Slide 1

Scott PearsonStanford University

Benefit-Cost Analysis

Scott Pearson is Professor Emeritus of Agricultural Economics at the Food Research Institute, Stanford University. He has participated in projects that combined field research, intensive teaching, and policy analysis in Indonesia, Portugal, Italy, and Kenya. These projects were concerned with studying the impacts of commodity and macroeconomic policies on food and agricultural systems. This effort culminated in a dozen co-authored books. These research endeavors have been part of Pearson’s longstanding interest in understanding better the relationships between a country’s policies affecting its food economy and the underlying efficiency of its agricultural systems. Pearson received his B.S. in American Institutions (1961) from the University of Wisconsin, his M.A. in International Relations (1965) from Johns Hopkins University, and his Ph.D. in Economics (1969) from Harvard University. He joined the Stanford faculty in 1968 and retired in 2002. The framework used in this lecture has been developed in conjunction with Carl Gotsch, the author of the Benefit-Cost computer tutorial included in this series. Materials in the lecture and computer tutorial have benefited from the work of J. Price Gittinger, Economic Analysis of Agricultural Projects. The book is on-line and, where possible, links have been made to it from the lecture and the tutorial. The book provides both a solid theoretical foundation and detailed examples for computing benefit-cost ratios (B-C) and internal rates of return (IRRs).

Slide 2

PAM Basics• Gather data on technical relationships (I-O

table) and private and social prices

• Use the I-O table to compute private and social profits (revenues minus tradable input and domestic factor costs)

• Subtract social from private entries (revenues, costs, profits) to identify divergences (distorting policies or market failures)

The Policy Analysis Matrix (PAM) approach is based on two sets of commodity budgets, one computed using private (market) prices, the second using social (efficiency) prices. Cells represent either individual commodities or a mix of activities that constitute a commodity system. The PAM analysis is an important step in determining which investments are likely to have a high payoff. Investing resources in expanding the production of commodities that are socially unprofitable is generally an unwise strategy.

Slide 3

Revenues Input Costs Factor Costs ProfitsPrivate

A B C DSocial

E F G HDivergences

I J K L

PAM Entries

This slide reviews all twelve entries for a PAM, given by the letter symbols A through L. The first row of a PAM contains measures of prices in private prices (the observed market prices). The symbol A measures revenues in private prices, the symbol B stands for tradable input costs in private prices, the symbol C represents domestic factor costs in private prices, and the symbol D is private profit. The second row of a PAM contains measures of prices in social prices (prices that would result in the best allocation of resources and thus the highest generation of income). The symbol E measures revenues in social prices, the symbol F stands for tradable input costs in social prices, the symbol G represents domestic factor costs in social prices, and the symbol H is social profit. The third row of a PAM is termed the Effects of Divergences row. Divergences arise from either distorting policies or market failures; either source of divergence causes observed market prices to differ from their counterpart efficiency prices. The symbol I measures divergences in revenues (caused by distortions in output prices), the symbol J stands for divergences in tradable input costs (caused by distortions in tradable input prices), the symbol K represents divergences in domestic factor costs (caused by distortions in domestic factor prices), and the symbol L is the net transfer effect (arising from the total impact of all divergences).

Slide 4

PAM and Public Investment Policy Analysis

• SBCR ratios – show comparative efficiency of systems before new public investment

• baseline social profits give critical information for investment planners

• only additions to social benefits count as social gains from public investment

• project analysis – altering technical coefficients, world prices, and factor prices –in future

The results of PAM analysis have wide use in the analysis of public investment policies (PAM, pp. 238, 240, 242, 244-245). This application can be especially important for local and regional government agencies. Analysts compute ratios to compare social results from agricultural systems that produce unlike outputs. The social benefit-cost ratio (SBCR) is equal to the ratio of social revenues to social costs, or SBCR = E/(F + G). The compilation of PAMs greatly assists evaluation of public investments. The PAM shows social profits (H) before the new public investment. In social benefit-cost analysis, only additions to social benefits count as gains from the public investment. The PAM analysis thus provides a baseline set of data and results for investment planners. The analysis of public investment projects then consists of altering technical coefficients, world prices, or factor prices in the underlying PAM budgets to calculate alternative future streams of revenues and costs. These additional results reflect the impact of the public investment on the initial conditions. To estimate the gains from public investment, the analyst then compares the social profits before the public investment (the original H in PAM) with the expected new social profits. These gains are then compared with the projected costs of the investment to calculate benefit-costs ratios and thereby evaluate alternative investment opportunities.

Slide 5

Benefit-Cost Basics• “Without project” case

• use PAM methods to compute private profitability (D) and social profitability (H)

• “With project” case• construct a second PAM using an input-output table that

incorporates the impact of a capital investment• use PAM methods to compute private profitability (D’) and

social profitability (H’)

• Compute capital investment costs, e.g., pumps, dams, extension programs, research projects.

