Coastal Services Center

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Benefit-Cost Analysis

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Introduction

A beach nourishment program may be comprised of a series of beach nourishment projects, termed beach renourishment, constructed over a 50-year period. The temporal nature of a beach nourishment project's impacts poses special problems for valuation, including extrapolating future costs and benefits, evaluating the effects of uncertainty associated with random future events, estimating future behavioral responses to the project, and discounting future costs and benefits. An economic model representing the beach nourishment program assists economists and engineers in predicting the results of the complex processes that take place over many years. An economic model consists of assumptions, relationships, and predictions or implications, and provides a framework to use in systematically assessing and measuring results.

Figure 1. Benefit Cost Schematic

The U.S. Army Corps of Engineers (USACE) requires a benefit-cost model or analysis for all beach nourishment projects seeking federal funds. Benefit-cost analysis compares all relevant beach nourishment project benefits to all relevant beach nourishment project costs. Benefits include the estimated storm damage reduction and recreational benefits. Costs include the expected costs of construction, the present value of periodic maintenance, and any external costs such as environmental costs associated with mitigation. If costs outweigh the benefits then the project is rejected. There are three common methods used to compare benefits and costs. Net present value (NPV) measures the difference between the project benefits and the project costs (NPV = $ Benefits - $ Costs). The benefit cost ratio (BCR) is a ratio of dollar benefits to dollar costs (BCR =$ Benefits/$ costs). The internal rate of return (IRR) is the implicit interest rate returned by the project. Usually only one method is reported in an analysis. A positive NPV, a BCR greater than one, or an IRR greater than the benchmark rate imply that the benefits of the project are greater than the costs. The implication is that the project should be undertaken. A negative NPV, a BCR less than one, and a IRR less than the bench mark rate implies that the benefits of the project are less than the costs and the project should not be undertaken. Although all three methods of comparison are used, the NPV method of comparison is theoretically preferred. Benefit cost analysis reduces a complex problem down to one number. It is important to understand the assumptions and theory behind the calculation of that one number.

The analytical process requires inputs from models representing a variety of disciplines. Arbitrarily these models have been divided into three broad areas: models of beach behavior, environmental models, and economic models. Figure 1 presents a schematic of the cost benefit process.

Inputs to Benefit Cost Analysis

The models of beach behavior used to evaluate project benefits are engineering models that describe physical beach processes. These models estimate the rates of beach erosion or the number of years before certain buildings or coastal structures are destroyed or impacted by erosion or storms. These models are also used to estimate the design life of a beach nourishment project and the time intervals between renourishment projects as required to maintain the beach. A simplified version of a physical beach behavior model can be described as follows. A segment of shoreline is studied and erosion rates over a period of time are calculated. An assumption is usually inferred in that the past long-term erosions rate will apply in the future. Then, given an initial starting point or baseline for the beach, the future position of the beach, and its proximity to upland structures, can be estimated for any year by applying the annual erosion rate over a specified time period. From this, an estimate of the land value and structure losses is calculated. The model can also be used to determine, given the erosion rates, how frequently a beach must be maintained or renourished. A more complex model will recognize that in any given year the actual erosion rate will be different from the long-term average rate. For protection purposes a safety margin based on the probability of the erosion rate exceeding a particular value may be estimated and the nourishment project design adjusted accordingly. The results of the model of beach behavior are used in the benefit-cost analysis to determine the value of storm damage reduction and storm protection benefits in the absence of a beach nourishment.

The beach model is also used to estimate the construction cost of the project, as these analytical models determine the amount of sand that is required to nourish the beach. The erosion rate and past weather patterns provide an estimate of how long the nourishment project will provide additional beach widths before a renourishment project is constructed. Since the beach model estimates future events, uncertainties create problems including estimating the actual severity and frequency of storms, variability in erosion rates for a given storm climate, and the continuing availability of sand sources. The results of the models of beach behavior essentially drive the cost estimation in the cost benefit analysis and the storm damage reduction benefit of the economic analysis. The cost project inputs, the sand, labor, and other materials, can be estimated using market prices. However, usually there are no market prices for storm damage reduction. There are several methods that can be used to assign monetary values to the projected storm damage reduction benefits. These include a) the contingent valuation method, b) the averting behavior approach, and c) the hedonic approach.

