Perhaps the traditional Controllers Congress measures of a good merchandising operation need re-examining. For, after all, profits are more precious than markup and a stock turn based on loss leaders puts no black ink on anybody's books. Capital budgeting based on contribution-return on inventory investment provides a new approach which could maximize profits.
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References
1.
For a more detailed discussion of the predecessors of merchandise management accounting, see McNairMalcolm P.MayEleanor G., “Pricing for Profit,”Harvard Business Review, Vol. 35 (May-June 1957), pp. 105–122.
2.
See note 1.
3.
See note 1.
4.
To be conceptually accurate, I in the equation above should be computed on the basis not only of the purchase price of the goods but also the cost of getting the goods into selling position. Professor McNair has suggested (in correspondence) that one should, in order to be completely accurate, compute the average investment to include the investment in the accounts receivable generated by the merchandise in question. Because we are interested in the return on the investment of cash in the merchandise, we should compute the turnover by dividing into 360 the estimated number of days between the outlay of cash and the collection of cash from the sale. This turnover figure would, therefore, reflect not only the length of time cash may be tied up in accounts receivable but also the credit terms on which the purchase was made. (I am indebted to Prof. S. C. Hollander for calling my attention to the problem of the credit terms.) Use of this adjusted turnover figure rather than the more common turnover measure may yield quite different results, particularly for goods with high turnover (as usually defined) rates.
5.
JonesRobert I., one of the initiators of merchandise management accounting, has emphasized the importance of the return on inventory investment in retailing, but he has not explicitly noted that maximizing the contribution return on inventory investment maximizes profits assuming a given investment in inventory. See his Merchandise Management Accounting—A Further Discussion, an address before the NRGDA Controllers' Congress Convention, May, 1957.
6.
See note 5.
7.
Strictly speaking, the turnover should refer to the turnover of the funds invested in the inventory in question. Thus a highly refined approach to this solution would call for an estimate of average investment which would be corrected for deferred billing and for the fact that accounts receivable are not immediately converted to cash.
8.
Here C'/I is the dollars of contribution per dollar of investment; multiplying by T converts the return to an annual rate; and multiplying by 100 converts the expression to a percentage annual rate.
9.
It is possible that the investment in a department could be so small that customers would overlook the department entirely; under these circumstances increments in investment might be associated with increases in the contribution percentage return on investment over a certain range. See BalderstonF. E., “Assortment Choice in Wholesale and Retail Marketing,”Journal of Marketing, 21 (October, 1956) 182.
10.
I am indebted to HymansSaul H. of the University of California, Berkeley, for working out the formal solution to this problem. His work appears in the Mathematical Appendix.
11.
No attempt is made here to introduce inventory investment in any dynamic sense.
12.
This statement of the problem bears a striking resemblance to a linear programming problem. Indeed, the linear programming approach may ultimately be the most useful for practical applications. This would easily permit inequality constraints which are certainly more reasonable than the equalities stated above.
13.
The second-order conditions can be explored by the use of the second directional derivative of the function. This would require that a quadratic form depending on the parameters of the function be negative in all directions away from the critical point determined by the first order conditions. It does not seem necessary to pursue this point in this general discussion because the nature of the critical point will usually be obvious for more specific contribution functions.
14.
The contribution function used in the general case made no assumption of independent demand functions. In fact the marginal contribution with respect to, say, X1 might well depend on (X2, X3, …, I1, I2, …) and so on.
15.
The conditions are also met by many other functions. This particular form is adopted only because it does not seem to be particularly unreasonable and serves quite well to illustrate more concretely the implications of the general solution.
16.
Professor Holton demonstrates this in the body of the article on a less abstract level, and makes use of it in his analysis of departmental balance in terms of both space and capital budgeting.
