EEP 101/ECON 125EEP 101/ECON 125Lecture 14: Natural Lecture 14: Natural

ResourcesResources

Professor David ZilbermanProfessor David Zilberman

UC BerkeleyUC Berkeley

Natural Resource EconomicsNatural Resource Economics

• Natural Resource EconomicsNatural Resource Economics addresses the addresses the allocation of resources allocation of resources over timeover time. .

• Natural Resource Economics distinguishes Natural Resource Economics distinguishes between between nonrenewable resourcesnonrenewable resources and and renewable resourcesrenewable resources. .

• Coal, gold, and oil are examples of Coal, gold, and oil are examples of nonrenewable resources. nonrenewable resources.

• Fish and water are examples of renewable Fish and water are examples of renewable resources, since they can be self-replenishing. resources, since they can be self-replenishing.

Natural Resource Economics Natural Resource Economics Cont.Cont.

• Natural Resource Economics suggests policy Natural Resource Economics suggests policy intervention in situations where markets fail intervention in situations where markets fail to maximize social welfare to maximize social welfare over timeover time . .– where market forces cause depletion of where market forces cause depletion of

nonrenewable natural resources too quickly or too nonrenewable natural resources too quickly or too slowly, or cause renewable resource use to not be slowly, or cause renewable resource use to not be sustainablesustainable over time (such as when species over time (such as when species extinction occurs) extinction occurs)

• Natural Resource Economics also investigates Natural Resource Economics also investigates how natural resources are allocated under how natural resources are allocated under alternative economic institutions.alternative economic institutions.

Key Elements of Dynamics: Key Elements of Dynamics: Interest RateInterest Rate

• One of the basic assumptions of Dynamic One of the basic assumptions of Dynamic Analysis is that individuals are impatient.Analysis is that individuals are impatient.

• They would like to consume the goods and They would like to consume the goods and services that they own today, rather than services that they own today, rather than saving for the future or lending to another saving for the future or lending to another individual. individual.

• Individuals will lend their goods and services Individuals will lend their goods and services to others only if they are compensated for to others only if they are compensated for delaying their own consumption. delaying their own consumption.

The Interest RateThe Interest Rate

• The The Interest RateInterest Rate (often called the (often called the Discount RateDiscount Rate in in resource contexts) is the fraction of the value of a resource contexts) is the fraction of the value of a borrowed resource paid by the borrower to the lender borrowed resource paid by the borrower to the lender to induce the lender to delay her own consumption in to induce the lender to delay her own consumption in order to make the loan. order to make the loan.

• The interest rate is the result of negotiation between The interest rate is the result of negotiation between the lender and the borrower. the lender and the borrower.

• The higher the desire of the lender to consume her The higher the desire of the lender to consume her resources today rather than to wait, and/or the higher resources today rather than to wait, and/or the higher the desire of the borrower to get the loan, the higher the desire of the borrower to get the loan, the higher the resulting interest rate. the resulting interest rate.

• In this sense, the interest rate is an In this sense, the interest rate is an equilibrium equilibrium outcomeoutcome, like the price level in a competitive market., like the price level in a competitive market.

ConsumptionConsumption

• Even an isolated individual must decide how Even an isolated individual must decide how much of his resources to consume today and much of his resources to consume today and how much to save for consumption in the how much to save for consumption in the future. future.

• In this situation, a single individual acts as In this situation, a single individual acts as both the lender and the borrower. both the lender and the borrower.

• The choices made by the individual reflect the The choices made by the individual reflect the individual's implicit interest rate of trading off individual's implicit interest rate of trading off consumption today for consumption tomorrow.consumption today for consumption tomorrow.

ExampleExample

• Suppose Mary owns a resource. Mary would like to Suppose Mary owns a resource. Mary would like to consume the resource today. consume the resource today.

• John would like to borrow Mary's resource for one year. John would like to borrow Mary's resource for one year.

• Mary agrees to loan John the resource for one year if John Mary agrees to loan John the resource for one year if John will pay Mary an amount to compensate her for the cost will pay Mary an amount to compensate her for the cost of delaying consumption for one year. of delaying consumption for one year.

• The amount loaned is called the The amount loaned is called the Principal.Principal.

• The payment from John to Mary in compensation for The payment from John to Mary in compensation for Mary's delayed consumption is called the Mary's delayed consumption is called the Interest Interest on the on the loan.loan.

Example Cont.Example Cont.

