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Finding the best credit policy
FINDING THE BEST CREDIT POLICY A model for studying the components
LEE A. TAVIS
The author is a faculty m e m b e r in the Finance D e p a r t m e n t at The University o f Texas at Austin.
Management can choose from many combinations o f credit period length and cash discount policy. Finding the best combination is important because these components are powerful elements in the firm's promotional mix. They are, however, difficult to identify and measure. The author has constructed a simplified and computerized model o f the firm's short-term investments and the means or financing these investments. Examining the model under a broad range o f environmental conditions and a number of different credit terms provides insight into the importance o f trade credit to the creditor firm. The credit period impact is modeled, and optimal credit periods and optimal cash discounts are examined. The result is a highly interrelated, delicately balanced, generally suboptimized system.
Trade credit is a potentially powerful b u t frequently unrecognized c o m p o n e n t of a firm's promotional mix. Like advertising, the sales results of extending credit are difficult
OCTOBER, 1970
to identify and measure. Less like advertising, identification and measurement of credit extension costs are as difficult as identifying the results. Nevertheless, management must weigh these costs and returns in establishing credit policy. Two components of that p o l i c y - t h e length of the credit period and cash d i s c o u n t s - e x e r t a great impact on a firm b u t are areas where analysis is particularly lacking. This article focuses on the many factors that must be considered as management seeks some best net credit period and cash discount policy from among the many combinations available. Terms of sale directly influence the demand for a firm's goods and the accounts receivable carried. Indirectly, terms have an impact on decisions regarding cash and materials inventories as well as financing decisions. These indirect relationships must be specified before realistic costs and returns associated with specific credit terms can be measured. In order to study the nature of these interrelationships as weil'as the net impact of credit periods and cash discounts, a simplified
33
LEE A. TAVIS
model of a firm's short-term investments (current assets, marketable securities, materials inventories, and accounts receivable) and the means of financing these investments was developed and computerized. Studying this model under a broad range of environmental conditions and a number of different credit terms provides an insight into the potential importance of trade credit to the creditor firm.
MODELING THE PERIOD IMPACT
34
Credit periods and cash discounts jointly influence demand and exert an indirect effect on current asset and financing decisions. Many firms, however, do not offer cash discounts; 1 in addition, cash discounts should be analyzed within the context of a given credit p e r i o d . Therefore, this section concentrates on the role of the credit period, its potential value to the buyer, and its impact on the creditor firm. The availability of trade credit is, in effect, a reduction in price for the buyer. During the period for which the credit is outstanding, the buyer has use of the seller's funds, and in the absence of cash discounts, there is no explicit cost to the buyer. The value of these funds to the buyer depends upon his use for them during the credit period. The opportunity he has to use funds elsewhere rather than pay cash can be translated into an effective price r e d u c t i o n - t h e reduction being the difference between the amount the buyer pays at the termination of the credit period less the present value of that a m o u n t discounted at his opportunity rate. A credit manager can t h u s measure the effective price reduction associated w i t h a n y credit period for a specific buyer by estimating his opportunity rate. For any given
1. Martin H. Selden, The Quality of Trade Credit (Occasional Paper 87; New York: National Bureau of Economic Research, 1964), p. 41.
period, there is a range of applicable effective prices because o f the variety of buyer discount rates. Potential buyers with relatively high opportunity rates would enjoy the lowest effective price and be the most likely customers. In trade credit, the customer with the lowest effective price would be the one with the highest opportunity rate coupled with a credit rating acceptable to the seller. A decrease in effective price can be viewed in the framework of a traditional demand curve. Each effective price is related to a specific number of units demanded, with lower effective prices related to higher quantities and vice versa. As the length of the credit period is increased, the effective price for each potential customer drops. Customers with the highest opportunity rates experience the greatest drop in their effective price. Quantity demanded becomes larger as new customers are attracted and existing ones buy more. The level of demand is a key determinant of optimal investments in current assets for the creditor firm. These balances and their relation to demand are outlined in an operating cycle diagram (Figure 1). Units demanded in period t3 is a major consideration in planning finished goods inventory (period t 2). The production of this finished goods inventory transfers the influence of demand to raw materials inventory (period tl).
The credit period directly influences the receivables carried b y a firm. When the period is lengthened, both the greater demand and the longer collection period lead to increases in receivables. More cash is committed to production and the collection of this cash is delayed longer. Another generally overlooked commitment of resources related to credit extension arises from the uncertainty injected into the firm's cash flows because of possible collection delays and bad debts. This uncertainty leads to the requirement for a precautionary cash balance; the cost of maintaining this balance is an important
BUSINESS HORIZONS
Finding the Best Credit Policy
FIGURE 1
The Operating Cycles
OPERATING PERIODS tl
t2 a
t3
Raw materials for planned p r o d u c t i o n in p e r i o d t 2 are purchased.
G o o d s to m e e t a n t i c i p a t e d dem a n d in p e r i o d t 3 as well as c h a n g e s in finished goods reserve i n v e n tories b e t w e e n t 2 a n d t 3 are produced,
Credit terms are set a n d demand established. Finished goods reserve i n v e n tories are m a i n t ain ed f0r variations in d e m a n d . Sales Occur.
t4, . . . , t 4 + x b
Accounts ceivable held.
reare
t5 +x
t6 +x
C a s h f l o w s in from receivables c o l l e c t e d w h e n d u e . Precautionary cash balances are r e q u i r e d ,
C a s h f l o w s in from receivables c o l l e c t e d one period late. Precautionary cash balances are r e q u i r e d .
