Forex rates movement-“Classical Interest rate differential theory” and its practical limitations

Let me start with a caveat, “inter se” movement between currencies and the premia or discount that one currency commands over another currency, over a period depend on various factors. Just to list a few,

a)       the respective Interest rates in each currency ,

b)      short term availability and requirement of the currencies,

c)      Balance of payments of trade movement in the short term between two countries ,and of course the most important ,

d)       Government regulations and restrictions imposed on the currency

e)       Intervention by the Government in buying/selling of the currencies

f)       Speculative play by private players

Discussion here would be on incremental inter se movements between currencies and not on the base rate itself. The base currency rate between two or more currencies depend on factors starting from Purchase power parity, Balance of payments of trade as of a certain date and various other factors  including historical,which is possibly a subject for discussion for another day.

Just to make it doubly clear this piece is only on movement of Forex rates between currencies and the way forward premia /discount gets fixed between the currencies. For the sake of simplicity, we will take USD and INR with which people are generally familiar.

 One compelling theory and what could be termed as a classical one on forex movement is the one with reference to “Interest rate differential between currencies”. This is the simplest, most logical and something which should work if the market is perfect and there are no restrictions on currency movement, investment or borrowing in the currencies under study.

 What is “Interest rate differential theory”?  First let us define what is interest rate? People understand that interest rate is the rate an investment fetches in a certain currency. A deposit in India in Indian rupee fetches anything between 5-10% depending on the period of deposit etc. Similarly a deposit in USD in US would fetch something in the region of 2%-4%. We all broadly know that Interest is a function of the underlying inflation of the country’s economy and the real return expectations.

The comparable difference between interests can be termed “Interest rate differential”.

Let us start off with a base rate of 1 USD = INR 55. To make understanding easy, let us also assume that the interest in USD is 2% and interest in INR is 8%. $ 1 deposit would at the end of one year be equal to $ 1.02 and a Rs. 55 deposited for one year would be Rs. 55*1.08=Rs 59.40. In an ideal situation, USD 1.02 should equal Rs. 59.40 that is 1 USD should be Rs. 59.4/1.02 ,that is, Rs. 58.24 one year from now. The one year forward premia on  USD ,which fetches you Rs. 55 immediately and where the interest rate differential is 6% (8%-2%) should be Rs 3.24 ,(58.24-55.00) to a USD. If this is not the case, there would be a situation of what is termed “arbitrage” or opportunities to make riskless profit. Let us see it can happen.

Let us do a simple one between USD and INR. Let us take the numbers from the same example. For the sake of simplicity we will have to assume no interest rate differential between borrowing and Investing .This is to make the example easier.

Normally the currency on which interest rate is lower will be at a premium and the one whose interest rate is higher will be at a discount.

Let us assume that at the interest levels specified, the actual forward rate quoted at the end of one year is at INR 55 to a USD, that is there is no premia or discount.

Easy way to make profit is

- borrow in USD,

- convert to INR immediately,

- deposit in INR,

- simultaneously take a forward cover to buy USD at INR 55.

Let us calculate the flows.

Since you have borrowed in USD, you will have to pay $ 1.02 with interest at the end of one year.

USD converted to INR 55 and deposited would become INR 59.40 at the end of one year since INR deposit attracts 8 % interest.

Since a forward cover has been taken, you would be in a position to buy USD of 1.02 for a total outflow of INR 1.02*55=Rs. 56.10.This leaves you Rs 59.40-Rs 56.10=Rs3.30 as riskless profit.

In the same case, if at the same interest rates, INR one year forward rate had been INR  62 to USD, we will be doing the borrowing in INR, depositing in USD, take one year forward cover to sell USD

Let us work out the simple math in this sequence.

You had borrowed INR 55 for a year, to be returned after a year would be Rs 55*1.08=59.40

INR borrowed was converted to 1 USD at the beginning has been deposited as USD deposit .At the end of one year we get USD 1.02.

Since we had a cover to sell USD at the rate of INR 62 to a USD, we will sell the $ 1.02 at INR 62 to a USD and get on hand INR 1.02*62 =63.24 at the end of one year.

