1. FUNDS MANAGEMENT BY BIYANI GIRLS COLLEGE: SOLUTION TO A PERSISTING OPTIMIZATION PROBLEM ANUBHAV LAMBA

2. Banking in India Commercial banks in India as universal banks Comprehensive financial services under one roof Reserve Bank of India (RBI) regulates the fund-based activities Securities and Exchange Board of India (SEBI) regulates the fee-based activities.

3. Working Capital Loan And Cash Credit System Working capital lending still a major functional area for commercial banks Conventionally, working capital financing in India is in the form of cash credit facility Under the cash credit system, the lending bank sanctions a maximum loan limit to a customer Utilisation is subject to availability of adequate assets pledged or hypothecated

4. Working Capital Loan And Cash Credit System The drawing power is adjusted at regular intervals (normally once a month) by considering the level of current asset that has been paid for and deducting margin(s) therefrom at stipulated rate(s) These margins are worked out in line with the lending norms of Tandon Committee. The amount of loan outstanding can vary freely within the drawing power and at times the balance in the cash credit account can even be in credit

5. Working Capital Loan And Cash Credit System Interest is payable based on the actual level of loan enjoyed on a daily product basis Thus, a fixed limit is worked out for any loan account by assessing the customers peak requirement on the basis of its projected holding of current asset Once this limit is set, the borrower becomes virtually entitled to draw, subject to sufficient current asset holding, any amount up to the limit.

6. Working Capital Loan And Cash Credit System The borrower has the option to draw at any point of time, without any prior notice, up to the extent of the limit but no corresponding obligation either to compensate the banker for this option or to ensure an optimum utilization of the facility at all points of time

7. Working Capital Loan And Cash Credit System Therefore, a banker may be called upon to arrange for large amounts of funds at short or no notice at pre-determined rate of interest. In such a situation, funds management and financial planning become relatively low priority issues for the borrowers They can pass on the consequences of inadequate planning and inefficient management on their part to the banking system The problem may manifest itself in the form of a serious strain on the banks cash management system.

8. Working Capital Loan And Cash Credit System The lending bank may try hard to arrive at a realistic estimate of the working capital requirement of a client company over a certain length of time in future But the latter has hardly any stake in the accuracy of this exercise so long as the sanctioned limit is set at a sufficiently high level The profitability of the lending bank may be adversely affected due to such indifference and inefficiency of its clientele. This is a drawback of the cash credit system

9. Working Capital Loan And Cash Credit System This is at variance with the cash loan system prevalent in various countries whereby the entire amount of loan limit is disbursed in one shot subject to renewal/review at regular intervals. Besides, in India, credit is considered a scarce commodity and need-based financing is one of the major planks underlying the central banks credit policy even in the liberalized regime. Systematic planning of credit and optimal utilization thereof are considered quite vital.

10. Working Capital Loan And Cash Credit System Any arbitrary break-up of working capital facility into fixed and variable components will thus not be in line with the spirit of the policy of the central bank.

11. Tandon Committee Norms – Style Of Credit The first and the most substantial work in the field of working capital finance in India was done by the Tandon Committee The Committee aimed at inculcating in the borrowers the habit of making an effective financial planning through a system of reward and penalty It suggested that the working capital facility should be bifurcated into two components

12. Tandon Committee Norms – Style Of Credit (i) A fixed or demand loan component, interest on which is to be charged at a certain fixed rate throughout the year (ii) A variable or cash credit component, interest on which is to be charged at a somewhat higher rate. This component would indicate by what amount the level of borrowing for a particular customer exceeds the demand loan component

13. Tandon Committee Norms – Style Of Credit If a borrower projects the demand loan component at a higher than necessary level, he would end up paying interest on amounts not actually required by it. If he projects the demand loan at a low level, much of its withdrawals will attract a higher rate of interest and the overall interest cost over the year would not be minimized.