OPERATING CYCLES
*A continuous input batch output production process is assumed. +Credit terms are extended in discrete timeperiods equal
to the production time. The variable, x, is the number of periods that credit is outstanding after the sales period. It is equal to two less than the number of periods of credit extended to buyers.
35
component of the over-all cost of credit extension. The relationship between the credit period and short-term investments and cash flows is emphasized in the case of lengthening the credit period. This results in (1) increased d e m a n d , (2) more production in the preceding period of the operating cycle to meet the increased demand, (3) increased raw material purchases in still an earlier period to support the added production, and (4) a larger precautionary cash balance at the time of anticipated collection. The short-term investments and cash flows of an operating cycle are thus a function of the credit period that initiated the demand in that cycle. A change in the credit period necessitates a change in financing of the cycle. In the case of longer terms, for example, m o r e funds are required to support the cycle. In most cases, the source of the financing is short-term borrowing. The availability and
OCTOBER, 1970
cost of this borrowing are largely established by the volume and structure of a firm's current assets. Hence, at a given point in time, all operating cycles underway at that time fix the requirements for short-term borrowing and, simultaneously, set the limits on the a m o u n t of this borrowing that is available as well as its cost. These relationships were formulated into a model of a "short-term funds system" including the investment in cash, marketable securities, accounts receivable, and materials inventories as well as the borrowing to finance these investments (see Figure 2). The model allows for the initiation of a series of operating cycles similar to the one in Figure 1 and the financing of all operating cycles underway over some future planning period. The short-term investments in each cycle are the optimal balances, given the demand in that cycle and the cost of financing at that
LEE A. TAVIS
FIGURE 2
A Computerized Short-Term Funds Systems
C/ J
BO~OI~TINtG
/
Short-Term ~ B.....
ing
/
CASHCROEMQUut-IIR~IMVEENTst/
/ /
36
* As s h o r t - t e r m investments are u n d e r t a k e n - t h u s increasing short-term borrowing capacity--the borrowing to finance the investments influences the carrying cost of the asset. The interrelationship between t h e short-term asset and liability structure is particularly close in t h e case of precautionary cash balances. The carrying cost of these balances depends partly u p o n the o p p o r t u n i t y cost of n o t using the funds to retire short-term debt. The Opposing cost, the cost of a cashout, is a function of available short-term borrowing capacity which, in turn, depends u p o n the current asset structure. The determination of an optimal balance, therefore, depends u p o n the structure of the whole shortt e r m funds system. t T h e available sources for short-term funds are formulated as a linear p r o g r a m m i n g problem, the optimal
point in the planning period. The financial structure is the least-cost combination of sources over the planning period. A number of different credit periods could be applied over a planning period. Each group of credit periods (each credit set) would result in a unique cash flow and structure of the system for the planning
mix being that c o m b i n a t i o n of sources that leads to the m i n i m u m cost of borrowing. In this LP problem, the overlaid operating cycles form the base for the requirements vector. The resulting funds flow, combined with exogenous funds available, sets the requirements for short-term borrowing over time. The investments in the operating cycles establish the capacities for each credit source in each operating period. The coefficients of the objective f u n c t i o n (to minimize the cost of short-term borrowing) are the time- and taxadjusted avoidable costs of borrowing from each source. The coefficients in the constraint matrix relate the borrowing from each source to the borrowing capacities, and reflect the r e q u i r e m e n t that, t h r o u g h o u t the credit planning period, sources of funds m u s t equal uses.
period. The present value of these flows provides a system net present value for each credit setfl The credit set leading to the greatest net present value would be the best of the many possible sets. Although actual firms are more complex than the simple, single-product firm modeled here, they can be viewed as consisting of
BUSINESS HORIZONS
Finding the Best Credit Policy
many sets of operating cycles in process at a given time. They are subject to similar parameters and interrelationships.
OPTIMAL CREDIT PERIODS Once the many facets of the short-term funds system that jointly influence the costs and returns associated with the credit period have been identified, the pressures toward optimal terms can be studied. In the preceding example, two identifiable cash flows are set i n t o motion a s the credit period is lengthened--operational flows and financing flOWS.
On the operational side, the incremental increase in demand leads to more sales. The present value of this operational inflow, however, is reduced by bad debts and the delay in collections. The outflows for production and other costs tied to the increased demand go up. In most circumstances, the net result of these flows is a positive net present value (NPV) as the credit period is lengthened. Financing flows are costs. As the creditrelated demand increases, borrowing must be undertaken to support cash production outlays for the added finished goods and the increase in precautionary balances. The longer credit period means more financing for units sold but carried on credit. With a longer credit period, the increase in the present value of operational flows is offset by the increase in the present value of the financing flows. The movement of these two classes of cash flows was tested by assigning values to the model parameters and computing the present value of these cash flows 2. The discount rate used in the model is the cost of t h e exogenous funds invested in the short-term funds system. These outside funds are drawn from the securities markets or generated internally and invested in the system rather t h a n in fixed assets. Short-term borrowing costs are included in t h e cash-financing flows rather than weighted in the discount rate. This procedure is based on the absorption of uncertainty through precautionary balances, and t h e j u d g m e n t that short-term borrowing capacity tied to optimal current asset balances would keep short-term financial leverage below the threshold of an increasing cost of exogenous funds.