At the end of one year, we can pay off the INR borrowings of Rs 55 with interest,   Rs.59.40 and would be left with INR 63.24-59.40=Rs.3.84 as riskless profit.

Through this iteration, one  will find that  forward premia of Rs 3.24 to a USD is the equilibria rate.

We have assumed no difference in interest rates between borrowing and investing and also no difference between buying and selling of currency. Margins between these two will make a slight difference in the calculations but the theory holds good.

As a thumb rule, arbitrage opportunity will arise when the currency forward rate is different from the interest rate differential. Normally in such situations the demand/supply for the currencies adjusts in such a way that the interest rates move and nullify the advantage. If this kind of anomaly were to persist, everyone will be doing this set of transaction and the interest rates and the demand for the currency will drastically undergo a change till such time equilibrium is attained.

This is a theory, a sound one at that  but  will continue to be theory till such time , we have free currency movements and unrestricted deposit and borrowings in any currency in any country or at least in the countries of the currencies in question/discussion.It has its practical limitations in the current economic milieu but can be very useful pointer for course corrections and to see through huge anamolies. 

This piece was posted in CAClub website by the undersigned a few weeks back.

Market Capitalisation Vs Enterprise value

Market Capitalisation Vs Enterprise value

Typically when people discuss about stocks and shares, few key parameters discussed are Price earnings and Market Capitalisation.

Market capitalization in simple terms is the cost of buying all the shares of the company or the cost of buying the Company. In a hypothetical case, in the case of two companies whose market capitalization is the same we may come to the conclusion that both the Companies are valued same. Major fallacy in coming to such a conclusion is the fact that the two companies could be leveraged quite differently, that is one Company could have a borrowing of say 1 times the equity and the other Company may be debt free.Buying shares of a company means that one is buying in effect all the assets of the Company but also take over the liabilities of the Company. True cost to an investor would be the cost of acquisition of a  debt free company. A company say whose market capitalization is Rs 2000 Crs with a debt of say Rs 1000 Crs. The total cost of debt free acquisition to an investor would be Rs 2000 Crs+Rs 1000 Crs= Rs 3000 Crs

Take the case of another Company which also has a market capitalization of Rs 2000 Crs but is total debt free. The cost of acquisition or the true enterprise value of this Company is Rs 2000 Crs.

Just to give a very simple example let us take the case of  One Hotel Company ,A, which has a market capitalization of Rs 200 Crs plus it has a debt in the books of Rs 100 Crs and exactly similar Hotel in another Company B , let us say has a market capitalization of Rs 250 Crs but has no debt. The numbers which are to be compared to  is A is valued at Rs 300 Crs (mkt cap of Rs 200 Crs plus debt of Rs 100 Crs whereas B whose market cap is Rs 250 Crs and has no debt would have a total value of  Rs 250 Crs

If  the performance of the Company B is as good as Company A, one can safely conclude that Company B comes cheaper to the Investor.

Enterprise value , is the value of the enterprise , without any  debt. Such an enterprise needs to run the enterprise both  capital assets or Fixed capital as well as certain amount of working capital (net current assets ) .The convention to arrive at enterprise value from market capitalization is to add the long term debts and deduct the cash and cash equivalents . But in the practical world , we have seen that net current assets can not be taken as a given and as something which is the same for similar enterprises. It may even a good idea to deduct  the net current assets to arrive at the enterprise value.This may be departure from conventions but a fair comparison to arrive at the respective values of enterprises with different net current assets.Correct method would be to leave out the theoretical requirement of net current assets and add or deduct (adjust ) for the balance to the market capitalization.

We can look at examples and also may be look at analysis of companies based on enterprise values and profits in a subsequent discussion.

When we talk of comparison of two companies based on their Enterprise values, the bottomline comparison which would be most appropriate would be Profit before Interest . More in next discussion.

