# Know Maths in Money Market Operations

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Money Market is an important ingredient for growth and development of an economy. India too is no exception for it. With the fastest growing economy, India has experienced significant growth in its Money Market operations. The Participants like the Reserve Bank of India along with financial institutions like the UTI, GIC, LIC, etc. have major role in this ever expanding short-term finance management market. But, still this market is blossoming and not yet at the matured stage.

### Distinct Features of Money Market

• Unlike the capital market, Money Market is a market of short term financing. It is collection of markets, such as, call money, notice money, repose term money, treasury bills, commercial bills, certificate of deposits, commercial papers, inter-bank participation certificates, inter-corporate deposits, swaps futures, options, etc. It is often also termed as liquid market.
• The competition is relatively pure.
• It is true money market i.e. investments are highly liquid.

## Mathematics in Money Market

Mathematics involved in money markets are calculations of Effective rate of interests and Bond Values.

The Bonds or Treasury Bills are short term liquid instruments. Which are often issued at discount. To calculate the yield (return in percentage), we use the formula: $Y = [\frac{F-P}{P}] \times \frac{365}{M} \times 100$

Where,

Y = Yield,

F = Face Value,

P = Issue Price/Purchase Price, and

M = Maturity Period (often in days).

If Maturity Period is given in months, the above formula can be modified by replacing 365 days with 12 months and ‘M’ with maturity periods in months.

The Effective rate of interest is calculated by converting the yield percentage into interest per annum rates.

The formula used to convert yield into per annum rate is – $[1 + \frac{i}{n}]^{n}-1$

Where,

i = yield

n = fraction of year ( for example if Treasury Bill is for 3 months, then n = 12/3 = 4; likewise if Treasury Bill is for 60 days, then n = 365/60 = 6.08)

One can also use 360 days instead of 365 days in Financial Management calculations to make calculations free from redundant decimals.

Also, sometimes we need to calculate the cost of issue for an issue. In such cases, we have to add all the interest costs as well as all other costs denoted in per annum charges. This is further illustrated through illustration no. 3.

Illustration 1 – RBI sold a 91-day T-Bill of face Value of ₹100 at yield of 8%. Calculate the issue price?

Answer – Let the issue price be ‘x’.

Then by the terms of the issue of the T-bills: $8\% = \frac{(100-x)}{x} \times \frac{365}{91} \times 100$

On solving, we get x = ₹ 98.04.

Illustration 2 – A Ltd. has excess cash of 10 lakhs. It wants to invest it in short term market securities. Expenses related to investment is 10,000. The annual yield of securities invested is of 10%. The Company wants to know –

1. The period of investment so as to earn a pre-tax income of 10%
2. The minimum period for the company to breakeven its investment expenditure overtime value of money.

1. Pre-tax income required on investment of 10 lakhs.

Let the period of Investment be ‘P’ and return required on investment ₹1,00,000 (10,00,000 x 10%)

Accordingly, $(10,00,000 \times \frac{10}{100} \times \frac{P}{12}) - 10,000 = 1,00,000$

On solving P = 13.2 months

1. Break-Even its investments expenditure $(10,00,000 \times \frac{10}{100} \times \frac{P}{12}) - 10,000 = 0$

On solving P = 1.2 months

Illustration 3 – Calculate the effective rate of interest p.a. and the total cost of funds to XYZ Ltd., when planning a CP issue:

Issue Price of CP is ₹96,600, Face Value is ₹1,00,000, Maturity Period is 6 Months and Issue Expenses are:

Brokerage 0.20% for 6 months, Rating Charges 0.50% p.a. and Stamp Duty 0.175% for 6 months $Nominal Interest or Bond Equivalent Yield = \frac{[F-P]}{P} \times \frac{12}{M} \times 100$

Where,

F = Face Value

P = Issue Price

M = Maturity Period

Therefore, $\frac{1,00,000 - 96,600}{96,600} \times \frac{12}{6} \times 100 = 7.04 \% p.a.$ $Hence, Effective Interest Rate = [1 + \frac{0.0704}{2}]^{2} - 1 = 7.16 \% p.a.$

Cost of Funds to the Company –

 Effective Interest 7.16 Brokerage (0.20 x 2) 0.40% Rating Charge 0.50% Stamp Duty (0.175 x 2) 0.35% Total Cost 8.41%

So, this is all about mathematics of money market operations in this Article. For any query and feedback, do make use of comment box.