• Suppose Mary's resource is $100 in cash. Suppose Mary's resource is $100 in cash.

• Suppose the interest amount agreed to by Suppose the interest amount agreed to by Mary and John is $10. Mary and John is $10.

• Then, at the end of the year of the loan, John Then, at the end of the year of the loan, John repays Mary the principal plus the interest, repays Mary the principal plus the interest, or $110:or $110:

– Principal + Interest = $100 + $10 = $110Principal + Interest = $100 + $10 = $110

Example Cont.Example Cont.

• The (simple) The (simple) interest rateinterest rate of the loan, of the loan, denoted denoted rr, can be found by solving the , can be found by solving the following equation for r:following equation for r:– Principal + Interest = (1 + r) PrincipalPrincipal + Interest = (1 + r) Principal

• For this example:For this example: $110 = (1 + r) $100$110 = (1 + r) $100

• So, we find:So, we find: r = 10/100r = 10/100 oror 10%10%

• Hence, the interest rate on the loan was 10%.Hence, the interest rate on the loan was 10%.

Example Cont.Example Cont.

• Generally, we can find the interest Generally, we can find the interest rate by noting that:rate by noting that:– B1 = B0 + r B1 = (1+r) B0B1 = B0 + r B1 = (1+r) B0

• where B0 = Benefit today, and B1 = where B0 = Benefit today, and B1 = Benefit tomorrow Benefit tomorrow

The Interest Rate is an Equilibrium of The Interest Rate is an Equilibrium of OutcomeOutcome

• C1 = consumption in period 1C1 = consumption in period 1

• C2 = consumption in period 2C2 = consumption in period 2

The Interest Rate is an Equilibrium of The Interest Rate is an Equilibrium of Outcome Cont.Outcome Cont.

• Delay of consumption (saving) in period 1 reduces current utility but Delay of consumption (saving) in period 1 reduces current utility but increases utility in period 2. increases utility in period 2.

• The inter-temporal production possibilities curve (IPP) denotes the The inter-temporal production possibilities curve (IPP) denotes the technological possibilities for trading-off present vs. future consumption.technological possibilities for trading-off present vs. future consumption.

• The curve S, is an indifference curve showing individual preferences The curve S, is an indifference curve showing individual preferences between consumption today and consumption in the future. between consumption today and consumption in the future.

• Any point along a particular indifference curve leads to the same level of Any point along a particular indifference curve leads to the same level of utility. utility.

• Utility maximization occurs at point A, where S is tangent to the IPP. Utility maximization occurs at point A, where S is tangent to the IPP.

• The interest rate, r, that is implied by this equilibrium outcome, can be The interest rate, r, that is implied by this equilibrium outcome, can be found by solving either of the following two equations for r:found by solving either of the following two equations for r:– slope of S at point A = - (1 + r)slope of S at point A = - (1 + r)– slope of IPP at point A = - (1 + r)slope of IPP at point A = - (1 + r)

The Interest Rate is an Equilibrium of The Interest Rate is an Equilibrium of Outcome Cont.Outcome Cont.

• Therefore, if we can determine the Therefore, if we can determine the slope of either S or IPP at tangency slope of either S or IPP at tangency point A, then we can calculate the point A, then we can calculate the interest rate, r. This is often done by interest rate, r. This is often done by solving the following individual solving the following individual optimization problem where I is the optimization problem where I is the total income available over the two total income available over the two periods:periods: { }Max U C C

subject to I CrC

C C. ( , )

:

,1 21 2

1 21

1 = +

+⎛⎝⎜

⎞⎠⎟

The Interest Rate is an Equilibrium The Interest Rate is an Equilibrium of Outcome Cont.of Outcome Cont.

• which can be written as:which can be written as:

L= + − ++

⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥

=

=+

⎫⎬⎪

⎭⎪⇒ = +

U C C I CrC

FOCS

U

Ur

U

Ur

C

C

C

C

( , )

:

1 2 1 21

1

11

1

2

1

2

λ

λλ

The Indifference CurveThe Indifference Curve

• The indifference curve is found by setting:The indifference curve is found by setting:

• The indifference curve simply indicates that The indifference curve simply indicates that the equilibrium occurs where an individual the equilibrium occurs where an individual cannot improve her inter-temporal utility at the cannot improve her inter-temporal utility at the margin by changing the amount consumed margin by changing the amount consumed today and tomorrow, within the constraints of today and tomorrow, within the constraints of her budget. her budget.