OCTOBER, 1970
for different credit periods. The results are outlined in the accompanying table. When minimum terms are offered (Credit Set A), the operational flows net to a present value of $220,000; financing costs are $20,000; and the result is an NPV for the system of $200,000 (column 5 in the table). With uniform terms of 105 days throughout the planning period (Set G), the system NPV was almost the same ($199,000) but the s t r u c t u r e was substantially different: operational inflows were $274,000, and financing outflows were $75,000. Between these extremes, system NPV was maximized with a mixture of 45- and 60-day credit periods (SCUD). At this point, a further lengthening of the credit periods leads to an increase in the present value of financing outflows that is greater than the present value increase in net operational inflows. In Part II of the table, the system NPV resulting from the optimal set is used as a base and a cost imputed to the nonoptimal sets. These imputed costs are plotted in Figure 3. This concave curve suggests guidelines for credit policy. The cost of nonoptimal credit policies is not significant over a wide range of possible t e r m s - S e t B through Set E. Beyond the relatively flat b o t t o m of the curve, the cost of nonoptimal behavior increases significantly to a present value cost of 7.4 percent at the extreme of Set H. Once a set of parameter values that results in an optimal credit set is established, slight changes in the value of any single parameter tends to shift the optimal set. Optimal periods are particularly sensitive to changes in the response of units demanded to different effective prices and the determinant of these prices, that is, the buyer opportunity rates. A slight change in the effective price demand function changes the optimal length of the credit period by a third. Small changes in the buyer opportunity rates have the same impact. Shifting buyer opportunity rates clearly demonstrate the total system response to factors influencing credit policy. If receivables are treated separately, a firm will extend
37
LEE A. TAVIS
Present Values and Imputed Present Value Costs of Selected Credit Sets (thousands of dollars) Present Values (1) Credit Sets* Set Set Set Set Set Set Set Set
A (minimum) B C D (optimal) E F G H (maximum)
Imputed Present Value Costs
(3=1--2) Net Operational Inflows
(4)
(5)
(6=7+8)
Collections
(2) Operational Outflows
Financing Outflows
Net System
$3,022 3,115 3,203 3,250 3,287 3,366 3,442 3,513
$2,803 2,878 2,953 2,995 3,026 3,097 3,167 3,236
$220 237 250 255 261 269 274 277
$20 30 42 45 54 65 75 83
$200 206 208 210 207 204 199 194
*Each credit set consists of a series of credit periods offered over a future time span (a credit planning period). The sets included in this table are arrayed from the set made up of the minimum length of credit throughout the planning period to the set consisting of the maximum terms considered feasible by management. The credit planning horizon for a firm would be determined by these longest possible terms. Management could select the maximum feasible terms as optimal only after comparing the system NPV results of those terms with all possible combinations of shorter terms over the same planning period.
System
(7) Net Operational
(8) Financing
$ (9.4)+ (3.2) (1.5) 00.0 (2.5) (5.5) (10.4) (15.5)
$(35.0) (18.3) (4.7) 00.0 6.1 14.1 19.4 22.2
$25.6) 15.1 3.1 00.0 (8.7) (19.8) (30.0) (37.8)
As indicated in Figure 1, credit terms in the model are set in discrete time increments equal to the production time--in this test assumed to be 15 days. The maximum credit terms allowed were seven operating periods in length--105 days. The optimal set (Set D) was a combination of 45- and 60-day terms offered during the 105-day credit planning period. In all other sets, there was no change in the terms offered over the planning period. tParentheses indicate less than optimal. Figures may not add to net due to rounding.
38 FIGURE 3
Imputed Present Value Cost of Less Than Optimal Credit Sets Imputed Costs ($000) 18
(Selected Credit Sets)
16
14
12 10 8 6 4
2 o
Imputed costs as a percent of optimal 4.5
1.5
0.7
-.
1.4
I
I
I
/
I
/
I
I
A Minimum
B
C
E
F
G
H Maximum
D Optimal
2.6
4.9
7.4
BUSINESS HORIZONS
Finding the Best Credit Policy
credit only when its cost of funds is less than that of its customer in the absence of collection risk. 3 In the test reported above, when the buyer opportunity rate is set equal to the cost of exogenous funds, the optimal set moves to the lower boundary (Set A) with a cost of 63 percent imputed to Set H. These results demonstrate the importance of recognizing the full cost of extending credit delineated earlier. Surprisingly, major differences in collections e x p e r i e n c e - a c c e l e r a t e d collections, delayed collections, and larger bad debt losses-fail to shift the optimal terms, although the system NPV is affected. 4 The introduction of seasonal demand patterns shifts the makeup of the optimal credit sets. With an upswing, optimal periods are shorter because of the rise in the per unit cost of borrowing as short-term borrowing increases relative to its capacity. The added cash requirements of these operating cycles as demand increases, and the associated borrowing needs, draw on higher cost sources, thus offsetting the additional net operational inflows, s Reciprocal pressures are in force on the downswing. Optimal credit terms are also sensitive to changes in the cost structure. Increasing operating leverage leads to a shift of the optimal credit set to longer terms and an increase in the system NPV. The reverse holds true when operating leverage is dropped. The tests clearly indicate the desirability of shifting credit policy with changes in operating leverage. This finding is relevant to
3. S e y m o u r Friedland, The Economics of Corporate Finance (Engtewood Cliffs, N. J.: Prentice-Hall, Inc., 1966), p. 74. 4. In each test, the percentage of bad debts was held c o n s t a n t over all possible credit periods. In those cases where t h e percentage of bad debts increases with the length of the credit period, there will be pressure toward shorter periods. 5. The marginal cost of borrowing is measured b y the value of the dual variables in the financial structure linear program. These costs s h o o t upward as borrowing approaches its capacity reflecting the added liquidity reserves required as t h e short-term borrowing cushion is lost, and the loss of unsecured borrowing capacity associated with secured borrowing, as well as t h e additional per unit borrowing cost.