Compounding and Annuities

Most of us would have heard the cliched "magic of compounding". The magic is  in the fact that the growth of an investment is exponential and not quite the linear grwoth that is generally experienced where  simple interest is worked out . The reason lies in the fact that the Interest is added to the base principal at regular intervals and that forms the basis for further Interest calcuation

Say at interest of 10% per annum, an investment of Re 1 at the beginning of year 1 , would becomes 1.1 at the end of year 1, in generic way it can be expressed as (1+i)

And at the end of say 3 years the same would be (1+i)^3 and at the end of n years, the same would be 

A =P(1+i)^n

A bit more complicated would be to ascertain the value of an  Annuity or the maturity value of a regular payment at a regular intervals at a regular rate of interest . The derivation is through a summation of a geometric expression and the simplified form is as follows

Sn     = R *{(1+i)^n  - 1}/i   where

Sn is the Annuity or the maturity value

R is the regular payment at regular intervals and 

i is the rate of interest at the intervals specified

Of course one assumption in this is that the amounts are either invested at the end of the regular interval and say the first investment earns interest for (n-1) year and the last regular investment - no interest.

A variation of this is where the regular payment is at the beginning of the interval and earns interest for the full quantum of n years/months as the case may be and the last one also earns interest for on year would be as follows.

Sn   = R * { {(1+i)^(n+1)}-(1+i)}/i

Rule of 72

 Rule of 72

 “Rule of 72” is a simple  rule of thumb to determine the number of years it takes for an investment at a certain rate of interest ( interest at annual rests) to double. As is the case with most thumb rules, it works well within a certain “normal” data range.One can use the same to determine the implicit interest rate given the amount invested and the maturity amount.

To illustrate the use of it, let us assume that an investment is made at 8% per annum and at yearly rests, it would take 72/8=9 years for it to double. The underlying assumption is that the annual return is reinvested at the same rate of interest .This rule works well within an interest range of 5% to 12% with best being at 8% 

(Not able to attach an excel table. Not quite sure how to do the same)

Just as when one is given a rate of interest, one can find the no of years it takes for the investment to double by dividing 72 by the rate of interest, given the fact that an initial investment doubles in a certain no of years, one can find the underlying rate of return .

If someone says that an investment doubles in 9 years, then the underlying annual return rate is 72/9= 8%.

Return on Equity, Return on networth -Stocks

Return on equity -Net profit ( net earnings)*100/Total outstanding equity
This gives the return from a shareholder's perspective and does not reflect how well the accumulted shareholder's money ( reflected in Reserves and surplus ) is utilised.

Better parameter would be Return on networth

This is Net profit after taxes *100/ Networth of the company constituting Equity and reserves & surplus.

This again does not reflect how well the total funds of the company( including borrowed funds are deployed. For that one has to take int o consideration the net ptofit before interest /total capital deployed
More in the next

Current ratio - Importance in Financial evaluation specifc reference to the Indian context

Current ratio which is nothing but current assets /current liabilities is quite a critical part of the overall financial evaluation. This is one of the critical parameters not only in evaluating the efficient use of resources but also is a test of the credibility of the financials. In quite a few Companies, one finds that most of the net profit for the year sits in the form of an Inventory or Debtors. This could be a clear indication that eithet the stocks are overvalued or the receivables may not be fully receivable. While this may not be true in all the cases, quite a few of the Indian companies have thgis problem. They keep reporting profits year after year , but you will see the burgeoning size of the Debtors and Inventory. Operational cashflow over the years is negative.
Clearsign that one should avoid such shares. There can be the odd Comapny where there could be geneuine reasons.But in general such Companies should be

Meaning of EPS and PE ratio in the share market

EPS is Earnings per share and PE is Price Earnings. These are two oft repeated expressions in the stocks evaluation and discussions

Earnings per share is the total net earnings ( net profit) of the Company divided by the number of shares of the Company

It is nothing but the earnings ( net profit ) per unit share held by the investor.
Example, if net profit of the Company is Rs 25 Crs, the Company has a total share of Rs 10 Crs and a total of 10 Cr shares, each share being of Rs 1 , then the EPS is Rs 25 Crs/ 10 Crs =Rs 2.5 per share.

Price earnings ratio or the PE multiple as they call it is the Price divided by the earnings per share. This will give the number of time , price is in relation to the EPS. Lower the multiple , more attractive is the price of the share.

Reverse of this is the return on equity shares, that is EPS divided by price of the share multiplied by 100 gives the return % on equity
Let us assume that the share price is Rs 50, the PE ratio is Rs 50/ 2.5 = 20
Return is Rs 2.5*100/50=5%