• B-C ratio = incremental revenues ( with project less without project) divided by investment cost

The data gathered for a benefit-cost analysis are very similar to the data collected in a PAM appraisal. There are two major additions: information on the cost of the project investment whose benefit is being evaluated, and a second input-output table that incorporates the impact of the investment. In the case of an investment in pumps, for example, the second input-output table would reflect increases in yields that irrigation makes possible as well as new crops that can be grown with the additional water. The initial PAM provides the data for the “without project” case. A second PAM, utilizing the information in the new input-output table, provides the profitability in the “with project” case. Subtracting the without project profits from the with project profits yields the incremental benefits of undertaking the investment. These incremental benefits are compared with the cost of the investment to determine if the benefits exceed the costs. When incremental benefit exceeds the cost of investment ( B/C > 1), the investment should be undertaken – unless investment funds are limited and the B-C ratios of other projects exceed that of this project.

Slide 6

Single-Period Benefit-Cost Analysis

HGFEW/O∆H/ISIS∆H

H’G’F’E’WSocial Calculations

∆D/IP

IP∆DDCBAW/OD’C’B’A’W

B-CI-CostProfitCostsRevPrivate Calculations

The PAM for the poor water control system reflects what is known in the project appraisal literature as the “without project” (W/O) case. It shows what would happen if there were no intervention in the farming system. The second “with project” (W) PAM, indicated by primes on the symbols in the table. incorporates the effects of changes in yields that would result from the application of additional fertilizer or chemical inputs. The slide illustrates the calculation of a single-period benefit-cost B-C ratio for the use of inputs such as fertilizers and chemicals. In the single-period example, both the investment and the returns to the investment occur in the same year. Incremental benefits from the investment are obtained by subtracting the private and social profits of the without project PAM from those of the with project PAM, resulting in ∆D, the change in private profitability, and ∆H, the change in social profitability. These incremental benefits are the numerators of the benefit-cost ratios. The costs of the fertilizer and chemicals, measured in private and social prices, are the denominators. The private benefit-cost ratio thus is ∆D/IP and the social benefit-cost ratio is ∆H/IS.

Slide 7

Single-Period Benefit-Cost Analysis Example

Private Calculations (‘000 Rp)

1.935009641,656.52,1421,0214,820W/O

2,620.52,1421,0215,784WSocial Calculations

2.415001,2052,976.52,028.59666,025W/O 4,181.52,028.59667,230W

FactorsInputsB-C I-CostProfitsCostsRev

A numerical example of a single-period benefit-cost calculation, using the PAM results generated in lecture 5, is shown in this slide. An investment of Rp 500,000 in short-term inputs, such as fertilizers, fuel, seeds, and chemicals, yields an increase in output of 1,000 kg/ha. The resulting incremental net revenue in private prices is Rp 1,205,000 (1,000kg/ha x Rp 1,205/kg), and the single-period private benefit-cost ratio is 2.41 (Rp 1,205,000/Rp 500,000). In social prices, the incremental net revenue is Rp 964,000 (1,000 kg/ha x Rp 964/kg) and the social benefit-cost ratio is 1.93 (Rp 964,000/Rp 500,000). The difference in the two benefit-cost ratios is caused by the trade policies (tariff on rice output) and subsidies (subsidy on chemical inputs) discussed in lecture 5.

Slide 8

NetBenefits

Years

Plus

Minus Without project benefitsMinus

With project benefits

Multi-Period B-C Basics

Most projects involving capital investments last for a number of years. Typically, agricultural investments, e.g., irrigation pumps, marketing facilities, or livestock shelters, yield little in the early years in which they are implemented and then produce a stream of benefits that may last well into the future. The slide depicts graphically the time stream that these types of projects generate. At first, the cash flow of net benefits (incremental benefits plus investment costs) is negative because investment costs dominate returns. As project costs decline and benefits increase, the picture is reversed and the cash flow becomes positive. This cash flow is discounted and summed to compute the project’s benefit-cost ratio. The project will have a positive benefit-cost ratio if the net present value of the plus (light yellow) region exceeds the net present value of the minus (olive green) region.