14. Tandon Committee Norms – Style Of Credit It would, therefore, be in the interest of the borrowing company to ensure an efficient financial planning and to project correct levels for its projected fund requirement Once the monthly requirement of working capital is submitted by a borrowing company, the lending bank has to work out the optimum level for demand loan that will minimize the annual interest burden

15. Formulation Of The Problem Once a customer submits the pattern of the working capital requirement over the next one year, the question arises as to how a practical banker will bifurcate the working capital requirement into a fixed and a variable component to minimise the annual interest burden

16. Formulation Of The Problem Let W(t) = working capital finance required by a borrowing company, expressed as a function of time, over the next one year, x = level of demand loan or fixed component, W(t) – x [where W(t) > x] = level of variable component, I = Interest burden for the company for the next one year a = Rate of interest for the fixed component (a + b) = Rate of interest for the variable component

17. Formulation Of The Problem Then, (1)I=a.x.dt + [W(t) – x].θ [W(t) – x]. (a+b) dt, where θ[W(t) – x] is the well-known step function Or, 12 12 (2)I=Σ (a/12).x + Σ [(a+b)/12].[W i – x]. θ[W i – x]. i=1 i=1 whereW i =level of working capital finance for the ith month

18. The Solution If a company works out its requirement of working capital finance for the next twelve months i.e. W i for i=1,2, …., 12, then the total interest burden for the company during the next twelve months works out to: 12 12 (3)I(x) = Σ x.(a/12) + Σ (Wi – x). θ(Wi – x). [(a+b)/12]. i=1 i=1 12 = a.x +[(a+b)/12] Σ (Wi – x). θ(Wi – x), i=1

19. The Solution Or, 12 (4)= a -[(a+b)/12] Σ[ θ(W i – x) + (W i – x)δ(W i – x)] i=1 12 = a – [(a+b)/12] n - [(a+b)/12] Σ (W i – x)δ(W i – x) i=1 = a – [(a+b)/12] n where n = number of months for which W i >x

20. The Solution Or, (5)n/12 = a/(a+b) for = 0

21. The Solution In other words, for I to be minimum, x is to be so chosen that for n months W i >x, where n/12 = a/(a+b)

22. The Implementation A.Let the levels of borrowing projected by a company for the next twelve months be 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51 and 52 units (the levels of borrowing need not occur in this chronological order). Also, let a = 10% p.a. and b=2% p.a. In such a situation, n/12 = 10/(10+2), or n=10. In other words, the demand loan component should be set at such a level that the level of borrowing would exceed the demand loan for 10 months. Thus, x 0 = 42 units or more but less than 43 units. The actual solution will be corresponding to the lowest value of x 0, i.e. x 0 = 42 units

23. The Implementation B. If the levels of borrowing be 45 units for 6 months and 50 units for the other 6 months, n/12 = 1 if the demand loan component is set below 45 units; n/12 = ½ if the demand loan component is set at 45 units or above, but below 50 units. Let a = 10% p.a. and a+b = 12% p.a. Then n/12 = 10/12 as per our formula. But, n/12 can be equal to only 1, ½, or 0. We shall choose the next lower permissible value for n/12, viz. ½. Further, as n/12 = ½ for all values of the demand loan from 45 units and above but less than 50 units, we shall select the lowest permissible value, viz. 45 units as the desired value of x 0.

24. The Final Prescription The readymade prescription for minimizing I now becomes: (i) Select x at such a level that n/12 = a/(a+b) or, if a/(a+b) is not available, the next lower available value. (ii) If a certain range of values of x satisfies (i), choose the lowest value of x from the range. Once we set the optimal of x i.e. x 0 at 45 units, the interest burden for the borrowing company over the next one year comes to (45 10% + 5 12% 6/12) = 4.8 units.

25. The Final Prescription If the demand loan component were set at 44 units, the overall burden of interest would have been (44 10% + 1 12% 6/12 + 6 12% 6/12) = 4.82 units. On the other hand, if the demand loan component were set at 46 units, the overall interest burden would have been (46 10% + 4 12% 6/12) = 4.84 units. Obviously, the overall burden due to interest is minimized if the demand loan is set at 45 units.

26. Conclusion The practical problem of banking can thus be solved by using a rather simple technique of optimization used so often in Physics. The result is perfect in the sense that no approximation is involved in its derivation. Also, the result is simple enough to be implemented by any practical banker. The outcome is thus interesting not only for its mathematical exactitude but also for its easy applicability.

27. Conclusion With such an easy and exact methodology available, banks can now go for a full- fledged implementation of the recommendations of the Tandon Committee, without having to resort to any arbitrary thumb rule