Nourishing a beach can have unintended environmental outcomes. A typical benefit cost study will attempt to include a monetary value for the unintended positive environmental outcomes as well as the unintended negative environmental outcomes. Doing so is a two-step process. The first step is to model what happens to the environment with and without the nourishment project. The second step is to assign monetary values to the projected outcomes. The contingent valuation method, the travel cost or Clawson approach, and the hedonic approach are widely used to assign monetary values to the projected environmental outcomes.

Nourishing the beach also may provide enhanced recreational opportunities. These models combine behavioral assumptions with supply and demand concepts to estimate recreational benefits attributable to the project. Once again, there are usually no market prices directly related to recreation. Indirect estimation methods must be employed. These include the a) the contingent valuation method, b) the travel cost or Clawson approach, and c) unit day value method.

Ideally, market prices would be used to ascertain estimates of a project's costs and benefits; however, since prices do not exist for many of the required estimates, indirect methods have been developed. The contingent valuation method relies on survey techniques to estimate the benefits of recreational beach use. The survey determines the individual's willingness to pay for the benefits of a nourishment project. Similarly, for determining recreational benefits, this technique may be used to determine storm protection and environmental benefits. For example, visitors to the beach will be asked a series of questions regarding why they visited, how often they visited, their expenditure patterns, and their willingness to pay for beach use to provide the economists with data used to estimate recreational benefits. A more detailed description of the contingent method may be found in the companion paper on "Recreational Valuation and Willingness to Pay" Web page.

The Clawson method or travel cost method, which uses travel costs as a proxy for market prices, has been used to estimate demand curves for semi-public goods. The Clawson method uses the total number and frequency of beach visits with data and information on distance from the beach to estimate the recreational value of the beach. However, the data requirements for application of this method are extensive, and there are problems involved in using this method where tourists are expected to visit a number of recreation sites. This method may be applicable to measuring recreational benefits at beaches where beach users are day visitors.

Hedonic pricing uses statistical analysis to estimate benefits from related goods that are sold in a market. For example, "beach valuation" for a house may be estimated using housing prices, housing characteristics, and proximity to the beach. One of the components of the value could be beach width, which would provide insight into storm protection (and recreation) for beachfront property. The averting behavior or opportunity cost approach involves estimating storm damage reduction benefit from the cost that property owners incur to avert storm damages if the nourishment project were not undertaken. One assumption is that beachfront property owners would build seawalls at great expense to armor their property to protect it from erosion related damages. Thus, the cost savings of not armoring the property become the storm damage reduction benefit of the beach nourishment project. Another method, unit day method, applies a standard daily value as the recreational value for the use of the beach. Current federal policy restricts the use of this method (Vincent 1986) in beach benefit-cost studies, and it is not covered in this paper. Additional information about the unit day method can be found in Vincent (1986).

Cost Benefit Analysis Issues

The basic model used to estimate whether or not a project is "worth it" is benefit cost analysis. The issues are similar to the issues in more traditional capital investment problems. The shoreline should be protected if the benefits of doing so outweigh the costs over the lifetime of the project. Planned expenditures on shore protection must be compared to expected benefits of the project, where the benefits are expected to accrue over many years. In the private sector capital budgeting techniques are used to analyze the problem of investing in projects where the benefits accrue over many years. In the public sector, costs and benefits are analyzed using benefit-cost analysis. The two methods are similar; each compares the present value of the benefits for a project (or alternative project) to the present value of the costs associated with the project. Each method follows a similar process including 1) identifying the relevant costs and categories of benefits, 2) measuring costs and benefits, 3) comparing the present value of the benefits to the present value of the costs, and 4) selecting the most economically and technically beneficial project.

Capital budgeting restricts benefits and costs to those that accrue to the organization making the investment decision, while cost benefit analysis attempts to capture a broader range of benefits and costs to society (Nas 1996). For example, a private group of homeowners will generally limit the benefits they consider to storm damage reduction for their own property and any recreation benefit they receive. recreational benefits received by tourists and the beneficial effect tourists contribute to the local economy are, in most cases, external to their decision and not considered. Nor will a private group typically consider any external benefits such as downdrift sand spreading, and thus benefiting adjacent property owners, in deciding whether to nourish adjacent beaches.

The types of benefits and costs evaluated may also depend on who is analyzing the project, as some of the benefits and costs are spatial. For example, a local entity may include local beach development as a benefit if the beach is nourished. However, it may be that without the beach nourishment, development will take place anyway, or this development will just take place somewhere else. From the national perspective, the development is not a benefit.

