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Web Appendix 17A

# Web Appendix 17A - 19819_17Aw_p1-3.qxd 10:43 AM Page 17A-1...

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17A-1 Both the AFN formula and the projected financial statement method as we initially used it assume that the ratios of assets and liabilities to sales (A*/S 0 and L*/S 0 ) remain constant over time. This, in turn, requires the assumption that each “spontaneous” asset and liabil- ity item increases at the same rate as sales. In graph form, this implies the type of relation- ship shown in Panel a of Figure 17A-1, a relationship that is (1) linear and (2) passes through the origin. Under those conditions, if the company’s sales increase from \$200 mil- lion to \$400 million, or by 100 percent, inventory will also increase by 100 percent, from \$100 million to \$200 million. The assumption of constant ratios and identical growth rates is appropriate at times, but there are times when it is incorrect. Three such conditions are described in the follow- ing sections. Economies of Scale There are economies of scale in the use of many kinds of assets, and when economies occur, the ratios are likely to change over time as the size of the firm increases. For exam- ple, retailers often need to maintain base stocks of different inventory items, even if cur- rent sales are quite low. As sales expand, inventories may then grow less rapidly than sales, so the ratio of inventory to sales (I/S) declines. This situation is depicted in Panel b of Figure 17A-1. Here we see that the inventory/sales ratio is 1.5, or 150 percent, when sales are \$200 million, but the ratio declines to 1.0 when sales climb to \$400 million. The relationship in Panel b is linear, but nonlinear relationships often exist. Indeed, if the firm uses one popular model for establishing inventory levels (the EOQ model), its inventories will rise with the square root of sales. This situation is shown in Panel c of Fig-

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