700 (Vo.14,No.17) IN PRACTICE A member's contribution generally can be inter- Employing Proposition 1, a rule for the split of the to- preted as the value of the matching potential it brings tal cash pool profit between creditors and debtors (e termined assume a situation in which creditors' total the second type of allocation rules), can be derived balance, C. is 100 and debtors'total bala D. is 80. In amounts to 80. Only a fraction of Min(C, D)/C, or 80/100, of an individual creditors balance, Ci, effectively con Equation ( 9) shows that net benefits are allocated fooL. In other words, if a creditor's balance amounts to properly between both groups, if interest rate spreads butes to the interest savings generated through the only a portion of eight is valuable to the pool in that equal the inverse proportion of creditors'and debtors' it can be used to finance debtors' cash demand. The re total balances. Considering the pools total budget con- straint, the following Proposition 2 results: 8 mainder of two is subject to market interest Now. assume an individual debtor's balance, di, is 5 Proposition 2. When applying the profit split method This makes up d /Min(C, D), or 580, of the pool's match in a cash pooling transaction, spreads between pool ing balance. Consequently, creditor i's contribution and market interest rates should equal the inverse ith respect to debtor j equals 10 times 80/100 times proportion of creditors' to debtors'total balances In 5/80 times j's individual interest savings. Formally, such a situation the cash pool residual profit is creditor i's total contribution to all other pool members shared equally between the group of creditors and can be expressed as the group of debtors Arms-Length Interest Rates ∑=4 Now that rules for a proper allocation of the pool where pi denotes creditor i's contribution. profits among creditors and debtors have been devel oped, arm's-length transfer prices can be determined Analogously, a debtor's contribution, p;, reads as 6x4=n∑a1cx(r-r2) I When applying profit split method, the pool's ef- (11) ficiency gains must be allocated contribution-wise, that is, pool benefits are properly allocated when each pool members benefit equals its contribution Equations (10) and (11) describe the arms-length pool interest rates for creditors and debtors. Each credi tor is granted an interest rate that equals the market in (7)-=p half of the cash pool profit in the absence of a pool, plus fit per unit of total credit bal ance. Analogously, a debtor is charged the market debit interest rate minus half of the pool profit per unit of to- Before dealing with the implications of (7)and(8) Proposition 3 summarizes the above pricing rules detail, please note that we need to derive two types of d profit allocation rules. The first type is to determine Proposition 3. When applying the profit split metho in cash pooling transactions, pool profits are allo be allocated to each individual creditor, and which part cated properly among all creditors and debtors, if of all debtors,' share should be allocated to each indi- market interest rates are adjusted according to pool vidual debtor. The second type divides the pool's total members' s-length benefits. Pool members rofit between the group of all creditors on the one arm's-length benefits equal half of the pool profit per hand and the group of all debtors on the other. Both unit of total credit or debit balance, respectively, As types of allocation rules jointly ensure that each credi- suming a positive pool residual profit, the arm's or and each debtor are allocated their proper th credit interest rate of a pool should always be contribution-based shares within the range of the market credit interest rate (ower bound) and the midpoint of the spread be Lets proceed with the first type of allocation rules ween debit and the market credit interest rate(up Using the above system of equations, the following in- utive Proposition I results per bound). Accordingly, the arm's-length debit in- terest rate of the pool should always be within the Proposition 1. When applying the profit split method range of the midpoint of the spread between debit in a cash pooling transaction, all creditors should face identical pool credit interest rates and all debt. 7 To arrive at(10), just insert(2) and to(7 and con rs should face identical pool debit interest rates sider identical spreads to market interest 8 The last sentence of Proposition 2 can easily be verified by Note that, Min(C, D) has been cancelled down in nomina tor and denominator to arrive at(5) ineng()and(3)in the budget constraint (4), and then apply- 6 For the credit side, use(7) together with(2)and(5); for Use Proposition I and Proposition 2 in the budget con the debit side, use(8) together with (3)and(6) straint (4)and solve for r and rd, respectively 22105 oyrighte 2005 TAX MANAGEMENT INC, a subsidiary of The Bureau of National Affairs, inc. TMTR ISSN 1063-2069