# DISCOUNTED CASH FLOW AND AGRICULTURAL INVESTMENT

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<ul><li><p>555 </p><p>DISCOUNTED CASH FLOW AND AGRICULTURAL INVESTMENT </p><p>K. D. COCKS University of Cambridge </p><p>In the protracted search for a useful and practicable criterion for evaluation of investment projects, the method of discounted cash flow (DCF) has been strongly recommended to manufacturing business men.* </p><p>The method is generally advocated for the (rather unrealistic) situation where management wishes to choose one of a number of different investment projects, each requiring an initial capital outlay, and each being feasible with respect to the investment capital available. The principle of the method is that each project can be associated with a DCF rate of interest, that this rate of interest measures the efficiency of the project in using capital and, therefore, the higher the DCF rate of interest, the more desirable the project. In the situation where the project giving the highest DCF rate requires less initial capital than a project giving a lower DCF rate, the choice is made by choosing the feasible project for which the product (initial outlay times DCF rate) is a maximum. This procedure identifies the project with the highest total return, rather than the highest rate of return. If the same capital is available whichever project is selected, then it becomes necessary to define a use for surplus capital in all projects before comparing DCF rates earned in different ways on the same initial sum. Our main concern here will be with the implications of the DCF rate itself, and we shall talk about the comparison of projects requiring identical initial capital outlays. </p><p>The rate of interest obtained by applying the DCF method is that discount rate which equates an initial outlay with the present value of a series of future net cash flows (not flows of book profits but flows of cash in hand after tax). Cash flow is also defined to include the value of any residual assets of the project at the end of its life. </p><p>Symbolically, the method is a search (by trial and error) for the discount rate (r) which satisfies the following relationship:- </p><p>(1) ,............... when I = an initial capital outlay. </p><p>ACi = the change in cash flow from the whole business in the i-th year (i= 1, 2, . . . . . .n) which is attributable to the making of the initial investment. ACi will be the resultant of the additional cash returns and additional cash costs which are entailed when the initial investment is made. ACi is a marginal entity measuring the net effect of the investment on the business in terms of cash which is assumed to be a sufficient parameter for describing management goals. </p><p>Guardian, 10th January, 1964, p. 10. Discounted Cash Flow-a Basis for Realistic Investment, Merrett, A. J. and Sykes. </p><p>Discounted Cash Flow and Corporate Planning, Alfred, A. M. Wmtwich Economic </p><p>* Economist, 29th August, 1964. </p><p>Allen. The Manager, December, 1963. </p><p>Papers No. 3, July, 1964. </p></li><li><p>556 </p><p>Compound Interest a t 10% p.a. </p><p>K. D. Cocks </p><p>On a Capital Sum being </p><p>This method might be used for evaluating a wide range of farm expenditures ranging from the purchase of an additional holding to the purchase of addi- tional breeding stock; in fact any marginal expenditure of capital, the effects of which are spread over more than one accounting period. However, whether DCF has merit or not, it seems likely that some effort wdl be made to introduce it for the evaluation of agricultural investments. I t is therefore perhaps worthwhile to note some implications of the method. </p><p>Alfred* gives a simple example of the method, one which could be given an agricultural context by regarding it as the purchase of a breeding sow. </p><p>Project A (Purchase of one breeding sow) </p><p>Investment a t end of year 0 (cost of sow) ... L31.70 Life of project (life of sow) ... ... ... 4 years Expected cash flow in each of four years Solution rate of interest (DCF rate) . . . . . . 10 per cent </p><p>. . . L l O </p><p>By definition, the solution rate of interest is the (decimal) rate (r) which satisfies the relationship:- </p><p>10 10 10 10 31.70 = -. ( l+r) l +(l+r)a + (l+r)3 + (l~r)3 :. r = 0.1 </p><p>We can divide the annual cash flows between interest earned and capital repaid as follows:- </p><p>Year Cash Flow (Q </p><p>I Composed of </p><p>10 </p><p>10 </p><p>10 </p><p>10 </p><p>40 - </p><p>1 0.91 </p><p>2 I .74 </p><p>3 2.49 </p><p>4 3-17 </p><p>8.30 </p><p>9.09 </p><p>8.27 </p><p>7.51 </p><p>6.83 </p><p>3 1 *70 </p><p>The capital investment of L31.70 has been completely repaid and total interest of L8.30 has been earned. The example shows this to be equal to interest at 10 per cent on the sums repaid. It is also equal to 10 per cent on the outstanding balance at any time, e.g.:- </p><p>__ _____ * Alfred, A . M., ibid. </p></li><li><p>Discounted Cash Flow and Agricultural Investment 557 </p><p>Cash Flow </p><p>(D </p><p>10 </p><p>10 </p><p>10 </p><p>10 </p><p>1 Capital outstanding 1 at beginning of year I (4 </p><p>Year Capital </p><p>(4 Repayment </p><p>6.83 </p><p>7.51 </p><p>8-26 </p><p>9.09 - </p><p>31.70 </p><p>24.87 </p><p>17.36 </p><p>9.09 </p><p>10% Interest