OCTOBER, 1970
c~ipital budgeting decisions. If a proposed fixed asset investment modifies the operating leverage of a firm, the changes in optimal short-term investments should be included in the anticipated incremental cash flows relevant to the investment.
AN APPROACH DISCOUNTS
TO
OPTIMAL
CASH
Management has the option of not only varying the length of the credit period as a c o m p o n e n t of credit policy but also offering cash discounts for early payment. As with the credit period, some cash discounts have a more favorable over-all impact than others. It is clear that the analysis of cash discounts entails full systematic consideration since discounts will influence the units demanded and the timing of cash flows as did the credit period. From the potential buyer's point of view, discounts offer the alternative of a lower cash price, rather than the effective price that results from paying at the end of the credit period. 6 In the presence of uniform credit terms the cash price for each potential buyer would be the same. As noted earlier, effective prices are different for each buyer. The effective price depends upon his own opportunity rate and is unique. The discounted price versus effective price trade-off is, therefore, different for each buyer. For the customer with a relatively low opportunity rate (and hence a relatively high effective price for any given credit period), a modest discount would drop the cash price below his effective price and he would opt for the discount. In this sense, potential customers with low opportunity rates are enticed more by cash discounts, whereas high opportunity rate buyers are attracted by the effective price reduction associated with the credit period. It takes a high discount indeed to lower the cash 6. I am indebted to a colleague, Robert Mettlen, for helping clarify this relationship.
39
LEE A. TAVIS
40
price sufficiently to meet the effective price of the high opportunity rate buyer. For the seller, cash discounts mean the receipt of less money, but it will come in earlier from those customers taking their discounts. In terms of the model, operating cycles would be shorter with less cash throwoff to the extent that discounts are taken. T h e complete structure of short-term investments and liabilities would change with these shifts in the cash flows of the system. The reduction in cash throw-off would be offset by the lower financing costs resulting from the shortened operating cycles. Therefore, meaningful evaluation of alternate discount policies can be accomplished only when their impact on the short-term funds system is recognized. Cash discounts, as a component of a firm's credit policy, should be analyzed within the context of an optimal credit period. The credit period is designed to attract the high o p p o r t u n i t y rate (low effective price) customer, whereas the cash discount is intended to decrease the cash price and entice the potential buyer whose effective price is relatively high due to a low opportunity rate. Each combination of a credit period and cash discount will result in a unique level of demand and structure of the system. The optimal credit terms will be that credit period and cash discount that optimizes the resulting system NPV. The large cash discounts typical in U.S. industry suggest that discounts are set to entice all customers to pay cash, including those with high opportunity rates. 7 Discounts thus serve as thinly disguised price reductions and are not making their full contribution to the selling firm's profits.
7. The notion is commonly held that buyers w h o do not take their discounts are p o o r credit risks. In a survey conducted by Welshans it was reported that "several credit managers stated flatly that t h e y . . , would not continue approving credit for customers who did not take their discounts." Merle T, Welshans, "Using Credit for Profit Making," Harvard Business Review (January-February, 1967), p. 144.
THE RESULTS Credit policies are a key determinant of the structure and cash flows of a closely interr e l a t e d short-term funds system. Each operating cycle is interconnected with decisions regarding materials inventories and precautionary cash balances, all tied to the demand resulting from the extension o f credit. And short-term borrowing is inextricably tied to current asset investments. Optimal credit periods result from a delicate balance of parameter values. Once an optimal credit set is achieved, a small adjustment of parameter values, in most cases, moves the optimal set toward its limits. Particularly significant are the buyer's opportunity rate and his demand response to different effective prices. Collection experience has great importance for the net present value of the system but little for optimal sets. Op crating leverage readily changes the optimal periods. Given the delicate balance associated with each credit set, it is probable that credit periods based on industrial standards are not optimal for most or all firms in an industry. Furthermore, judging by the way optimal terms move toward the boundary sets with small changes in parameter values, it is unlikely that, for many firms, the optimal set falls within a spectrum of periods considered feasible b y management. Even though optimal periods are highly sensitive to the state of the system, the imputed cost of errors is not great for periods close to the optimum. At the limits of credit extension, however, the cost of making credit errors is great. Cash discounts are relevant only within the context of an optimal credit period. They should be used to attract the marginal potential buyer with a low opportunity rate and, hence, a relatively high effective price for any given credit period. The size of traditional cash discounts suggests that firms are attempting t o entice all credit customers to take their discounts--in m a n y cases a suboptimizing decision.
