A Studentís Guide to Cost Benefit Analysis for Natural Resources


Lesson 6 - The Social Discount Rate



I. Introduction to SDR


Recall: We discount future values in CBA to make costs & benefits when they occur across time algebraically comparable (i.e., so you can add them and subtract them).

In order to discount, you obviously need a discount rate.

For government CBA projects, we call the discount rate the Social Discount Rate.

A quote from Baumol: few topics in our discipline rival the social rate of discount as a subject exhibiting simultaneously a very considerable degree of knowledge and a very substantial level of confusion.


How important is the choice of a Social Discount Rate (SDR)? The discount rate for government projects has critical implications for federal budgets, for regional development, for choices, for the environment and for the size of government.

Too high an SDR can mean under-investment in social programs; smaller public sector.

Too low an SDR can mean over-investment; larger public sector.

Thus, the choice of discount rates can have ramifications that transcend the mathematics.


II. Social Discount Rate in Theory

There is a body of theoretical literature on the choice of SDR. Theory maintains that, if there was a single capital market that was perfectly competitive, there will be one interest rate that prevails, and this one interest rate would equate marginal time preference of savers with the marginal productivity of capital.


But economists recognize that in a multifaceted economy with many investment instruments with varying degrees of risk, no single discount rate exists that will measure all possible time preferences and returns to capital. There are many possible discount rates.

[Note: risk = probabilities of outcomes are known, vs. uncertainty = probabilities of outcomes are unknown].


There are 2 Core Building Blocks of SDR Theory:


1) Social Rate of Time Preference (SRTP) - a measure of society's willingness to postpone private consumption now in order to consume later. An indicator of SRTP is the earning rate on personal savings (i.e., by individuals). Key concept: what rate entices individuals to save rather than to consume?


2) Social Opportunity Cost of Capital (SOC) - a measure of the marginal earning rate for private business investments. Key concept: what rate attracts business capital?


These 2 provide some high and low-bound possibilities for determining the SDR. (SRTP=low; SOC=high)


Measuring SRTP and SOC:

1) SRTP: The after tax real rate of return on fixed rate government T-bills is often taken as an approximation of SRTP, and is the

SRTP = i rate on T-bills - tax rate - inflation


* SRTP averages about 0-4%

* it attempts to measure the rate at which society refrains from current consumption (i.e., saves).

* SRTP is a lower bound for SDR; i.e., suggests a relatively low discount rate (risk free T-bills, after taxes, minus inflation)

* SRTP is a liberal standard; it will permit more projects to pass muster


2) SOC : Economists have several ideas on how SOC should be approximated:

1) The book approximates SOC as the variable before tax real rate of return for business investments.

2) Some experts (e.g., Modigliani and Miller, Nobel laureates) used the cost of funds (i.e., commercial borrowing rates, for debt & equity).


Canada and White, Capital Investment Decision Analysis say normal standards for expected returns on private investment are:

1. High Risk (40%): new products, new business, acquisitions

2. Moderate Risk (25%): plant expansion

3. Low Risk (15%): investment in cost reducing measures


* SOC is an upper bound for SDR; i.e., suggests a relatively high discount rate (riskier private investment, before taxes)

SOC is a conservative standard; it will permit fewer projects to pass muster


Summary: SOC is > SRTP.

SOC and SRTP represent sideboards for establishing the SDR; in effect they establish upper and lower bounds.

Some argue that the SDR should =SRTP (maybe even = 0), while others say SDR should= SOC. But most say SDR is somewhere in between SOC and SRTP.


III. A High or Low SDR?

Arguments for Low SDR/Against High SDR:

1. lower discount rates favor investment in future generations

2. high discount rates violates our ethical intuition

3. government has an infinite life, whereas individuals do not and hence are more impatient (i.e., government should have lower time preference)


Arguments for Higher SDR/against low SDR:

1. future generations inherit capital and knowledge from the present generations

2. future generations are always better-off economically & technologically than past generations

3. high discount rates avoid present generations make unreasonable sacrifices

4. high discount rates cause the present generation to invest in high yield projects which will best benefit the future


IV. Weighted Average Method (WAM)

Weighted Average Method (WAM) is a method for establishing the SDR by using weighted averages of SRTP and SOC.


Logic behind WAM methods:

1. all government expenditures must be funded from (hence come from) either:

1. business investment, or

2. private consumption.


This is based on the simple macro economic model:

Y = C + I + G

where: Y = national personal income; C= private consumption; I=business investment; G=government spending.


If Y is fixed, then any increase in G, must come either from: 1) taxes, or 2) government borrowing which will, in turn, reduce either/or planned personal consumption (C) or private investment (I). Key point: G must come from C or I.


2. SRTP is a measure of C, private savings/consumption. SOC is a measure of private investment.


3. Thus, SDR must reflect proportionally the source of where G funds are derived, i.e., either investment (SOC) or consumption (SRTP).


Calculating WAM:


SDR = WAM = (a)SOC + (1-a)SRTP; where; a = proportion of government project cost funded from current private investment and 1-a = proportion of project cost funded from current consumption.


