefit from road improvement, but will ha= ve to pay the costs. =

The gravel road will = not be strong enough for the family farm to drive their tractor on so they will not benefit from this, but will benefit from the paving.

= 6)&n= bsp; Sensitivity of results.

As you have seen by n= ow, the assumptions can lead to changed assessment.

With regard to the di= scount rate, it is sometimes useful to identify where is the “crossing point”.

If we keep the origin= al values, it is never going to make more sense to gravel than pave given these values.

If we change our orig= inal problem and make the cost of gravelling cheaper (say it is 18,000 rather th= an 28,000) we choose paving when r is less than 12% and gravel when r is great= er than 12%. <= /p>

Also, the values we c= ame up with for our benefits could be off. Say the costs were as reported in the original problem, but the bene= fits of the gravel and paved road were overstated by half (like in the windmill example).

NPV for the gravel ro= ad is -$20,640, while for the paved road it is -$12,920.

Neither project makes= sense at a discount rate of 10% - alternative uses of the resources offer better options.

One other source of uncertainty (as if ambiguity about the discount rate, the way we can make the prediction change by changing the benefit estimation is not enough) is the length of the time horizon.= Are we really sure the time horizon is 10 years?

If for example we use= the 6% rate and have a horizon of 2 years, it is better to gravel than pave (recal= l we picked pave). If it is anythi= ng more than 10 years, we have understated the NPV (for example, the paved road NPV if it lasts 20 years is 2.7 times as large as the NPV if it lasts 10 years).

Longer time horizons = tend to flatten out future costs and benefits as suggested by the Costanza et al. result above.

= 7)&n= bsp; Interpreting results.

Look at NPV, and if y= ou want other perspectives, the internal rate of return and the benefit cost ratio.=

Consider how sensitiv= e the results are to your assumptions and how sure you are of your assumptions.

Consider the NPV resu= lt as statement of economic efficiency and balance this against other objectives = that may be important: equity, tar= geting specific sub-groups, righting historical wrongs, politi= cal stability – whatever.

Realize that as a pro= ducer of this information, how important it is for you to act carefully and ethicall= y.

Realize that as a con= sumer of this information that the careful ethical approach is not always adopted.