U d U dd

d

U

UrC C C C

C

C

C

C1 1 2 2

2

1

1

2

0 1+ = ⇒ =−

=− + ( )

The Components of Interest The Components of Interest RateRate• Interest rates can be decomposed into several Interest rates can be decomposed into several

elements:elements:• • Real interest rate, rReal interest rate, r• • Rate of inflation, IRRate of inflation, IR• • Transaction costs, TCTransaction costs, TC• • Risk factor, SRRisk factor, SR

• The interest rate that banks pay to the government The interest rate that banks pay to the government (i.e., to the Federal Reserve) is the sum r + IR. (i.e., to the Federal Reserve) is the sum r + IR. – This is the This is the nominal interest ratenominal interest rate. .

• The interest rate that low-risk firms pay to banks is The interest rate that low-risk firms pay to banks is the sum r + IR + TCm + SRm, where TCm and SRm the sum r + IR + TCm + SRm, where TCm and SRm are minimum transactions costs and risk costs, are minimum transactions costs and risk costs, respectively. respectively. – This interest rate is called the This interest rate is called the Prime RatePrime Rate..

The Components of Interest The Components of Interest Rate Cont.Rate Cont.

• Lenders (banks) analyze projects Lenders (banks) analyze projects proposed by entrepreneurs before proposed by entrepreneurs before financing them. financing them.

• They do this to assess the riskiness They do this to assess the riskiness of the projects and to determine SR. of the projects and to determine SR.

• Credit-rating services and other Credit-rating services and other devices are used by lenders (and devices are used by lenders (and borrowers) to lower TC.borrowers) to lower TC.

Some Numerical ExamplesSome Numerical Examples

(1)(1) If the real interest rate is 3% and If the real interest rate is 3% and the inflation rate is 4%, then the the inflation rate is 4%, then the nominal interest rate is 7%.nominal interest rate is 7%.

(2)(2) If the real interest rate is 3%, the If the real interest rate is 3%, the inflation rate is 4% and TC and SR inflation rate is 4% and TC and SR are each 1%, then the Prime Rate is are each 1%, then the Prime Rate is 9%.9%.

DiscountingDiscounting• Discounting is a mechanism used to compare streams of net benefits Discounting is a mechanism used to compare streams of net benefits

generated by alternative allocations of resources over time. generated by alternative allocations of resources over time.

• There are two types of discounting, depending on how time is measured. There are two types of discounting, depending on how time is measured.

• If time is measured as a discrete variable (say, in days, months or years), If time is measured as a discrete variable (say, in days, months or years), discrete-time discounting formulas are used, and the appropriate real discrete-time discounting formulas are used, and the appropriate real interest rate is the "simple real interest rate".interest rate is the "simple real interest rate".

• If time is measured as a continuous variable, then continuous-time If time is measured as a continuous variable, then continuous-time formulas are used, and the appropriate real interest rate is the formulas are used, and the appropriate real interest rate is the "instantaneous real interest rate". "instantaneous real interest rate".

• We will use discrete-time discounting in this course. We will use discrete-time discounting in this course.

• Hence, we will use discrete-time discounting formulas, and the real Hence, we will use discrete-time discounting formulas, and the real interest rate we refer to is the simple real interest rate, r. interest rate we refer to is the simple real interest rate, r.

• Unless stated otherwise, assume that r represents the simple real Unless stated otherwise, assume that r represents the simple real interest rate.interest rate.

Lender’s PerspectiveLender’s Perspective

• From a lender's perspective, 10 dollars received From a lender's perspective, 10 dollars received at the beginning of the current time period is at the beginning of the current time period is worth more than 10 dollars received at the worth more than 10 dollars received at the beginning of the next time period. beginning of the next time period.

• That's because the lender could lend the 10 That's because the lender could lend the 10 dollars received today to someone else and earn dollars received today to someone else and earn interest during the current time period. interest during the current time period.

• In fact, 10 dollars received at the beginning of the In fact, 10 dollars received at the beginning of the current time period would be worth $10(1 + r) at current time period would be worth $10(1 + r) at the beginning of the next period, where r is the the beginning of the next period, where r is the interest rate that the lender could earn on a loan.interest rate that the lender could earn on a loan.

A Different Perspective & A Different Perspective & Discounting Cont.Discounting Cont.