Example:††††††††††† WAM = (a)SOC + (1-a)SRTP

WAM = (.75)16% + (1- .75) 4% = 13 %


If a > 0, WAM will lie between SOC and SRTP [ SOC > WAM > SRTP].


But the problem: what is a? It is difficult knowing this value; i.e., what proportion of government funds come from private investment versus current consumption. Empirical evidence suggests that most government expenditures are financed by what would have been private investment, not consumption. Some suggest that a = .75 of higher.


V. What Discount Rates Do Agencies Actually Use?

The methods used for actual choice of a discount rate often diverges substantially from theory.

The theories may help us to better understand what the SDR should be. But the designation of an SDR for an agency tends to be as much a political as academic process.


Boardman et al says that the preference for a discount rate depends on whether one is: 1) a spender, or 2) guardian. Spenders favor low discount rates, approximating the SRTP. Guardians favor high discount rates approximating the SOC. My experience indicates that agencies benefiting from the project tend to be spenders. In other words, agencies tend to be budget maximizers. There are 3 principal oversight agencies that set discount rates for most federal agencies:


Office of Management and Budget - OMB's predominant mission is to assist the President in overseeing the preparation of the Federal budget and to supervise its administration in Executive Branch agencies. In helping to formulate the President's spending plans, OMB evaluates the effectiveness of agency programs, policies, and procedures, assesses competing funding demands among agencies, and sets funding priorities.


Congressional Budget Office - The CBO's mission is to provide the Congress with the objective, timely, nonpartisan analyses needed for economic and budget decisions and with the information and estimates required for the Congressional budget process.


General Accounting Office - GAO is the investigative arm of Congress. GAO's mission is to help the Congress oversee federal programs and operations to assure accountability to the American people.


Discount rates for evaluation of general public investments:

* OMB uses 10% real, but agencies may justify other rates (e.g., BLM uses 10%, real. US Fish & Wildlife Service use 7.8%, nominal. US Forest Service uses 4%, real.)

* CBO uses 2% plus or minus 2% for sensitivity analysis

* GAO uses average cost of Treasury Debt (i.e., borrowing costs rather than SRTP or SOC.)

*Municipal governments use about 3% real.

This wide discrepancy is admittedly difficult to understand.


Often, the safest practice with CBA analysis is to use several discount rates. We call this sensitivity analysis, because you are examining the sensitivity of your calculations to changes in discount rates. It is a way of dealing with uncertainty. You could also vary things other than just discount rates.>


VI. Very Long-Term Discounting

Some very long-term government projects, such as projects to prevent global warming, raise questions about the ethics of discounting. Because discounting reduces virtually all distant benefits to zero.


Some related thoughts:

1. R.C. Lind suggests that we should not discount at all beyond a normal human life-span (i.e., 70 years).

2. For longterm analyses, other schemes suggest differential discounting (use a lower rate for long-term environmentally sensitive projects)

3. or even declining discount rates such as:

0-25 years, 3-4%

25-75 years, 2%

75-300 years, 1%

300+ years, 0%


However, most economists advocate using a constant discount rate for project evaluation

In the final analysis, longterm discounting is an ethical issue not yet resolved by public policy.


VII. Adjusting Discount Rates for Risk†

Risk - the probability that actual future returns from an investment will be lower than expected returns; risk is often measured by the standard deviation of historic returns.

Risk is a statistical concept. The greater the expected standard deviation of the investment's return, the riskier is the investment.


Adjustment of discount rates for risk is common in corporate finance. If you are interested in the topic, read a textbook in corporate finance (e.g., Brealey and Myers, Weston and Brigham).


Private sector risk adjustment:

In short, corporate finance theory adjusts the MARR to compensate for systematic (market) risk as follows:


risk adjusted discount rate = rf + [E(rm )- rf ]B;

where: rf = a risk free return (like T-bills)

E(rm) = expected (i.e., historic) mean of overall stock market return; usually taken as the Standard and Poor's Composite Stock Index.

B = the asset's Beta; the sensitivity of the investment's return to market movements. Beta indicates that a 1% change in the market interest rate will change the investment return by B%). Beta's are calculated from historic data.


[E(rm )- rf ]B; = risk premium



risk adjusted i = rf + [E(rm )- rf ]B;


= 4% + [12 - 4] 0.5


= 8%

Public Sector Risk Adjustment:

Little attention has been given to risk adjustment to government SDRs.

As Boardman, et al says the state of knowledge (i.e., of Beta's) does not allow us to determine the exact magnitude of the adjustment for government SDRs.

Furthermore, SDRs are set by government policy, so the analyst does not usually have the latitude of computing a risk adjusted discount rate.


Boardman is not strong on adjusting SDRs for risk. However, he suggests these rules for adjustment of government projects:


1) when expected net benefits are negatively correlated with national economic activity, you could use a downward-adjusted (i.e.,lower) SDR.


2) when expected net benefits are positively correlated with national economic activity, should use a upward-adjusted (i.e.,higher) SDR.


Q: But, how much exactly how much should you adjust SDR? This depends on Betas for the government investments and very little information exists on these.


Conclude: As Boardman et al says, the state of knowledge does not allow us to determine the exact magnitude of the adjustment for government SDRs.




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