Treatment of Financial Flows

The economic analysis of projects is normally effected on the basis of a flow of funds expressed at constant prices. However, flows of funds expressed at "constant prices" are often found in which the receipt and repayment of loans have not been deflated by the expected rate of inflation. As this section will show, this inconsistency does not affect the "efficiency" analysis, but does have important consequences for the identification and quantification of distributional effects.

Let us consider the case of a $100 loan received at the beginning of year zero, and repaid in five equal annual payments from the beginning of year one at a nominal interest rate of 10%. This financial transaction will appear in a flow of funds at current prices as shown in the first four rows of Table 9.6.

However, given the existence of a non-zero inflation rate, the reductions in future income required to repay the loan each year cannot be compared with one another, or with the amount of the loan received, until all these values are expressed in the same unit, i.e. in prices of the same year. Given that in cost-benefit analysis, year zero is traditionally used as the base period, it will be necessary to deflate the repayment flow by using the inflation rate in years one to five, which we assume is known, constant and equal to 10%. Thus, to construct the last two columns of Table 9.6, each annual repayment amount R,

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Table 9.6 Flows of Funds from a Loan

must be divided by (1 + 0.1)'; for example, the outflow of funds in year three, #3, can be expressed at constant prices as

Given that in this example the nominal interest rate is equal to the future inflation rate, the real interest rate is equal to zero. In fact, by using Table 9,6 the reader may check that

that is, the amount of the loan received is equal to total repayment values expressed at constant prices. Now, once they have been expressed in real terms, future income flows will have to be discounted at year zero using discount rate d, which will also be assumed equal to 10%. Consequently the present value of the repayment flow at constant prices /?* will be equal to

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AN INDUSTRIAL PROJECT

in which p is the inflation rate. In other words, the recipient of a loan in the circumstances indicated will repay only 78% of what he has received or, in other words, will receive a transfer equal to 22 % of the loan.

In more general terms, if the project receives various loans for an annual total at current prices P, in each year t, the present value of the inflow for a constant inflation raiep will be

If Rt is the annual debt servicing at current prices of the loans, the present value of repayments at year zero prices will be

and the present value of transfers T* = P* — /?* will be

Quantifying the present value of the transfers received through long-term finance (not indexed) means knowing future inflation ratep, which obviously would not be possible. In some countries, in which the type of economic policy expected in the future does not differ substantially from that followed in the past, the analyst will be able to make an approximate projection of a constant rate p. In others, the margin of error will be considerably bigger and there will be no way of avoiding them.²

Deciding who grants transfer PV(T*t) will be postponed until Sections 9.4 and 9.5, but for the moment let us only consider the direct effect, meaning that it is the lending bank that grants the transfer.

We can now go back to Table 9.1, which contains the present value of the flows generated by the project, and consider the values that appear under the heading Finance. In accordance with the notation used,

2, There are countries whose rate of inflation is determined by that of some developed coun-tries, so that the economic policy of the country concerned is not the only determining factor. In the United States, "when Richard Nixon came to power in January 1969 he was greeted by 5%

inflation, a figure which in the eighties would cause rejoicing in the higher spheres, but which at that time alarmed a public used to practically stable prices and worried by the trend away from the stability of the previous three or four years" (Lekachman, 1982, Page 37). In Argentina in 1971 (p71 = 0.35), nobody in his right mind would have forecast the rate of inflation in 1984 (pM =. 6).

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Table 9.7 Present Value of Credits and Their Repayments

is the present value of the long-term loans received and

the present value of the corresponding repayment flow. The loan would be granted by the National Development Bank (NDB), which in Table 9.7, is shown granting a loan to the project of 86,000 and receiving repayments of 48,000.

According to the financial statements contained in the project document, during the first few years, the project will have to rely on short-term loans to finance the formation of working capital. These financial statements show that, as time goes by, the short-term loans will be replaced by internally generated funds. However, short-term credit is offered (and supposedly will continue to be offered during the life of the project) at real interest rates appreciably below the profit rates firms can achieve from the use of such funds. As a result, the demand for such loans greatly exceeds availability and credit is rationed by the banking system. Considering that due to its character-istics, the project is not expected to experience difficulties in obtaining short-term credit, the initial loan will not be replaced by internally generated funds.

Instead, the original line of credit will be maintained and renewed periodi-cally. It will then be useful to explain the procedure for calculating the present value of short-term loans received and the present value of their repayments, shown in Table 9.7.

Let us suppose that at the beginning of period k the project receives a loan P_k to be repaid within 180 days whose value at year zero prices is P\ = Pkl(\ -\-p)^k.³ At the end of the period, the project will have to repay the loan for a total at year zero prices of P\ (1 +/)/(! +/?). At the same time, it will obtain another loan for an amount at year zero prices equal to what is

3. The hyphen above the variables p and further on i and d indicates that the variable is defined for the duration of the loan. For example, if the period is three months, d will indicate the quarterly discount rate equivalent to annual rate d.

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AN INDUSTRIAL PROJECT

necessary to replace the previous loan, plus the project's additional working capital requirements AF£. Thus, in period k+1

At the end of this period, the project will pay P*k+l (1 +/)/(! +p) and will take out a loan P*k+2, and so on until the period k+n+l begins when it will repay P'k+n+i (l+i)/(l+p). The flows resulting from these operations are given in schematic form in Table 9.8. The present value of the loans received, less the present value of their repayments, both at year zero constant prices, will be equal to

By rearranging the terms, the above expression can be rewritten as

[9-1]

where the expression between square brackets indicates the proportion of the present value of the loans that the project receives (grants) as a transfer due to a real interest rate that is less (greater) than the discount rate. Note that if this interest rate is equal to the discount rate, the transfer is nil.

Formula [9.1] is valid when the term limit for all the loans is the same which, although not necessarily true in practice, is a reasonable approxima-tion if we keep in mind that we will be working with annual estimates of the use of short-term loans.

Furthermore, recall that the financing being considered is for working capital and not for current assets, even though the value of current assets better approximates the additional needs for short-term financing for the econ-omy as a whole attributable to the project. For example, if the firm makes

Table 9.8 Receipt and Repayment of Short-Term Loans Year

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purchases of $100 per month due in 30 days and sells goods for $250 payable in 30 days, the monthly demand for 30-day finance created is $350. However, the need for working capital for the project is $350—$100 = $250 since the remaining $100 is financed by the supplier.⁴

9.4 Summary of the Distribution of Income Changes