on Capital </p><p>outstanding </p><p>3.17 </p><p>2.49 </p><p>1.74 </p><p>0.91 </p><p>8.31 - </p><p>Thus, the DCF rate of interest is the annual rate of return on the capital outstanding each year. Another viewpoint is to regard the DCF rate as the no profit rate of interest which can just be paid by the project if the initial investment capital is borrowed. In Alfreds example the cash flows are the same each year and could be thought of as amortization payments wiping out a loan of ,631.7 in four years when the loan bears interest a t I0 per cent on reducing balance. If cash flows are not the same each year, the DCF rate is the maximum interest rate which could be borne if the lending authority did not specify equal annual repayments of principal and interest. </p><p>If the fanner uses his own capital for the project and consumes cash flows as they eventuate, the DCF rate of interest can be regarded as the maximum personal discount rate (applicable to consumption) at which the project remains acceptable. In the above example, using farmer capital, the project is accept- able only if the farmer is prepared to postpone consumption whenever future consumption can be increased by 10 per cent compound (or less) over each year that consumption is delayed. If the farmer has a personal discount rate, or time preference for consumption, of I0 per cent or less, the project is acceptable. </p><p>It does not follow, however, that the higher this maximum personal discount rate, the more desirable the project (even when we leave aside considerations of the magnitude of the initial investment and of negative cash surpluses). </p><p>Assuming that personal discount rates are an adequate measure of utility we can measure the utility of a series of future cash flows as a present money value. This amount will be the summed present values of the future cash flows when discounted at the personal discount rate. The difference between the magnitude of the initial investment and this aggregated present value will measure the desirability of the project. The gain in utility from making the investment will be measured by a gift of money to be spent on con- sumption today. We can call this increment the net present value of the project. </p><p>Suppose in our example (project A) that the appropriate personal discount rate is 5 per cent per annum. Four annual cash flows of LlO each will have a summed present value as follows:- </p></li><li><p>558 K. D. Cocks </p><p>PV. ... Year1 10 x ... ... 9.52 </p><p>( 1.05) </p><p>Year2 ... 10 x - ... ... 9.07 1 (1-05)e </p><p>... ... 8-64 1 Year 3 10 x- (1 *05) Year4 10 x - ... ... 8.23 1 </p><p>(1.05)' </p><p>1 </p><p>... </p><p>... </p><p>Summed present value . . , 35-46 Less initial investment ... -31.70 Net present value ... ... 3-76 </p><p>Thus, if the investment is made, the utility gained is equal to a gift of L3-76 to be consumed today. </p><p>Let us consider a further project (project B) in which an investment of ,631-7 gives cash flows which yield a DCF rate of return of 9 per cent (c.f. 10 per cent, project A). Perhaps we could think of this investment as the purchase of a sow which does not take the boar for three years and then over- reacts by producing four-fold. </p><p>Project B </p><p>Cash flow- E Year 1 ... ... ... 0 .. 2 ... ... ... 0 .. 3 ... ... ... 0 .. 4 ... ... ... 44-75 </p><p>The sum of l44.75 discounted at 9 per cent for four years yields E31.70. Thus the DCF rate of return is 9 per cent. If the DCF rate were taken as the sole criterion for choosing a project, project A would be preferred to project B. </p><p>If we work out the utility or net present value of project B, it comes to E5.12:- </p><p>1 Summed P.V. = 44.75 x - (1.05)' ... 36.82 </p><p>Less initial investment ... ... -31.70 Net present value ... ... ... 5-12 ... </p><p>Thus, although project B has a lower DCF rate of interest than project A, </p><p>The reason for this conflict is that the DCF method implicitly assumes </p><p>A further example will illustrate this point. Consider an initial investment </p><p>project B is more desirable because it has a higher utility than project A. </p><p>that the rate of personal discount is equal to the calculated DCF rate itself. </p><p>of L31.7 (project C) which yields the following cash flows:- </p></li><li><p>Discounted Cash Fbw and Agricultural Investment 559 </p><p>Cash flow discounted Year Cash flow a t 10% </p><p>1 10 9.09 2 9.09 7.51 3 1 1 8-26 4 10 6-83 </p><p>31-70 - When the cash flows for project C are discounted a t 10 per cent they equal </p><p>the initial investment and thus the DCF rate is 10 per cent. If DCF rate is the sole criterion, project C is as desirable as project A. If the two projects are equally desirable the method is asserting that a fall in consumption from L l O to l9.091 at the end of year 2 is just compensated for by a rise in con- sumption at the end of the third year from ,510 to L11. </p><p>For this to be so, the personal rate of discount (d) must be such as to satisfy:- </p><p>(10-049) ( l f d ) ' ~ (11-10) i.e. 0.91 (l+d)l = 1.0 i.e. d = 0.1 </p><p>= 10% Thus, where cash flows are consumed, the relative desirability of two </p><p>projects is measured by the DCF rate only if the personal discount rate for each project is equal to the DCF rate itself. If we