Complementary information package for the Delphi study

Public University of Navarra (Spain) University of Murcia (Spain)

Discounting

The incorporation of the intergenerational

equity objective may have made the traditional

Cost-Benefit Analysis (CBA) approach obsolete

for the evaluation of certain types of projects,

particularly those exhibiting a large number of

environmental externalities and those with very

long term effects.

Different discounting

approaches1. To question the CBA technique, as the right approach in

the decision making process when dealing with problems bearing significant intergenerational consequences.

2. To consider unnecessary and/or inappropriate any reduction in the traditional Social Discount Rate (SDR) due to intergenerational equity issues.

3. To promote the use of reduced discount rates.

4. To apply for time-variable discount rates : hyperbolic discounting.

5. To apply for different discount rates for certain time spans (“Gamma” or “Green Book” propose).

6. To use different discounting rates for tangible and intangible effects, simultaneously, in the same CBA application.

If you are in favour of

using reduced discount rates…

0 < EDR SDR

SDR = Social Discount Rate

EDR = Environmental Discount Rate

... what specific value of EDR?

0

100.000

200.000

300.000

400.000

500.000

600.000

0 10 20 30 40 50 60 70 80 90 100Time (years)

Cur

rent

val

ue (E

uros

)

5%

3%

1%

Exponential discount factor (100 years)

505 797 €/year

27 161 €189 242 €

4 047 €

A numerical example(*)

(*)

Alm

an

sa

an

d

Cala

trava

(20

07

)

0

50.000

100.000

150.000

200.000

250.000

300.000

350.000

400.000

450.000

500.000

0 100 200 300 400 500

Time (years)

Cu

rren

t va

lue

(Eu

ros)

1%

3%

5%

What would you recommend for a 500 year horizon?

Exponential discount factor (500 years)

Would you recommend a time-

variable discount factor (in time span of

centuries?) … (e.g. hyperbolic)

0

100.000

200.000

300.000

400.000

500.000

600.000

0 100 200 300 400 500

Time (years)

Cu

rren

t va

lue

(Euro

s)

hiperbolic discount factor r=1%

hiperbolic discount factor r=3%

hiperbolic discount factor r=5%

t1

1DFa

ab

a=b=2r

Hyperbolic discount factor

(500 years)

0

50.000

100.000

150.000

200.000

250.000

300.000

350.000

400.000

450.000

500.000

0 100 200 300 400 500

Time (years)

Cu

rren

t va

lue

(Eu

ros)

1%

3%

5%

Exponential discount factor

(500 years)

Would you vary the discount rate with

the time span?

Discount rate

3,5 %

3%

2,5 %

2 %

1,5 %

1%

0 - 30

31 - 75

76 - 125

126 - 200

201 - 300 años

> 301 Treasury Green Book proposal

H M Treasury (2003): The Green Book: Appraisal and Evaluation in Central Government. HM Treasury, London. http://greenbook.treasury.gov.uk/

Time span (years)

Discount rate Time span (years)

3 - 4 %

2 %

1 %

0 %

0 - 25

25 - 75

76 - 300

> 301

Weitzman, M.L. (1999) Just Keep Discounting, But.… In: Portney, P.R. and Weyant, J.P. (eds.). Discounting and intergenerational equity. Resources for the future. Washington.

Gamma-Weitzman discounting

505.797

188.869

43.885 27.108

-

100.000

200.000

300.000

400.000

500.000

600.000

SDR =0 % SDR =1 % TSD =2,5 % SDR =3 %

Green BookWeitzman

A n

um

eri

cal exam

ple

: A

lman

sa a

nd

Cala

trava (

20

07

)

The effect of Discounting:

The present value in year + 100

505.797

3.494 0

45.982 16.316

-

100.000

200.000

300.000

400.000

500.000

600.000

SDR =0 % SDR =1 % SDR =3% HDF (r =1 %) HDF (r = 3%)

Exponential Discounting Factors Hyperbolic Discounting Factors

Green BookWeitzman

t1

1HDFa

ab

; a=b=2r

The effect of Discounting:

The present value in year + 500

A n

um

eri

cal exam

ple

: A

lman

sa a

nd

Cala

trava (

20

07

)

Would you recommend different discount rates

for tangible and intangible effects,

in the same CBA?

v1

CiBi

r1

CtBtt

nt

0tt

nt

0t

NPV

SDR 0 < EDR SDR

Market costs and benefits (tangible effects)

Non-market costs and benefits; e.g. environmental goods (intangible effects)

Almansa and Calatrava (2007) Reconciling sustainability in Cost Benefit Analysis: a methodological proposal. Ecological Economics, 60 (4): 712-725 .

Net Present Value (1/2)

SDR = ce + pce represents the principle known as decreasing marginal utility of consumption. This term may decrease since this hypothesis does not hold.Thus, if in 200 years’ time, people are going to be worse off in terms of “environmental well-being”, the damage to them in terms of loss of natural recreational spaces, for example, will be no less than that suffered by the current population, as usually affirmed.

The term p is the pure temporal preference rate, and it is logical to assume that p is lower in the case of environmental goods, either because of an “imperative” of inter-generational equity, or simply, due to certain empirical evidence.

Reasoning for EDR SDR

(2/2)

Almansa and Calatrava (2007) Reconciling sustainability in Cost Benefit Analysis: a methodological proposal. Ecological Economics, 60 (4): 712-725 .

If you are interested in receiving references to works concerning the discounting approaches described in this presentation, please let us know.

Thank you very much for your participation!