Slide 9

Multi-Period B-C Analysis Private Calculations (‘000 Rp)33

24%4,76213,86922,8952.9B-C

1,205454.21,20520

……………

1,2051,0931,20525%Rate(5,000)4,7621Period

DiscoUndisc

5,0001,2052,9772,028.59666,025W/O

(IRR)4,1822,028.59667,230WFactorsInputs

Cash Flow

I-CostProfitsCostsRev

The multi-period example in slide shows the impact of discounting on private benefit-cost ratios. If an investment of Rp 5,000,000 were made in a single-period model and the profits were the same as in the previous example (Rp 1,205,000), the B-C ratio would be .24. The project would not be feasible. However, the actual activity envisaged in the table improves the field’s water control by leveling the land, strengthening the bunds, and deepening the surrounding drainage ditches. It is assumed that each plot can be farmed three times a year, i.e., there is triple cropping. In the season when the work on the land is undertaken, there would be no production. In the subsequent 20 periods (roughly 7 years), however, increased profits would accrue without further investment. Evaluation of these profits and costs, at full development and without discounting, would yield a benefit-cost ratio of approximately 4.6 (Rp 22,895,000/Rp 5,000,000). Discounting the elements of the project at an annual discount rate of 15 percent (5 percent per period or season) yields a benefit-cost ratio of 2.9 (Rp 13,869/Rp 4,762). Costs, because they occur in the first year of the project, are discounted very little. The discount factor in that year is only .9523. Benefits in the 21st period, on the other hand, are discounted more heavily because they occur much further in the future; the discount factor in that period is .3769. The result is a significantly smaller B-C ratio (2.9) than that computed with undiscounted data (4.6). The benefits of improving the water control on the plot would probably continue for a decade or more. However, the discounting procedure would make these benefits very small and they would have little effect on the sum of the benefits. For example, at 10 years (30 periods) the discount factor, using a rate of 5 percent per season, would be .2313. Fifteen years with three crops each year would yield a discount factor of .1113. The lesson of the discounting calculations is that most of the benefits of the project must be realized within the first 10 years (30 periods) to have an impact on the benefits of the B-C ratio.

Slide 10

( )

( )∑

∑=

=

=

=

+

+∆

nt

tt

Pt

nt

tt

t

iI

iD

1

1

1

1

where:

i = interest rate

n = life of the project in years

Multi-Period Benefit-Cost Formula

The multi-period formula yields a discounted benefit-cost ratio. This ratio is obtained when the present value of the benefit stream is divided by the present value of the cost stream. The numerator of the multi-period benefit-cost formula sums the discounted benefits, and the denominator sums the discounted investment costs. The benefit-cost ratio was developed originally to evaluate water resource projects in the U.S., and it is still used by the U.S. Army Corps of Engineers and the Bureau of Reclamation. However, the B-C ratio is not widely used in developing countries where the internal rate of return (IRR) is more popular. The time series in empirical example shows each element of the discounted cash flow. Algorithms available in spreadsheets bypass the need to compute each element separately and yield the net present value of a time series at a specified interest rate. In Excel, the formula for computing the net present value of a time series is =NPV(rate, range) where rate = the discount rate, and range = the cells containing the time series.

Slide 11

Computing an Internal Rate of Return (IRR)

( ) 011

=+−∆∑

=

=

nt

tt

Ptt

iID

IRR = the discount rate (i) such that:

internal rate of return – interest rate at which project breaks even – used by World Bank and aid agencies

The internal rate of return (IRR) is the discount rate that would make the net present value of the benefit stream (incremental benefits minus investment costs) equal to zero. It is the maximum interest rate that can be paid for an investment if the project is to break even. The formal selection criterion for the IRR measure of a project is to accept all independent projects having an internal rate of return equal to or greater than the opportunity cost of capital. The internal rate of return is the measure used by the World Bank and most other international financing agencies for practically all benefit-cost analyses. In Excel, the formula for computing the internal rate of return is =IRR(range, guess) where range is the range of cells that make up the time series and guess is an interest rate that will help the algorithm begin the iterative procedure it uses to find an answer, i.e., an “i” that satisfies the equation.

Slide 12

Numerical IRR Analysis• Internal Rates of Return – Indonesian paddy system

• private prices – 24% – Table 6.2 (PAM book)• social prices – 19% – Table 6.3 (PAM book)• private higher – 25% tariff on rice• both above opportunity costs of capital• will be implemented if IRR is higher than alternatives

• planners prefer social IRR – efficient use of capital

• but private IRR must exceed private opportunity costs of capital – or farmers will not increase output

The spreadsheet’s algorithm, when applied to the time stream of benefits and costs in the private profits table, yields an IRR estimate of 23.8 percent. The IRR of the cash flow shown in the social profits table is 19 percent. The social IRR is lower than the private IRR for the same reasons that the social benefit-cost ratio was lower than the private ratio in previous analyses. (These rates can be tested by inserting them as discount rates in the benefit-cost calculation. The result should be a B-C ratio of 1.) Both of these IRRs are well above the usual estimates of the private and social costs of capital for Indonesia. However, it is not difficult to see that marginal projects might produce contradictory results, i.e., the private benefit-cost ratio might be greater than one while the social benefit-cost ratio was less than one or vice-versa. Planners would prefer to use the social rate because it reflects the real costs of capital to the economy as a whole. Care must be exercised, however, in undertaking projects based only on social profitability (efficiency). If the incremental private profits are negative, the private incentives needed for implementation of the efficient project will not be adequate. Differences between private and social rates of return on projects make the same case for policy reform that arise from examining the results of the original PAMs on which the calculations are based. For example, in the example above, the yield increase from improving water control was substantial, 1000 kgs/ha. When valued at social prices, the resulting B-C ratio was 1.9. Because rice production was protected, private profits were greater than social profits and yielded a B-C ratio of 3.0. In this example, private and social benefit-cost ratios pointed in the same direction and planners can proceed with the knowledge that private incentives are consistent with social efficiency. But in many situations, farmers are directly or indirectly taxed on their output. The result can be a social B-C ratio that is greater than one while the private B-C ratio is less than one. In that instance, farmers will have little interest in expending resources to undertake their share of the project. Without policy reforms that remove the output taxes, the project is unlikely to be implemented successfully.