Question

International Finance Problem Set on Working Capital Management 1. Rossignol Co. manufactures and sells skis and snowboards in France, Switzerland and Italy, and also maintains a corporate account in Frankfurt, Germany.  Rossignol has been setting separate operating cash balances in each country at a level equal to expected cash needs plus two standard deviations above those needs, based on a statistical analysis of cash flow volatility. Expected operating cash needs and one standard deviation of those needs are below.
Rossignol’s Frankfurt bank suggests that the same level of safety could be maintained if all precautionary balances were combined in a central account at the Frankfurt headquarters.
a. How much lower would Rossignol’s total cash balances be if all precautionary balances were combined? Assume cash needs in each country are normally distributed and are independent of each other.
b. How much would the company save annually, if financing costs are 6% p.a., from centralizing its cash holdings?
a.		Expected		One
Country of subsidiary		cash need		standard deviation
Switzerland		€ 4,000,000		€ 1,000,000
Italy		3,000,000		800,000
France		2,000,000		500,000
Germany		2,000,000		700,000
Total		€ 11,000,000		€ 3,000,000

Answer 1

Please note that if cash requirements are combined, mean requirement of combined entity can be simply summed up, but same is not true for standard deviation as it is not additive.

So first we need to calculate the variance by taking square of SD, then we sum it for all the location to get variance of combined entity and then we take square root again to get the SD of combined entity.

Keep in mind that we can take a simple summation of variance due to the fact that requirement in different locations are independent of each other and their correlation coefficient is = 0.

Solution is given through following excel sheet -

B Mean 4000000 2 Switzerland 3 Italy 4 France 5 Germany D Variance =POWER(C2,2) =POWER(C3,2) =POWER(C4,2) =POWER(C5,2) Std Dev 1000000 800000 500000 700000 Cash Needed Individually =B2+2*C2 =B3+2*C3 3000000 2000000 2000000 =B5+2*C5 6 =SUM(B2:B5) =SUM(D2:05) =POWER(B8, 1/2) 7 Combined Mean 8 Combined Variance 9 Combined SD 10 11 Total Cash Needed if no combination 12 Total Cash Neded if combined 13 Cash Saved 14 Interest Saved 15 =SUM(E2:E5) =B7+2*B9 =B11-B12 =B13*6%

Mean 40,00,000 30,00,000 20,00,000 20,00,000 Std Dev 10,00,000 8,00,000 5,00,000 7,00,000 Variance 10,00,00,00,00,000 6,40,00,00,00,000 2,50,00,00,00,000 4,90,00,00,00,000 Cash Needed Individually 60,00,000 46,00,000 30,00,000 34,00,000 2 Switzerland 3 Italy 4 France 5 Germany 6 7 Combined Mean 8 Combined Variance 9 Combined SD 1,10,00,000 23,80,00,00,00,000 15,42,725 10 11 Total Cash Needed if no combination 12 Total Cash Neded if combined 13 Cash Saved 14 Interest Saved 1,70,00,000 1,40,85,450 29,14,550 1,74,873

Hence, Total Cash Requirement goes down by 2,914,550.
Interest saved on this amount = 174,873