Chapter 6. Benefit-Cost Analysis

Introduction

Once private and social budgets for high yielding paddy have been calculated according to the description in Chapters 3 and 4, the computation of B-C ratios and internal rates of return (IRR) on agricultural investments is quite straightfoward. The first step is to set up a second PAM that describes a production system that has not yet had the benefits and costs of land leveling, deep plowing, grading, and ditching. Such a system falls into the Indonesian category of a “medium” or “poor” water control. It could be expected to yield considerably less, say, approximately 5,000 kgs/ha instead of the 6,000 kgs/ha expected in areas having good water control.

The good water control area from which the previous manual exercises have been drawn will be called the “with” project area. At some point in the past, the necessay leveling, structure construction, and channeling deepening were completed. The poor control area is less fortunate and the land is more uneven, the structures less precise, and the water less certain. This more backward area will be called the “without” project site.

The incremental benefits from the project are obtained by the poor area (without project) from the improved “with project: case.1 The period-specific stream of incremental costs and benefits yields a “cash flow” that will be analyzed to determine the economic desirability of the desired investment.

Evidence from surveys indicates clearly that areas in Indonesia in which water control is poor have lower paddy yields and fewer high valued crops, including double and triple cropping of paddy. Good water control is differentiated from poor control by the extent of the control structures, the quality of the land forming, the strength of the bunds, the adequancy of drainage, etc. The costs of improving the degree of water control involve a wide range of expenditures including engineers, construction workers, agriculturalists, equipment, administrators, etc. It is the return to these investments that the B-C ratio and the IRR developed in this exercise measures.

Chapter 6 is divided into a series of steps that will be largely familiar from previous chapters:

computing the private and social budgets for the “without” project case,

computing the private and social budgets for the “with” project case,

subtracting the “with” from the “without” project budgets to compute a flow of incremental net revenues,

estimating the cost of the investment being investigated,

computing the discounted IRR (internal rate of return) or Benefit-cost (B/C) ratio of the capital expenditure.

Without Project at Private and Social Prices

Private Prices

As noted above, the project’s return lies in the incremental benefits --the difference-- between farming systems with and without investments. Therefore an accurate characterization of the without project case is just as important as the projection of the benefits expected from the project implementation. Theoretically, at least, overly pessimistic views of what would transpire in the absence of a project can be as important in producing inflated B-C ratios and IRRs as overly optimistic views of what the project is likely to accomplish. It is the difference between the two budgets that determines project benefits.

Table 6.1 provides data on the technical coefficients (units per ha) of the crops in the without project farming system. For the purpose of illustrating the benefit-cost concepts. Ordinarily, it would differ from the with project input-output table in a number of ways. However, in the interest of simplicity, it is the same as Table 3.1 in Chapter 3 except for the crop yield which is 5,000 kgs/ha rather than 6,000 kgs/ha. Open a new workbook and call it “B-CTutorial.” Label the first worksheet “P-Without” for without project at private prices. Copy the worksheet in Chapter 3 into the newly created worksheet in the new workbook.

Table 6.2 is identical to Table 3.2. Private and social prices are assumed to remain unchanged in the with and without project conditions.

Table 6.3 is the same as Table 3.3 except that figures relating to revenues and profits differ as a result of the new assumption about yields.

Social prices

Utilize the technique applied in the previous section to create a without project budgt at social prices. Rename the second spreadsheet in the B-CTutorial workbook as S-without. Then copy the worksheet created in Chapter 4 of the PAMTutorial into the newly created worksheet. Rename Table 4.1. Physical Input-Output to Table 6.4. Physical Input-Output (Poor Control)

Rename Table 4.2 to Table 6.5. Social Prices (Poor Control).

Rename Table 4.3 to Table 6.6.

Be sure that the yield coefficient in Table 6.4 has been changed from 6,000 kgs/ha to 5,000 kgs/ha to reflect that this latter sequence refers to the poor water control area. Comparison of the newly created social budget table with the one created in Chapter 4 shows the impact of the changed yields on total revenues and on profits. It is the latter that is crucial in determining the difference between the with and without budgets.

With Project Budgets at Private and Social Prices

Improving water control ordinarily leads to a number of increases in revenue streams. In Indonesia, the two most important are raising the yields of paddy, and replacing lower-valued palawija crops (corn, soybeans) with additional paddy crops.

Private Prices

In this exercise, it is assumed that the with project conditions, with their good water control, yield approximately 6 tons per acre, the same as those used to compute the original PAMs in the PAMTutorial. Copy these to two new worksheets entitled P-With and S-With. Re-label Table 3.1 Physical Input-Output to Table 6.7. Physical Input-Output (Good Control).

Change the other table numbers in the private prices tables accordingly. Table 3.2 becomes Table 6.8.