• Viewed from a different perspective, if 10 dollars were received Viewed from a different perspective, if 10 dollars were received at the beginning of the next time period, it would be equivalent at the beginning of the next time period, it would be equivalent to receiving only $10/(1 + r) at the beginning of the current to receiving only $10/(1 + r) at the beginning of the current time period. time period.

• The value of 10 dollars received in the next time period is The value of 10 dollars received in the next time period is discounted discounted by multiplying it by 1/(1+r). by multiplying it by 1/(1+r).

• Discounting is a central concept in natural resource economics. Discounting is a central concept in natural resource economics.

• So, if $10 received at the beginning of the next period is only So, if $10 received at the beginning of the next period is only worth $10/(1 + r) at the beginning of the current period, how worth $10/(1 + r) at the beginning of the current period, how much is $10 received much is $10 received twotwo periods from now worth? periods from now worth?

• The answer is $10/(1 + r)The answer is $10/(1 + r)22. .

Present ValuePresent Value• In general, the value today of $B received t periods from now is In general, the value today of $B received t periods from now is

$B/(1 + r)t. $B/(1 + r)t.

• The value today of an amount received in the future is called the The value today of an amount received in the future is called the Present ValuePresent Value of the amount. of the amount.

• The concept of present value applies to amounts The concept of present value applies to amounts paidpaid in the future in the future as well as to amounts received. as well as to amounts received.

• For example, the value today of $B paid t periods from now is For example, the value today of $B paid t periods from now is $B/(1 + r)$B/(1 + r)tt. .

• Note that if the interest rate increases, the value Note that if the interest rate increases, the value todaytoday of an of an amount received in the future declines. amount received in the future declines.

• Similarly, if the interest rate increases, then the value Similarly, if the interest rate increases, then the value todaytoday of an of an amount paid in the future declines.amount paid in the future declines.

You Win the Lottery!You Win the Lottery!

• You are awarded after-tax income of $1M. You are awarded after-tax income of $1M. However, this is not handed to you all at once, However, this is not handed to you all at once, but at $100K/year for 10 years. If the interest but at $100K/year for 10 years. If the interest rate is, r = 10%, net present value:rate is, r = 10%, net present value:

• • NPV = 100K+(1/1.1)100K+(1/1.1)NPV = 100K+(1/1.1)100K+(1/1.1)22100K + 100K + (1/1.1)(1/1.1)33100K + … + (1/1.1)100K + … + (1/1.1)99100K.100K.

= $675,900= $675,900• • The value of the last payment received is: The value of the last payment received is:

NPV = NPV = (1/1.1)(1/1.1)99100K = $42,410.100K = $42,410.

• That is, if you are able to invest money at r = That is, if you are able to invest money at r = 10%, you would be indifferent between receiving 10%, you would be indifferent between receiving the flow of $1M over 10 years and $675,900 the flow of $1M over 10 years and $675,900 today or between receiving a one time payment today or between receiving a one time payment of $100K 10 years from now and $42,410 today. of $100K 10 years from now and $42,410 today.

The value of The value of time :discountingtime :discountinginterest

rate 0.05 0.1

TimeFuture earning

Discounting

Future earning

Discounting

0 100 100 100 1001 105 95.24 110 90.912 110.25 90.7 121 82.643 115.76 86.38 133.1 75.134 121.55 82.27 146.41 68.35 127.63 78.35 161.05 62.096 134.01 74.62 177.16 56.457 140.71 71.07 194.87 51.328 147.75 67.68 214.36 46.659 155.13 64.46 235.79 42.41

10 162.89 61.39 259.37 38.5511 171.03 58.47 285.31 35.0512 179.59 55.68 313.84 31.8613 188.56 53.03 345.23 28.9714 197.99 50.51 379.75 26.33

The Present Value of an The Present Value of an AnnuityAnnuity

• An An annuityannuity is a type of financial property (in the same is a type of financial property (in the same way that stocks and bonds are financial property) that way that stocks and bonds are financial property) that specifies that some individual or firm will pay the owner specifies that some individual or firm will pay the owner of the annuity a specified amount of money of the annuity a specified amount of money atat each time each time period in the futureperiod in the future, , forever!forever!

• Although it may seem as if the holder of an annuity will Although it may seem as if the holder of an annuity will receive an infinite amount of money, the Present Value of receive an infinite amount of money, the Present Value of the stream of payments received over time is actually the stream of payments received over time is actually finite. finite.