Temporal Issues

Figure 2. Cost Benefit Time Line

A recurring theme in the benefit cost analysis model is that project costs and benefits must be projected into the future for the life of the project. This creates several problems. First, there are difficulties projecting benefits into the future. Past erosion rates, past storm frequency and intensity, and past recreational behavior are assumed to carry forward. But the future is uncertain, so the actual experience may differ from the projected one.

Second, some of the costs and benefits accrue in the future. Figure 2 shows a time line for costs and benefits for a 5-year project where the initial costs are $2,000, $1,000 maintenance is projected for year 3, and benefits are estimated at $1,000 each year. Five years is very short for a beach nourishment program; it is used for simplicity. Since a dollar spent or received now is not the same as a dollar received or spent in the future, the future values must be discounted back to the present. That is, typically the costs are incurred at the beginning of the project, although there may be periodic maintenance every few years. A project with a design life of 50 years generates the estimated dollar benefit each year for 50 years. But, because we are looking at future benefit flows, and $1 benefit received next year, 5 years from now, or 50 years from now is not the same as a dollar valued today, it is necessary to reduce or discount these future flows back to the present.

Figure 3 shows a spreadsheet for a simple benefits cost analysis for a five-year project where the benchmark interest rate, or discount rate, is 10 percent. Benefits accruing each year, as well as costs associated with each year into the future, must be discounted to the present year. The PV sum of benefits is shown as $3,790.79 and the PV sum of the costs is shown as $2,751.31. Thus NPV is $1,039.48. The positive NPV means that there are greater benefits than costs associated with the project and it should therefore be considered for construction.

The values in the present value factor (row) are used in the PV calculation. These values can be obtained from a present value table, computed on a financial calculator, or calculated from the present value functions in spreadsheets such as Excel. Without further details of the mathematics of discounting, it is important to recognize that the selection of the interest rate used to discount future benefits back to the present value influences the outcome of the benefit cost analysis. The selection of rates is important because higher interest rates result in lower present values of the future "expected" benefits for the project such that higher interest rates effectively lower the present value of benefits. If the present value of benefits falls below the present value of costs, the project is likely to be deemed to be economically unjustifiable and thus should not be chosen. In general, using either the pretax rate of return to private capital or the federal government's borrowing rate as the discount rate seems appropriate. The treasury borrowing rates are published at http://www.slgs.gov/opd/opdirtb.htm for various maturities (Circular No. A-94 Revised).

Summary

Beach nourishment programs are complex projects spanning up to 50 years with benefits to cost analysis used to evaluate the economic viability of these programs. While the analysis reduces the final evaluation down to one number (that is, the benefit-cost ratio), that number is highly sensitive to the assumptions made while performing the analysis. Cost and benefits are quantified and evaluated in present value terms. Economic benefits reflect individuals' willingness-to-pay for benefits such as beach use or their willingness-to-pay to avoid costs as in the case of storm damage reduction. A large percentage of the cost and benefit quantification involves using techniques such as the avertive behavior approach to storm damage reduction benefits or the contingent valuation method for recreational benefits to estimate willingness to pay where prices are not available. The final stage of the analysis involves discounting the benefits and cost. In general, since the percentage of costs that are front-loaded is greater than the percentage of benefits that are front-loaded, higher discount rates lower the benefit-cost ratio.

References

Nas, Tevfik F. 1996. Cost-Benefit Analysis: Theory and Application. Thousand Oaks, CA. Sage Publications, Inc.

National Research Council, Committee on Beach Nourishment and Protection. 1995. Beach Nourishment and Protection. Washington D.C. National Academy Press.

Office of Management and Budget - Circular No. A-94 Revised (Transmittal Memo No. 64), Guidelines and Discount Rates for Benefit-Cost Analysis of Federal Programs, 1992. http://www.whitehouse.gov/omb/circulars/a094/a094.html.

Seitz, Neil, and Mitch Ellison. 1999. Capital Budgeting and Long Term Financing Decisions. Third Edition. Fort Worth, TX. Dryden Press.

Vincent, Mary K., D. A. Moser, and W. J. Hanson. 1986. National Economic Development Procedures Manual - Recreation, Vol. 1 Recreation Use and Benefit Estimation Techniques. IWR Report 86-R-4. U.S. Army Corps of Engineers.