BUSINESS HORIZONS
LEE A. TAVIS
The author is a faculty m e m b e r in the Finance D e p a r t m e n t at The University o f Texas at Austin.
Management can choose from many combinations o f credit period length and cash discount policy. Finding the best combination is important because these components are powerful elements in the firm's promotional mix. They are, however, difficult to identify and measure. The author has constructed a simplified and computerized model o f the firm's short-term investments and the means or financing these investments. Examining the model under a broad range o f environmental conditions and a number of different credit terms provides insight into the importance o f trade credit to the creditor firm. The credit period impact is modeled, and optimal credit periods and optimal cash discounts are examined. The result is a highly interrelated, delicately balanced, generally suboptimized system.
Trade credit is a potentially powerful b u t frequently unrecognized c o m p o n e n t of a firm's promotional mix. Like advertising, the sales results of extending credit are difficult
OCTOBER, 1970
to identify and measure. Less like advertising, identification and measurement of credit extension costs are as difficult as identifying the results. Nevertheless, management must weigh these costs and returns in establishing credit policy. Two components of that p o l i c y - t h e length of the credit period and cash d i s c o u n t s - e x e r t a great impact on a firm b u t are areas where analysis is particularly lacking. This article focuses on the many factors that must be considered as management seeks some best net credit period and cash discount policy from among the many combinations available. Terms of sale directly influence the demand for a firm's goods and the accounts receivable carried. Indirectly, terms have an impact on decisions regarding cash and materials inventories as well as financing decisions. These indirect relationships must be specified before realistic costs and returns associated with specific credit terms can be measured. In order to study the nature of these interrelationships as weil'as the net impact of credit periods and cash discounts, a simplified
33
LEE A. TAVIS
model of a firm's short-term investments (current assets, marketable securities, materials inventories, and accounts receivable) and the means of financing these investments was developed and computerized. Studying this model under a broad range of environmental conditions and a number of different credit terms provides an insight into the potential importance of trade credit to the creditor firm.
MODELING THE PERIOD IMPACT
34
Credit periods and cash discounts jointly influence demand and exert an indirect effect on current asset and financing decisions. Many firms, however, do not offer cash discounts; 1 in addition, cash discounts should be analyzed within the context of a given credit p e r i o d . Therefore, this section concentrates on the role of the credit period, its potential value to the buyer, and its impact on the creditor firm. The availability of trade credit is, in effect, a reduction in price for the buyer. During the period for which the credit is outstanding, the buyer has use of the seller's funds, and in the absence of cash discounts, there is no explicit cost to the buyer. The value of these funds to the buyer depends upon his use for them during the credit period. The opportunity he has to use funds elsewhere rather than pay cash can be translated into an effective price r e d u c t i o n - t h e reduction being the difference between the amount the buyer pays at the termination of the credit period less the present value of that a m o u n t discounted at his opportunity rate. A credit manager can t h u s measure the effective price reduction associated w i t h a n y credit period for a specific buyer by estimating his opportunity rate. For any given
1. Martin H. Selden, The Quality of Trade Credit (Occasional Paper 87; New York: National Bureau of Economic Research, 1964), p. 41.
period, there is a range of applicable effective prices because o f the variety of buyer discount rates. Potential buyers with relatively high opportunity rates would enjoy the lowest effective price and be the most likely customers. In trade credit, the customer with the lowest effective price would be the one with the highest opportunity rate coupled with a credit rating acceptable to the seller. A decrease in effective price can be viewed in the framework of a traditional demand curve. Each effective price is related to a specific number of units demanded, with lower effective prices related to higher quantities and vice versa. As the length of the credit period is increased, the effective price for each potential customer drops. Customers with the highest opportunity rates experience the greatest drop in their effective price. Quantity demanded becomes larger as new customers are attracted and existing ones buy more. The level of demand is a key determinant of optimal investments in current assets for the creditor firm. These balances and their relation to demand are outlined in an operating cycle diagram (Figure 1). Units demanded in period t3 is a major consideration in planning finished goods inventory (period t 2). The production of this finished goods inventory transfers the influence of demand to raw materials inventory (period tl).
The credit period directly influences the receivables carried b y a firm. When the period is lengthened, both the greater demand and the longer collection period lead to increases in receivables. More cash is committed to production and the collection of this cash is delayed longer. Another generally overlooked commitment of resources related to credit extension arises from the uncertainty injected into the firm's cash flows because of possible collection delays and bad debts. This uncertainty leads to the requirement for a precautionary cash balance; the cost of maintaining this balance is an important
BUSINESS HORIZONS
Finding the Best Credit Policy
FIGURE 1
The Operating Cycles
OPERATING PERIODS tl
t2 a
t3
Raw materials for planned p r o d u c t i o n in p e r i o d t 2 are purchased.
G o o d s to m e e t a n t i c i p a t e d dem a n d in p e r i o d t 3 as well as c h a n g e s in finished goods reserve i n v e n tories b e t w e e n t 2 a n d t 3 are produced,
Credit terms are set a n d demand established. Finished goods reserve i n v e n tories are m a i n t ain ed f0r variations in d e m a n d . Sales Occur.
t4, . . . , t 4 + x b
Accounts ceivable held.
reare
t5 +x
t6 +x
C a s h f l o w s in from receivables c o l l e c t e d w h e n d u e . Precautionary cash balances are r e q u i r e d ,
C a s h f l o w s in from receivables c o l l e c t e d one period late. Precautionary cash balances are r e q u i r e d .