• In fact, it is equal to the periodic payment divided by the In fact, it is equal to the periodic payment divided by the interest rate r (this is the sum of an infinite geometric interest rate r (this is the sum of an infinite geometric series).series).

Annuity Cont.Annuity Cont.• Let’s consider an example where you own an annuity that specifies that Let’s consider an example where you own an annuity that specifies that

Megafirm will pay you $1000 per year forever. Megafirm will pay you $1000 per year forever.

• Question: What is the present value of the annuity? Question: What is the present value of the annuity?

• We know that NPV = $1000/r. Suppose r = 0.1 then the present value We know that NPV = $1000/r. Suppose r = 0.1 then the present value of your annuity is $1000/0.1 = $10,000.of your annuity is $1000/0.1 = $10,000.

• That is a lot of money, but far less than an infinite amount. That is a lot of money, but far less than an infinite amount.

• Notice that if r decreases, then the present value of the annuity Notice that if r decreases, then the present value of the annuity increases. increases.

• Similarly, if r increases, then the present value of the annuity Similarly, if r increases, then the present value of the annuity decreases. decreases.

• For example, you can show that a 50% decline in the interest rate will For example, you can show that a 50% decline in the interest rate will double the value of an annuity.double the value of an annuity.

Transition from flow to stockTransition from flow to stock

• If a resource is generating $20.000/year If a resource is generating $20.000/year for the forth seeable future future and the for the forth seeable future future and the discount rate is 4% the price of the discount rate is 4% the price of the resource should be $500.000resource should be $500.000

• If a resource generates $24K annually If a resource generates $24K annually and is sold for $720K, the implied and is sold for $720K, the implied discount rate is 24/720=1/30=3.333%discount rate is 24/720=1/30=3.333%

The impact of price The impact of price expectationexpectation

• If the real price of the resource (oil) is If the real price of the resource (oil) is expected to go up by 2%expected to go up by 2%

• The real discount rate is 4%- The real discount rate is 4%- • What is the value of an oil well which What is the value of an oil well which

provides for the for seeable 5000 barrel provides for the for seeable 5000 barrel annually, and each barrel earns 30$ (annually, and each barrel earns 30$ (assume assume zero extraction costs)?zero extraction costs)?

• 1. Is It (A) $3.750K (B) $7.500K ?1. Is It (A) $3.750K (B) $7.500K ?

• 2.If the discount rate is 7% will you Pay $2 2.If the discount rate is 7% will you Pay $2 millions for the well?millions for the well?

• 3.What is your answer to 1. If inflation is 3.What is your answer to 1. If inflation is 1%?1%?

AnswersAnswers• 1.B 5000*30/(.04-.02)=150.000/.021.B 5000*30/(.04-.02)=150.000/.02

=$7.500.000=$7.500.000

• 2. 150.000/(.07-.02)=150.000/.05=2. 150.000/(.07-.02)=150.000/.05=

3000000>2000000 -yes3000000>2000000 -yes

• 3. If inflation is 1% real price growth is 3. If inflation is 1% real price growth is only 1% and only 1% and 150.000/(.04-.03)=150.000/.03=150.000/(.04-.03)=150.000/.03=

$5000000$5000000

• One percentage interest reduce value by One percentage interest reduce value by 1/3.1/3.

The Social Discount RateThe Social Discount Rate• The social discount rate is the interest rate used to The social discount rate is the interest rate used to

make decisions regarding public projects. It may make decisions regarding public projects. It may be different from the prevailing interest rate in the be different from the prevailing interest rate in the private market. Some reasons are:private market. Some reasons are:• • Differences between private and public risk Differences between private and public risk preferences—the public overall may be less risk preferences—the public overall may be less risk averse than a particular individual due to pooling of averse than a particular individual due to pooling of individual risk.individual risk.• • Externalities—In private choices we consider only Externalities—In private choices we consider only benefits to the individuals; in public choices we benefits to the individuals; in public choices we consider benefits to everyone in society.consider benefits to everyone in society.

• It is argued that the social discount rate is lower It is argued that the social discount rate is lower than the private discount rate. In evaluating public than the private discount rate. In evaluating public projects, the lower social discount rate should be projects, the lower social discount rate should be used when it is appropriate.used when it is appropriate.