calculate the net present value of project C, discounting a t 5 per cent, it is l3-79, indicating that project C is slightly more desirable than project A. </p><p>We can now look at the obverse case in which the project is undertaken but cash flows are re-invested rather than consumed. For this t o be logical, two conditions are necessary:- </p><p>(a) the maximum personal discount rate for the project (DCF rate) must </p><p>(b) the re-investment rate must be greater than the actual personal </p><p>Suppose that the re-investment rate available is 20 per cent per annum throughout project life. The result of re-investing cash flows at 20 per cent can be compared for projects A and C (which, assuming re-investment, we can </p><p>Firstly we can calculate the magnitude of the fund which wi l l be accumu- lated in each project at the end of year 4. This is done by compounding cash flows at 20 per cent for each project. The result of doing this is that a t the end of year 4, project AR shows a fund of L53.68 and project CR shows a fund </p><p>When cash flows are known to be re-invested, the value of the terminal fund can be used to directly compare the two projects. In this case, project AR yields a slightly larger fund than project CR. </p><p>These funds can be discounted a t the personal discount rate (5 per cent) to get the present value of the future cash flows, and hence the net present value for each project:- </p><p>be greater than the actual personal discount rate. </p><p>discount rate. </p><p>AR and CR). </p><p>of L53.57. </p><p>Project AR Project CR Value of terminal fund ( E ) . . . 53.68 53.57 Present value (d=0.05) (a ... 44.16 44.07 Net present value (subtract 31.7) 12.46 12.37 </p></li><li><p>560 K. D. Cocks </p><p>Thus differences in the re-investment rate, within and between projects could lead to either project being marked as the more desirable. It is only when the available re-investment rate for each project equals the calculated DCF rate that the DCF is a sufficient criterion for comparison. </p><p>When terminal funds are discounted to obtain present values, the projects will retain the ranking indicated by terminal fund magnitudes. Thls is because both funds are multiplied by the same discount factor. In short, when cash flows are re-invested, the terminal fund and the net present value of the terminal fund are equivalent criteria. </p><p>A third equivalent criterion is the average rate of capital accumulation (R) this is measured by:- </p><p>+T- 1.0 ....., 9 R = (2) ............ (e: T = Q(l+R)n) </p><p>where T is the terminal value of the fund, Q is the initial investment, n is the project life. </p><p>When cash flows are re-invested, the terminal fund can be thought of as the result of the initial investment being compounded annually through the life of the project. If it is felt necessary to attach a rate figure to an invest- ment project this would seem to be more useful than the DCF rate. </p><p>In this simple form the rate of capital accumulation cannot be directly used when only part of cash flows are re-invested. Three possible criteria for this mixed situation suggest themselves:- </p><p>(a) net present value, consisting in discounted consumption (personal rate) </p><p>(b) accumulated future value, consisting in compounded consumption </p><p>(c) the interest rate which equates initial outlay and accumulated future </p><p>These three measures are mutually consistent and will always rank projects the same way. They all avoid the weakness in DCF of assuming the re-invest- ment rate or the personal discount rate to equal the DCF rate. They also show that subject to being able to define a rate of personal discount, valid over the money quantities being considered, there is no conflict between present value and rate of return criteria provided that these entities are carefully defined. </p><p>An Example </p><p>plus discounted terminal fund (personal rate) less initial outlay. </p><p>(personal rate) plus terminal fund. </p><p>value. </p><p>Consider a farmer who, pnor to making an on-farm investment, intended to operate, for a five-year planning period, a stable combination of enterprises, the same each year. At the beginning of the planning period he has Ll,OOO </p><p>the bank, accumulated prior t o the planning moment. The farmer is considering two possible investments on the farm:- </p><p>Buy a second-hand tractor for #00 and grow more barley than has previously been possible. If he does this, his annual peak working capital requirement will rise by L200 and his annual cash surplus will rise by L250, after allowing for a necessary reduction in other land using activities. At the end of five years i t is estimated that the tractor will be worth jE380. </p></li><li><p>Discounted Cash FJow and AgricuJturaJ Investment 561 </p><p>When he grows more barley, there is no change in his annual (non-cash) depreciation bill, apart from the tractors depreciation. </p><p>(b) Extend his pigsties at a cost of L500, and raise more pigs. To stock the extra housing he will have to incur an increase of L500 in his annual peak working capital. The extra pigs will raise his annual cash surplus by ;6230. At the end of five years it is estimated that the L500 of extra housing will add to the value of the farm. If we calcu...</p></li></ul>