OPERATING CYCLES
*A continuous input batch output production process is assumed. +Credit terms are extended in discrete timeperiods equal
to the production time. The variable, x, is the number of periods that credit is outstanding after the sales period. It is equal to two less than the number of periods of credit extended to buyers.
35
component of the over-all cost of credit extension. The relationship between the credit period and short-term investments and cash flows is emphasized in the case of lengthening the credit period. This results in (1) increased d e m a n d , (2) more production in the preceding period of the operating cycle to meet the increased demand, (3) increased raw material purchases in still an earlier period to support the added production, and (4) a larger precautionary cash balance at the time of anticipated collection. The short-term investments and cash flows of an operating cycle are thus a function of the credit period that initiated the demand in that cycle. A change in the credit period necessitates a change in financing of the cycle. In the case of longer terms, for example, m o r e funds are required to support the cycle. In most cases, the source of the financing is short-term borrowing. The availability and
OCTOBER, 1970
cost of this borrowing are largely established by the volume and structure of a firm's current assets. Hence, at a given point in time, all operating cycles underway at that time fix the requirements for short-term borrowing and, simultaneously, set the limits on the a m o u n t of this borrowing that is available as well as its cost. These relationships were formulated into a model of a "short-term funds system" including the investment in cash, marketable securities, accounts receivable, and materials inventories as well as the borrowing to finance these investments (see Figure 2). The model allows for the initiation of a series of operating cycles similar to the one in Figure 1 and the financing of all operating cycles underway over some future planning period. The short-term investments in each cycle are the optimal balances, given the demand in that cycle and the cost of financing at that
LEE A. TAVIS
FIGURE 2
A Computerized Short-Term Funds Systems
C/ J
BO~OI~TINtG
/
Short-Term ~ B.....
ing
/
CASHCROEMQUut-IIR~IMVEENTst/
/ /
36
* As s h o r t - t e r m investments are u n d e r t a k e n - t h u s increasing short-term borrowing capacity--the borrowing to finance the investments influences the carrying cost of the asset. The interrelationship between t h e short-term asset and liability structure is particularly close in t h e case of precautionary cash balances. The carrying cost of these balances depends partly u p o n the o p p o r t u n i t y cost of n o t using the funds to retire short-term debt. The Opposing cost, the cost of a cashout, is a function of available short-term borrowing capacity which, in turn, depends u p o n the current asset structure. The determination of an optimal balance, therefore, depends u p o n the structure of the whole shortt e r m funds system. t T h e available sources for short-term funds are formulated as a linear p r o g r a m m i n g problem, the optimal
point in the planning period. The financial structure is the least-cost combination of sources over the planning period. A number of different credit periods could be applied over a planning period. Each group of credit periods (each credit set) would result in a unique cash flow and structure of the system for the planning
mix being that c o m b i n a t i o n of sources that leads to the m i n i m u m cost of borrowing. In this LP problem, the overlaid operating cycles form the base for the requirements vector. The resulting funds flow, combined with exogenous funds available, sets the requirements for short-term borrowing over time. The investments in the operating cycles establish the capacities for each credit source in each operating period. The coefficients of the objective f u n c t i o n (to minimize the cost of short-term borrowing) are the time- and taxadjusted avoidable costs of borrowing from each source. The coefficients in the constraint matrix relate the borrowing from each source to the borrowing capacities, and reflect the r e q u i r e m e n t that, t h r o u g h o u t the credit planning period, sources of funds m u s t equal uses.
period. The present value of these flows provides a system net present value for each credit setfl The credit set leading to the greatest net present value would be the best of the many possible sets. Although actual firms are more complex than the simple, single-product firm modeled here, they can be viewed as consisting of
BUSINESS HORIZONS
Finding the Best Credit Policy
many sets of operating cycles in process at a given time. They are subject to similar parameters and interrelationships.
OPTIMAL CREDIT PERIODS Once the many facets of the short-term funds system that jointly influence the costs and returns associated with the credit period have been identified, the pressures toward optimal terms can be studied. In the preceding example, two identifiable cash flows are set i n t o motion a s the credit period is lengthened--operational flows and financing flOWS.
On the operational side, the incremental increase in demand leads to more sales. The present value of this operational inflow, however, is reduced by bad debts and the delay in collections. The outflows for production and other costs tied to the increased demand go up. In most circumstances, the net result of these flows is a positive net present value (NPV) as the credit period is lengthened. Financing flows are costs. As the creditrelated demand increases, borrowing must be undertaken to support cash production outlays for the added finished goods and the increase in precautionary balances. The longer credit period means more financing for units sold but carried on credit. With a longer credit period, the increase in the present value of operational flows is offset by the increase in the present value of the financing flows. The movement of these two classes of cash flows was tested by assigning values to the model parameters and computing the present value of these cash flows 2. The discount rate used in the model is the cost of t h e exogenous funds invested in the short-term funds system. These outside funds are drawn from the securities markets or generated internally and invested in the system rather t h a n in fixed assets. Short-term borrowing costs are included in t h e cash-financing flows rather than weighted in the discount rate. This procedure is based on the absorption of uncertainty through precautionary balances, and t h e j u d g m e n t that short-term borrowing capacity tied to optimal current asset balances would keep short-term financial leverage below the threshold of an increasing cost of exogenous funds.