Table 6.9 Private Prices Budget (Good Control) is shown below for reference. (This is the same table as Table 3.3)

Social Prices

The With Project Physical Input-Output table is the same as Table 4.1. Copy these tables (4.1-4.3) into the worksheet named S-with. Rename Table 4.1 to Table 6.10. Rename the other tables accordingly. Table 4.3 is called Table 6.12 Social Prices Budget (Good Control). The tables are shown for reference. All contain a reminder in the heading that they refer to an area that has the benefits of good water control, i.e., they are the “with” project example.

With and Without Project PAMs

It is helpful to organize the incremental benefits calculation from two (with and without) PAMs. In the final steps of project analysis, it will be important to compare private and social B-C ratios. If the B-C ratios do not yield the same conclusions regarding project feasiblity, knowledge about which policies are causing the divergences and likelihood that they are amenable to reform will be important in reaching a final conclusion before committing resources to the activity.

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Insert a new worksheet and call it B-C Pams. Create two PAMs that reflect the with and without budgets. Name the without PAM Table 6.13. Without Project PAM (Poor Water Control). Name the with project PAM Table 6.14. With Project PAM (Good Water Control). Create the two PAMs from the private and social budgets. The tables are shown below for reference.

Table 6.15 shows how the two PAM tables (Table 6.13 and Table 6.14) can be reorganized to produce the stream of benefits and costs that are needed to compute the project’s feasiblity.

The new “project PAM” for private prices consists of the private prices line from Table 6.13 and from Table 6.14. Subtracting the profitabilities of the poor control (without) PAM from the good control (with) PAM produces incremental benefits for the life of the project.

Some adjustments are needed because no production will be forthcoming during the first period under good water control and full development will not occur until period 4. These are shown in column 5.

A new column is needed in Table 6.15 to accommodate investment costs. (A new worksheet containing the details of the investment costs will also be needed. Elements that might be in a project to improve water control are indicated in Table 6.18 below.)

Once the stream of benefits has been created, the next step is to calculate the net present value (NPV) of benefits and costs. The formula for computing the NVP in Excel is =NVP(rate, range) where the rate is the discount rate and range is the range of cells that make up the benefit or cost stream. Dividing the discounted benefits by the discounted costs yields the B-C ratio relevant to determining the feasiblity of the project at private prices. The formula for the computation is:

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The numerator of the expression is the discounted stream of incremental benefits obtained when the profits of the without PAM are subtracted from the profits of the with PAM. The denominator is the stream of discounted investment costs. Table 6.15 indicates that the B-C ratio for a project that improves water control on a hectare of land, given the investment costs, is 2.8.

Table 6.16 shows the same set of calculations for social prices. As expected, the B-C ratio of 1.72 is less than the ratio at private prices. The difference is again the effect of subsidies to rice growers that increase the value of domestically produced rice by approximately 25 percent over its world market price.

The discount rate in the B-C calculations is assumed to be higher than the private rate. That is, the opportunity cost of capital to the economy as a whole is greater than the cost of capital to private borrowers. The higher the discount rate, the less benefits in future years are worth, and the lower will be the B-C ratio.

Table 6.17. provides a breakdown of investment costs at private prices. It is purely illustrative but it is worth making this step explicit in the model. Insert a new worksheet and rename it Invest. Copy in the items shown in Table 6.17. Create a similar table (Table 6.18) and add it to the Invest worksheet. Link the results of the investment tables to the Tables 6.15 and 6.16. Investment costs ordinarily receive a great deal of attention in project work and integrating them into the framework of B-C calculation provides a mechanism for making changes as better engineering information becomes available. (It is at this point that software such as Microsoft Project become helpful.)

The Internal Rate of Return

Once net revenues at the farm level have been computed and investment costs estimated, the cash flow from which the project’s internal rate of return (IRR) can be calculated. Column 9, the last column in Tables 6.15 and 6.16, is the sum of Column 6 (benefits) and Column 7 (costs). At the bottom of the column, use Excel’s algorithm to compute the IRR for the columnm.

The Excel formula for computing the IRR is =IRR(range, guess) where “range” refers to the cells that describe the project’s cash flow and “guess” is the user’s conjecture about what the IRR will be. If there is only one sign change in the stream of benefits and costs, virtually any guess will do. The algorithm is able to converge with little outside input. However, if there is more than one change of sign, several guesses may be required before a potential interest rate is found that will produce a successful IRR convergence.

After the IRR is calculated, it can be compared to the appropriate private or social cost of capital to determine if the project is economically feasible. For example, if the private rate of return is greater than the prevailing cost of capital to private borrowers from banks and other lending institutions, it would be a signal that the project was worth implementing. The social IRR should be compared to longer term instruments such as long-term bonds to determine if the project is socially desirable.

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Price Gitinger’s book, The Economic Analysis of Agricultural Projects, provides a more detailed guide to the concepts and the organization of the IRR computations. (The book is on-line at http://www.stanford.edu/group/FRI/indonesia/documents/gittinger/Output/title.html .) This chapter provides an overview of these concepts, along with a numerical example that provides concrete data to reinforce the concepts discussed.