¹ For example, see McGrath, James J., “Improved Credit Evaluation with a Weighted Application Blank,” Journal of Applied Psychology, Vol. XLIV (October 1960)Google Scholar, and Smith, Paul F., “Measuring Risk on Consumer Installment Credit,” Management Science, Vol. XI (November 1964).Google Scholar

² Credit-related profits are a form of economic contribution profits. “Economic” because they have present value components and “contribution” because some of the fixed costs attributable to credit selling (e.g., the cost of screening the first order of a new credit applicant) are not relevant for determining the optimal number of credit applicants to accept. A company will sell for credit if credit-related profits are greater than the fixed costs attributable to credit selling. Since credit-related profits include a measure of the effect on the present value of profits from cash sales due to credit selling, they measure the incremental worth of cash plus credit selling compared to cash-only selling.

³ In defining the components of a company's credit-related profits, we make the following assumptions to avoid a proliferation of terms and for the sake of clarity: (1) companies will not make future sales to current period customers who default; (2) customers who default on credit purchases may still be cash purchasers in the stores in which they default; (3) the average number of add-on orders made per customer equals the average number of add-on orders accepted per customer; (4) the time value of money during the current period is approximately accounted for by the term “variable cost of capital invested in accounts receivable”; (5) the average credit sales to a credit customer who pays are the same as the average credit sales to a credit customer who defaults; and (6) customers who default make no payments prior to defaulting

⁴ Since trade creditors record sales dollars gross of discounts, customers who discount reduce the revenues of the creditor compared to what they otherwise would have been. For purposes of classification, we consider this reduction as a current period cost of credit granting.

⁵ In addition to changing when x changes, the variables included in equation (1.12) will be affected by changes in credit term and collection policies as well as by other company policies regarding pricing, product mix, etc. Environmental influences such as competitors' actions and the level of economic prosperity will also affect the terms in equation (1.12). However, for the purposes of this article, we assume as constants all factors other than the number of accepted credit applicants.

⁶ For increases in x where x>x*, the following relationships occur. (1) The probabilities of default and of delinquency for each additional accepted credit applicant are asymptotic constants towards which a₃(x) and a₇(x) increase at a decreasing rate. (2) The total time during which accounts receivable from credit customers who pay are outstanding increases at a constant rate if collection expenditures are made because the number of credit customers who pay increases at a constant rate. This causes a₄(x) and a₁₂(x) to increase at a decreasing rate while approaching asymptotes related to the time that the account receivable from the last accepted customer who pays is outstanding. (3) The variables a₈(x) and a₉(x) increase at a decreasing rate while approaching asymptotes because the marginal returns per each additional collection dollar approach zero. (4) The variable a₆(x) increases at a decreasing rate because the screening expenditure per order will be constant. (5) The variables a₁(x), a₂(x), a₁₄(x), a₁₅(x), a₁₇(x), a₁₈(x), and a₁₉(x) decrease at a decreasing rate while approaching asymptotes with low values because credit applicants beyond x* do not have sufficient resources to make large or frequent credit and cash purchases, to discount, or to pay their debts.

⁷ See, for example, Greer, Carl C. “Measuring the Value of Information in Consumer Credit Screening,” Management Services, Vol. 4 (May–June 1967), pp. 44–54.Google Scholar

⁸ For aggregated department store data, see: U. S. Congress, Senate Committee on Banking and Currency, Truth in Lending—1963–64: Hearings on S.750 88th Congress, 1st and 2nd Sess., Part 2 (Washington: U.S. Government Printing Office, 1964) pp. 1493–1542Google Scholar; or see: Samit, George P., “1964 Credit Department Operating Results,” Credit Management Year Book, 1965–66 (New York Management Division, National Retail Merchants Association, 1965), pp. 134–135.Google Scholar

⁹ The most crucial functional relationship that must be estimated in equation (1.12) is a₃(x), the proportion of credit customers that default. Companies using discriminant analysis to score credit applicants could use their scoring procedures to aid in estimating a₃(x). By attributing a probability of default to a score interval and by estimating the number of applicants in each score interval, a company could relate the probability of the next applicant's defaulting to the number of applicants already accepted. The integral of this function represents, the total number of customers defaulting as a function of the number of accepted applicants. The expression for a₃(x) is obtained by dividing the expression for the total number of applicants that default by the number of accepted applicants.