OCTOBER, 1970
for different credit periods. The results are outlined in the accompanying table. When minimum terms are offered (Credit Set A), the operational flows net to a present value of $220,000; financing costs are $20,000; and the result is an NPV for the system of $200,000 (column 5 in the table). With uniform terms of 105 days throughout the planning period (Set G), the system NPV was almost the same ($199,000) but the s t r u c t u r e was substantially different: operational inflows were $274,000, and financing outflows were $75,000. Between these extremes, system NPV was maximized with a mixture of 45- and 60-day credit periods (SCUD). At this point, a further lengthening of the credit periods leads to an increase in the present value of financing outflows that is greater than the present value increase in net operational inflows. In Part II of the table, the system NPV resulting from the optimal set is used as a base and a cost imputed to the nonoptimal sets. These imputed costs are plotted in Figure 3. This concave curve suggests guidelines for credit policy. The cost of nonoptimal credit policies is not significant over a wide range of possible t e r m s - S e t B through Set E. Beyond the relatively flat b o t t o m of the curve, the cost of nonoptimal behavior increases significantly to a present value cost of 7.4 percent at the extreme of Set H. Once a set of parameter values that results in an optimal credit set is established, slight changes in the value of any single parameter tends to shift the optimal set. Optimal periods are particularly sensitive to changes in the response of units demanded to different effective prices and the determinant of these prices, that is, the buyer opportunity rates. A slight change in the effective price demand function changes the optimal length of the credit period by a third. Small changes in the buyer opportunity rates have the same impact. Shifting buyer opportunity rates clearly demonstrate the total system response to factors influencing credit policy. If receivables are treated separately, a firm will extend
37
LEE A. TAVIS
Present Values and Imputed Present Value Costs of Selected Credit Sets (thousands of dollars) Present Values (1) Credit Sets* Set Set Set Set Set Set Set Set
A (minimum) B C D (optimal) E F G H (maximum)
Imputed Present Value Costs
(3=1--2) Net Operational Inflows
(4)
(5)
(6=7+8)
Collections
(2) Operational Outflows
Financing Outflows
Net System
$3,022 3,115 3,203 3,250 3,287 3,366 3,442 3,513
$2,803 2,878 2,953 2,995 3,026 3,097 3,167 3,236
$220 237 250 255 261 269 274 277
$20 30 42 45 54 65 75 83
$200 206 208 210 207 204 199 194
*Each credit set consists of a series of credit periods offered over a future time span (a credit planning period). The sets included in this table are arrayed from the set made up of the minimum length of credit throughout the planning period to the set consisting of the maximum terms considered feasible by management. The credit planning horizon for a firm would be determined by these longest possible terms. Management could select the maximum feasible terms as optimal only after comparing the system NPV results of those terms with all possible combinations of shorter terms over the same planning period.
System
(7) Net Operational
(8) Financing
$ (9.4)+ (3.2) (1.5) 00.0 (2.5) (5.5) (10.4) (15.5)
$(35.0) (18.3) (4.7) 00.0 6.1 14.1 19.4 22.2
$25.6) 15.1 3.1 00.0 (8.7) (19.8) (30.0) (37.8)
As indicated in Figure 1, credit terms in the model are set in discrete time increments equal to the production time--in this test assumed to be 15 days. The maximum credit terms allowed were seven operating periods in length--105 days. The optimal set (Set D) was a combination of 45- and 60-day terms offered during the 105-day credit planning period. In all other sets, there was no change in the terms offered over the planning period. tParentheses indicate less than optimal. Figures may not add to net due to rounding.
38 FIGURE 3
Imputed Present Value Cost of Less Than Optimal Credit Sets Imputed Costs ($000) 18
(Selected Credit Sets)
16
14
12 10 8 6 4
2 o
Imputed costs as a percent of optimal 4.5
1.5
0.7
-.
1.4
I
I
I
/
I
/
I
I
A Minimum
B
C
E
F
G
H Maximum
D Optimal
2.6
4.9
7.4
BUSINESS HORIZONS
Finding the Best Credit Policy
credit only when its cost of funds is less than that of its customer in the absence of collection risk. 3 In the test reported above, when the buyer opportunity rate is set equal to the cost of exogenous funds, the optimal set moves to the lower boundary (Set A) with a cost of 63 percent imputed to Set H. These results demonstrate the importance of recognizing the full cost of extending credit delineated earlier. Surprisingly, major differences in collections e x p e r i e n c e - a c c e l e r a t e d collections, delayed collections, and larger bad debt losses-fail to shift the optimal terms, although the system NPV is affected. 4 The introduction of seasonal demand patterns shifts the makeup of the optimal credit sets. With an upswing, optimal periods are shorter because of the rise in the per unit cost of borrowing as short-term borrowing increases relative to its capacity. The added cash requirements of these operating cycles as demand increases, and the associated borrowing needs, draw on higher cost sources, thus offsetting the additional net operational inflows, s Reciprocal pressures are in force on the downswing. Optimal credit terms are also sensitive to changes in the cost structure. Increasing operating leverage leads to a shift of the optimal credit set to longer terms and an increase in the system NPV. The reverse holds true when operating leverage is dropped. The tests clearly indicate the desirability of shifting credit policy with changes in operating leverage. This finding is relevant to
3. S e y m o u r Friedland, The Economics of Corporate Finance (Engtewood Cliffs, N. J.: Prentice-Hall, Inc., 1966), p. 74. 4. In each test, the percentage of bad debts was held c o n s t a n t over all possible credit periods. In those cases where t h e percentage of bad debts increases with the length of the credit period, there will be pressure toward shorter periods. 5. The marginal cost of borrowing is measured b y the value of the dual variables in the financial structure linear program. These costs s h o o t upward as borrowing approaches its capacity reflecting the added liquidity reserves required as t h e short-term borrowing cushion is lost, and the loss of unsecured borrowing capacity associated with secured borrowing, as well as t h e additional per unit borrowing cost.