Uncertainty and Interest Uncertainty and Interest RatesRates

• Lenders face the risk that borrowers may Lenders face the risk that borrowers may go bankrupt and not be able to repay the go bankrupt and not be able to repay the loan. To manage this risk, lenders may loan. To manage this risk, lenders may take several types of actions:take several types of actions:• • Limit the size of loans.Limit the size of loans.• • Demand collateral or co-signers.Demand collateral or co-signers.• • Charge high-risk borrowers higher Charge high-risk borrowers higher interest rates. (Alternatively, different interest rates. (Alternatively, different institutions are used to provide loans of institutions are used to provide loans of varying degrees of risk.)varying degrees of risk.)

Risk-Yield TradeoffsRisk-Yield Tradeoffs

• Investments vary in their degree of risk. Investments vary in their degree of risk.

• Generally, higher risk investments also tend to Generally, higher risk investments also tend to entail higher expected benefits (i.e., high yields). entail higher expected benefits (i.e., high yields).

• If they did not, no one would invest money in the If they did not, no one would invest money in the higher risk investments. higher risk investments.

• For this reason, lenders often charge higher For this reason, lenders often charge higher interest rates on loans to high-risk borrowers, while interest rates on loans to high-risk borrowers, while large, low-risk, firms can borrow at the prime rate. large, low-risk, firms can borrow at the prime rate.

Criteria for Evaluating Criteria for Evaluating Alternative Allocations of Alternative Allocations of Resources Over TimeResources Over Time

• Net Present Value (NPV)Net Present Value (NPV) is the sum of the is the sum of the present values of the net benefits accruing from present values of the net benefits accruing from an investment or project. an investment or project.

• Net benefit in time period t is Bt - Ct, where Bt Net benefit in time period t is Bt - Ct, where Bt is the Total Benefit in time period t and Ct is the is the Total Benefit in time period t and Ct is the Total Cost in time period t.Total Cost in time period t.– The discrete time formula for N time periods The discrete time formula for N time periods

with constant r:with constant r:NPV =

(Bt −Ct)(1+ )r t .

t=0

N∑

NFV and IRRNFV and IRR

• Net Future Value (NFV) is the sum of Net Future Value (NFV) is the sum of compounded differences between project compounded differences between project benefits and project costs.benefits and project costs.– The discrete time formula for N time periods with The discrete time formula for N time periods with

constant r:constant r:

• Internal Rate of Return (IRR) is the interest rate Internal Rate of Return (IRR) is the interest rate that is associated with zero net present value of that is associated with zero net present value of a project. IRR is the x that solves the equation:a project. IRR is the x that solves the equation:

NFV = (Btt=0

N

∑ −Ct)⋅1 + r( )N−t

0 =(Bt −Ct)(1+ )x t

t=0

N

∑

The Relationship Between IRR The Relationship Between IRR and NPVand NPV

• If r < IRRIf r < IRR then the project has a then the project has a positive NPVpositive NPV

• If r > IRRIf r > IRR then the project has a then the project has a negative NPV negative NPV

• It is not worthwhile to invest in a It is not worthwhile to invest in a project if you can get a better rate of project if you can get a better rate of return on an alternate investment.return on an alternate investment.

Familiarizing Ourselves with Familiarizing Ourselves with the Previous Conceptthe Previous Concept• Two period model:Two period model: If we invest $I today, and If we invest $I today, and

receive $B next year in returns on this receive $B next year in returns on this investment, the NPV of the investment is: -$I investment, the NPV of the investment is: -$I + $B/(1 + r). Notice that the NPV declines as + $B/(1 + r). Notice that the NPV declines as the interest rate r increases, and vice versa.the interest rate r increases, and vice versa.

• Three period model:Three period model: Suppose you are Suppose you are considering an investment which costs you considering an investment which costs you $100 now but which will pay you $150 next $100 now but which will pay you $150 next year.year.– If r = 10%, then the NPV is: -100 + 150/1.1 = If r = 10%, then the NPV is: -100 + 150/1.1 =

$36.36 $36.36 – If r = 20%, then the NPV is: -100 + 150/1.2 = $25If r = 20%, then the NPV is: -100 + 150/1.2 = $25– If r = 50%, then the NPV is: -100 + 150/1.5 = $0If r = 50%, then the NPV is: -100 + 150/1.5 = $0

Familiarizing Ourselves with Familiarizing Ourselves with the Previous Concept Cont.the Previous Concept Cont.

