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FUNDS MANAGEMENT BY BANKS IN INDIA:

SOLUTION TO A PERSISTING OPTIMIZATION PROBLEM

UDAYAN KUMAR BASU

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.

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


• 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


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 customer’s 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.


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


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 bank’s cash management 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


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 bank’s credit policy even in the liberalized regime.

Systematic planning of credit and optimal utilization thereof are considered quite vital.


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.

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


(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


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.


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

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


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


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].[Wi – x]. θ[Wi – x].

i=1 i=1

whereWi=level of working capital finance for the ‘i’th

month

The Solution

If a company works out its requirement of working capital finance for the next twelve months i.e. Wi 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

The Solution

Or, 12

(4) = a -[(a+b)/12] Σ[ θ(Wi – x) + (Wi – x)δ(Wi – x)]

i=1

12

= a – [(a+b)/12] n - [(a+b)/12] Σ (Wi – x)δ(Wi – x)

i=1

= a – [(a+b)/12] n

where n = number of months for which Wi >x

dx

dI

The Solution

Or,

(5) n/12 = a/(a+b) for = 0 dx

dI

The Solution

In other words, for I to be minimum, x is to be so chosen that for n months Wi>x, where n/12 = a/(a+b)

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, x0 = 42 units or

more but less than 43 units.

The actual solution will be corresponding to the lowest value of x0, i.e. x0 = 42 units

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 x0.

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. x0 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.

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.

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.

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

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