OCTOBER, 1970
c~ipital budgeting decisions. If a proposed fixed asset investment modifies the operating leverage of a firm, the changes in optimal short-term investments should be included in the anticipated incremental cash flows relevant to the investment.
AN APPROACH DISCOUNTS
TO
OPTIMAL
CASH
Management has the option of not only varying the length of the credit period as a c o m p o n e n t of credit policy but also offering cash discounts for early payment. As with the credit period, some cash discounts have a more favorable over-all impact than others. It is clear that the analysis of cash discounts entails full systematic consideration since discounts will influence the units demanded and the timing of cash flows as did the credit period. From the potential buyer's point of view, discounts offer the alternative of a lower cash price, rather than the effective price that results from paying at the end of the credit period. 6 In the presence of uniform credit terms the cash price for each potential buyer would be the same. As noted earlier, effective prices are different for each buyer. The effective price depends upon his own opportunity rate and is unique. The discounted price versus effective price trade-off is, therefore, different for each buyer. For the customer with a relatively low opportunity rate (and hence a relatively high effective price for any given credit period), a modest discount would drop the cash price below his effective price and he would opt for the discount. In this sense, potential customers with low opportunity rates are enticed more by cash discounts, whereas high opportunity rate buyers are attracted by the effective price reduction associated with the credit period. It takes a high discount indeed to lower the cash 6. I am indebted to a colleague, Robert Mettlen, for helping clarify this relationship.
39
LEE A. TAVIS
40
price sufficiently to meet the effective price of the high opportunity rate buyer. For the seller, cash discounts mean the receipt of less money, but it will come in earlier from those customers taking their discounts. In terms of the model, operating cycles would be shorter with less cash throwoff to the extent that discounts are taken. T h e complete structure of short-term investments and liabilities would change with these shifts in the cash flows of the system. The reduction in cash throw-off would be offset by the lower financing costs resulting from the shortened operating cycles. Therefore, meaningful evaluation of alternate discount policies can be accomplished only when their impact on the short-term funds system is recognized. Cash discounts, as a component of a firm's credit policy, should be analyzed within the context of an optimal credit period. The credit period is designed to attract the high o p p o r t u n i t y rate (low effective price) customer, whereas the cash discount is intended to decrease the cash price and entice the potential buyer whose effective price is relatively high due to a low opportunity rate. Each combination of a credit period and cash discount will result in a unique level of demand and structure of the system. The optimal credit terms will be that credit period and cash discount that optimizes the resulting system NPV. The large cash discounts typical in U.S. industry suggest that discounts are set to entice all customers to pay cash, including those with high opportunity rates. 7 Discounts thus serve as thinly disguised price reductions and are not making their full contribution to the selling firm's profits.
7. The notion is commonly held that buyers w h o do not take their discounts are p o o r credit risks. In a survey conducted by Welshans it was reported that "several credit managers stated flatly that t h e y . . , would not continue approving credit for customers who did not take their discounts." Merle T, Welshans, "Using Credit for Profit Making," Harvard Business Review (January-February, 1967), p. 144.
THE RESULTS Credit policies are a key determinant of the structure and cash flows of a closely interr e l a t e d short-term funds system. Each operating cycle is interconnected with decisions regarding materials inventories and precautionary cash balances, all tied to the demand resulting from the extension o f credit. And short-term borrowing is inextricably tied to current asset investments. Optimal credit periods result from a delicate balance of parameter values. Once an optimal credit set is achieved, a small adjustment of parameter values, in most cases, moves the optimal set toward its limits. Particularly significant are the buyer's opportunity rate and his demand response to different effective prices. Collection experience has great importance for the net present value of the system but little for optimal sets. Op crating leverage readily changes the optimal periods. Given the delicate balance associated with each credit set, it is probable that credit periods based on industrial standards are not optimal for most or all firms in an industry. Furthermore, judging by the way optimal terms move toward the boundary sets with small changes in parameter values, it is unlikely that, for many firms, the optimal set falls within a spectrum of periods considered feasible b y management. Even though optimal periods are highly sensitive to the state of the system, the imputed cost of errors is not great for periods close to the optimum. At the limits of credit extension, however, the cost of making credit errors is great. Cash discounts are relevant only within the context of an optimal credit period. They should be used to attract the marginal potential buyer with a low opportunity rate and, hence, a relatively high effective price for any given credit period. The size of traditional cash discounts suggests that firms are attempting t o entice all credit customers to take their discounts--in m a n y cases a suboptimizing decision.
BUSINESS HORIZONS