• Consider the "stream" of net benefits Consider the "stream" of net benefits from an investment given in the from an investment given in the following table:following table:

Time Period:Time Period: 0 0 11 22

Bt - Ct: -100Bt - Ct: -100 66 66 60.5 60.5

• The NPV for this investment is:The NPV for this investment is:NPV =−100+

661 + 0.1( )1

+60.5

1+ 0.1( )2=10

Time net benefits 0.02 0.03 0.04 0.050.00 -1000.00 -1000.00 -1000.00 -1000.00 -1000.001.00 100.00 98.04 97.09 96.15 95.242.00 100.00 96.12 94.26 92.46 90.703.00 100.00 94.23 91.51 88.90 86.384.00 100.00 92.38 88.85 85.48 82.275.00 100.00 90.57 86.26 82.19 78.356.00 100.00 88.80 83.75 79.03 74.627.00 100.00 87.06 81.31 75.99 71.078.00 100.00 85.35 78.94 73.07 67.689.00 100.00 83.68 76.64 70.26 64.46

10.00 100.00 82.03 74.41 67.56 61.3911.00 100.00 80.43 72.24 64.96 58.4712.00 100.00 78.85 70.14 62.46 55.6813.00 100.00 77.30 68.10 60.06 53.0314.00 100.00 75.79 66.11 57.75 50.51NPV 210.62 129.61 56.35 -10.14

IRR=.049

Benefit-Cost AnalysisBenefit-Cost Analysis

• Benefit-cost analysisBenefit-cost analysis is a pragmatic method of is a pragmatic method of economic decision-making. The procedure consists of economic decision-making. The procedure consists of the following two steps:the following two steps:

• Step 1Step 1:: Estimate the economic impacts (costs and Estimate the economic impacts (costs and benefits) that will occur in the current time period and in benefits) that will occur in the current time period and in each future time period.each future time period.

• Step 2Step 2:: Use interest rate to compute net present value Use interest rate to compute net present value or compute internal rate of return of the or compute internal rate of return of the project/investment. Use internal rate of return only in project/investment. Use internal rate of return only in cases in which net benefits switches sign once, meaning cases in which net benefits switches sign once, meaning that investment costs occur first and investment that investment costs occur first and investment benefits return later. benefits return later.

Benefit-Cost Analysis Cont.Benefit-Cost Analysis Cont.• A key assumption of benefit-cost analysis is the notion of A key assumption of benefit-cost analysis is the notion of potential potential

welfare improvement. That is, a project with a positive NPV has welfare improvement. That is, a project with a positive NPV has the potential to improve welfare, because utility rises with NPV. the potential to improve welfare, because utility rises with NPV.

• Some issues in benefit-cost analysis to consider include:Some issues in benefit-cost analysis to consider include:

– How discount rates affect outcomes of benefit-cost analysis. How discount rates affect outcomes of benefit-cost analysis.

– When discount rates are low, more investments are likely to be justified.When discount rates are low, more investments are likely to be justified.

– Accounting for public rate of discount vs. private rate of discount.Accounting for public rate of discount vs. private rate of discount.

– Incorporating nonmarket environmental benefits in benefit-cost analysis.Incorporating nonmarket environmental benefits in benefit-cost analysis.

– Incorporating price changes because of market interaction in benefit-cost Incorporating price changes because of market interaction in benefit-cost analysis.analysis.

– Incorporating uncertainty considerations in benefit-cost analysis.Incorporating uncertainty considerations in benefit-cost analysis.

Time Case1 case2 case3 case4 case50.00 -1000.00 -1000.00 -1000.00 -1000.00 -1000.001.00 100.00 100.00 100.00 120.00 100.002.00 120.00 120.00 120.00 140.00 120.003.00 140.00 140.00 140.00 160.00 140.004.00 150.00 150.00 150.00 170.00 150.005.00 160.00 160.00 160.00 180.00 160.006.00 180.00 180.00 180.00 200.00 180.007.00 160.00 160.00 160.00 180.00 160.008.00 140.00 140.00 140.00 140.00 140.009.00 160.00 160.00 160.00 160.00 160.00

10.00 140.00 140.00 140.00 140.00 140.0011.00 -40.00 -40.00 -40.00 -40.00 -40.0012.00 -80.00 -80.00 -80.00 -80.00 -80.0013.00 -120.00 -120.00 -120.00 -120.00 -120.0014.00 -160.00 -160.00 -160.00 -160.00 0.00

interest 0.05 0.03 0.01 0.05 0.05npv -106.725 -44.732 18.5524 9.0029 -25.914