Question

Would increases or decreases in rate of time preference, the elasticity of the marginal utility consumption, and rate of growth rate of the economy make projects more or less justifiable according to dynamic efficiency?

Answer 1

Answer :

The discount rate is the rate at which society as a whole is willing to trade off present for future benefits. When weighing the decision to undertake a project with long-term benefits (e.g., wetland protection programs) versus one with short-term benefits and long-term costs (e.g., logging forests near aquatic ecosystems), the discount rate plays an extremely important role in determining the outcome of the analysis. Indeed, a number of reasonable decision measures (e.g., net present value, benefit-cost ratio, internal rate of return, return on investment) depend critically on the chosen discount rate.

Because a dollar received today is considered more valuable than one received in the future. There are four primary reasons for applying a positive discount rate. First, positive rates of inflation diminish the purchasing power of dollars over time. Second, dollars can be invested today, earning a positive rate of return. Third, there is uncertainty surrounding the ability to obtain promised future income. That is, there is the risk that a future benefit (e.g., enhanced fish catches) will never be realized. Finally, humans are generally impatient and prefer instant gratification to waiting for long-term benefits.

Discount rates are used to compress a stream of future benefits and costs into a single present value amount. Thus, present value is the value today of a stream of payments, receipts, or costs occurring over time, as discounted through the use of an interest rate. Present value calculations of benefits and costs are then compared to determine benefit-cost ratios. For example, if the present value of all discounted future benefits of a restoration project is equal to $30 million and the discounted present value of project costs totals $20 million, the benefit-cost ratio would be 1.5 ($30 million / $20 million), and the net benefit would be $10 million ($30 million — $20million). Any benefit-cost ratio in excess of 1.0 or net benefit above 0.0 demonstrates positive economic returns to society. Note that values used for benefit-cost analysis are often amortized over the project time horizon, yielding annualized benefits and costs. This practice allows for comparison of projects with different timeframes.

Mathematically, the present value of a future benefit or cost is computed based on Equation 1.

PV = FV / ( 1+i) n.....................Equation 1

Where PV = the present value of a benefit or cost, FV = its future value, i = the discount rate and n = the number of periods between the present and the time when the benefit or cost is expected to occur. The following example illustrates how the equation is used. Assume that a future benefit of a salmon habitat restoration project is an expanded catch valued at $10,000,000 in Year 10. Here is how we would calculate the present value of that benefit, assuming a 3 percent discount rate.

PV	=	$10,000,000 / (1+.03) 10
	=	$10,000,000 / 1.34
	=	$7,440,940

The present value will vary widely based on the discount rate used in the analysis. For example, use of a 10 percent discount rate would reduce the present value of the aforementioned benefit associated with salmon habitat restoration to $3,855,433, a 48 percent reduction in present-value benefits. High discount rates, therefore, tend to discourage projects that generate long-term benefits (e.g., wetland restoration) and favor those that create short-term benefits and significant long-term costs (e.g., damming rivers).

Another way of thinking about discount rates is as the inverse of compound interest. That is, whereas compounding measures how much present-day investments will be worth in the future, discounting measures how much future benefits are worth today.

Discounting reflects how individuals value economic resources. Empirical evidence suggests that humans value immediate or near-term resources at higher levels than those acquired in the distant future. Thus, discounting has been introduced to address the issues raised by the existence of this phenomenon, which is known as time preference. Time preference is of significant interest to economists but the weight it is given depends on the discount rates used to perform present-value calculations.

To understand better how time preference works, consider the perspective of the residents who fund a local public project. Most residents would exhibit some degree of impatience and value short-term benefits more highly than those that accrue over the long-term. For example, some of the current residents who bear the costs of the project may die or move out of the local area before the long-term benefits are realized. Many of the benefits would accrue to individuals who later move into the area but played no part in the funding of the project. It may not be possible or practical for those who invested in the project to receive compensation from the ultimate beneficiaries. In addition to time reference, there are a number of justifications for discounting the value of future benefits and costs.

First, inflation is common within most economies. Inflation is a sustained increase in the general price level. The rate of inflation reflects the pace at which general prices are increasing. Deflation is the opposite of inflation or a sustained decline in the general price levels. Deflation rarely occurs. In fact, the last period of sustained deflation in the United States occurred during the Great Depression between 1929 and 1933. Due to the effects of inflation, $10 could be exchanged for more goods and services today than it could be in 10 years. For example, at a 3 percent rate of inflation, the real purchasing power of $10 will decline by nearly 26 percent in the next 10 years. Thus, economists are generally concerned with real, as opposed to nominal, values. Nominal values reflect value without accounting for inflation or applying a discount rate. The real value of a benefit is equal to its nominal value adjusted for inflation. The real discount rate is the nominal rate minus the expected rate of inflation.

Inflation is a primary reason for discounting; however, independent of inflation, discounting is an import tool for assessing environmental benefit streams. Discount rates also reflect the opportunity cost of capital. The opportunity cost of capital is the expected financial return forgone by investing in a project rather than in comparable financial securities. For example, if $10 is invested today in the private capital markets and earns an annual real rate of return of 10 percent, the initial $10 investment would be valued at $25.94 at the end of 10 years. Therefore, discount rates reflect the forgone interest earning potential of the capital invested in the public project. The real opportunity cost of capital is often considered to be higher than the pure time preference rate. The former reflects the productivity of capital; the difference over time is not between the value of a dollar’s worth of services consumed now and a dollar’s worth of services consumed later, but rather a dollar’s worth of services consumed now and the higher future consumption made possible by the return on investment.

Third, public projects involve uncertainty and risk. When public projects are undertaken, including those that involve coastal or wetland restoration, there is a chance that future benefits will not be fully realized or realized at a higher level than estimated (there are also uncertainties associated with costs). For example, natural disaster could undermine efforts to restore wetland habitat, thus reducing or eliminating the future benefits that a restoration project would have generated. The further out into the future these benefits are expected to be realized, the greater the risk that some unexpected event or factor will occur and diminish the value of the future benefit. This uncertainty argues either for reducing the benefits and the costs of a project to reflect risk, or else adding a risk premium to the discount rate, much as “junk bonds” have a higher interest rate than less risky securities. Usually, the preferred method for dealing with uncertainty is directly to adjust benefits and costs (or to perform the analysis quantifying the uncertainty and explicitly considering it in the estimates of benefits and costs), not change the discount rate.

Fourth, humans prefer near-term to future benefits. The inability to defer gratification results in decisions that are slanted toward obtaining near-term benefits, often at the cost of those available in the long-term. Regardless of whether this represents a sound policy, economic value is established based on human preferences, and humans prefer near-term benefits to those that accrue in the distant future.

The social rate of time preference is the rate at which society is willing to substitute present for future consumption of natural resources. The federal opportunity cost of capital and the rate of productivity growth are commonly used as proxies for the social rate of time preference. The argument for using the federal opportunity cost of capital as a proxy for the social rate of time preference is that in the absence of the public project, the federal government could put the funds to productive use reducing the national debt. When using the federal cost of capital, the generally accepted practice is to apply the effective yield on comparable-term Treasury securities (e.g., 20-year Treasury bonds for a study with a 20-year analysis timeframe). During the decade of the 1990s, the average 10-year Treasury bond rate was 6.01 percent whereas inflation averaged 2.88 percent. Thus, the real rate of interest on Treasury bonds was roughly 3.13 percent during the 1990s.

Social policy is also concerned with an equitable distribution of consumption over time. Based on this premise, the rate of productivity growth can be used as a proxy for the social rate of time preference. This policy reflects the opportunity cost argument that the incremental or marginal benefit to the country generated by the public project should grow as fast as the productive capacity of industry. From 1990 to 2003, real Gross Domestic Product grew by 2.96 percent. Thus, using productivity over that period as the basis of the discount rate generates a roughly 3.0 percent rate. The National Oceanic and Atmospheric Administration (NOAA) recommends using the social, or consumer, rate of time preference for discounting interim service losses and restoration gains when scaling compensatory restoration.

Conclusion :

Debate in the literature on discounting has often focused on how to select the correct discount rate. In reality, there is no one, single accepted discount rate used by all economists when performing benefit-cost analysis. Due to the nature of time preference and the opportunity cost of capital, however, economists generally agree that, as ethically challenging as the decision can be, a positive discount rates should be used when valuing future benefits and costs. In practice, discount rate are generally prescribed by the funding agency.

Political concerns, in some cases, are considered when discount rates are chosen. However, arbitrarily selecting discount rates to meet short-term political goals could have long-term consequences. For example, high discount rates tend to discourage projects with high up-front costs and long paybacks, such as dam construction and new mineral extraction operations, but they also discourage coastal restoration and wetlands protection programs. Conversely, low discount rates encourage coastal restoration and wetland protection programs but also encourage dam construction and mineral extraction. Regardless of the rate chosen, it is important to remember that the discount rate is a key determinant in the outcome of an analysis, and for each project, a single rate must be applied to all future benefits and costs.