## Wednesday, August 19, 2009

### Part 5: All about returns - time for some math

Pay Yourself first. Open a Third Bank Account. Make it investment ready. Have a spending target. Put the balance into the TBA.

Understand that there are different kinds of risk – Physical risk, Risk of default a.k.a. Credit Risk, Risk due to inherent volatility, and Interest Rate Risk.  Evaluate assets on the criteria of Risk, Return and Liquidity.  In general, higher risk needs to be compensated by higher return.  Now that we have done some revision, we can move ahead!

Talking about return, it is measured in terms of percent per annum.  What would Rs. 10,000 in an 8% fixed deposit amount to, in five years?  Dredging our memories will yield the compound interest formulae last used in Class Six:

Amount = Principal x  (1 + Rate/100) ^ Period

Hence in this case, (10,000) x (1.08)^5 = Rs. 14,693, i.e. 1.47 times your Principal.

8% for ten years works out to 2.16 times; twenty years to 4.66 times; thirty years to 10.6 times; forty years to 21.72 times; fifty years to 46.9 times; sixty years to 101.2 times;   Notice that as the time period increases, the rate of increase increases too!

Over a thirty year time period: 8% yields 10.06 times; 10%, 17.45 times; 12%, 30 times; 14%, 51 times; and 16%, 86 times.  Notice that over a long time period, an arithmetical increase in interest rate results in an exponential increase in return!

Moral of the story?  Every one percent increase in interest rate matters over the long term.  And the longer the time period, the more the beneficial effects of compounding.

Compound interest is the eighth wonder of the world! To use this principle to your advantage, you need to resist the itchy-fingers syndrome – once your money is invested somewhere, don’t give in to the temptation of booking profits in a hurry – be in it for the long term!

Continuing with the above example, if your Rs.10,000 is invested at 8% for 30 years it grows to Rs. 100,626.  If inflation in the meanwhile was running at 6%, what is your Rs. 100,626 thirty years hence worth in today’s terms?  That would obviously be:

100,626 / (1.06)^30 = 17,520 in today’s terms.  You can imagine what will happen if you keep your money lying around without earning interest.

Your grandfather bought a piece of land 50 years back at Rs.50,000.  It is worth 1.25 crores today.  You don’t have access to Excel – how would you calculate the approximate rate of return using only an ordinary calculator?  The money has grown 250 times.  2 raised to 8 is close to 250 (256).  Hence the money has doubled 8 times – 50/8 gives one doubling per 6.25 years.  If your money doubles in 6.25 years, what is the rate of interest?  It’s not 100 / 6.25 since it is compound interest we are talking about.  When you are dealing with compound interest you should use the “rule of 72” – calculate 72 / 6.25.  That gives 11.52 percent.  The actual rate works out 11.68 percent which is close enough. Remember the “rule of 72”.  It’s useful.

In the financial world 1% is sometimes referred to as 100 basis points.  So, an increase of 25 basis points means a 0.25% increase.

How does one measure Risk?  Let us say you are evaluating which mutual fund is better among a range of options.  They are all similar Equity Funds and all of them measure their performance against the BSE Index.  You first list down the “returns” that each of them has generated, say, in the last five years, along with the return on the BSE Index for comparison.  The absolute return is one measure and it’s a good one; but how do you account for the fact that some funds may be following a more risky investment strategy, i.e. their returns may be more volatile in comparison to other funds? Here you need some measure of measuring “risk” which in this case means the risk inherent in variability of returns.  There are several specific formulae to measure this (which we shall see much later in this series) but in general the principle followed is the same.  In order to measure risk, what is measured is the range and amount of deviation of the yearly (or any period’s) return from the average/mean return for each particular fund.  The resultant number, whichever formula is used, indicates the “risk” in the investment strategy followed by fund.

Coming back to the subject of “return” - you must use the principles explained above to discount any future returns to today’s terms in order to compare two different options.  Let me illustrate this with an example.  You invest Rs. one lakh upfront in Bond A which gives you a cash flow as follows:

Year 1: 25,000
Year 2: 45,000
Year 3: 50,000

There is another Bond, Bond B, where the returns on your one lakh are as follows:

Year 1: Nil
Year 2: 30,000
Year 3: 95,000

Which is the better bond to invest in? Assume that they are both equivalent on the risk scale.

Bond A gives Rs.120,000 over three years.  Bond B gives 125,000 over three years.  Bond B is better.  Hey, wait a minute!  What about time value of money?  If another Bond C yields two lakhs but after twenty years, would that make Bond C better?  We need to discount all the above cash flows to today’s terms. Let’s do that.

We have to first decide what interest rate to use for discounting.  Let’s use the long term average inflation rate, say, 7%.  The Net Present Values of the cash inflows on Bond A will be: (25,000 / (1.07)) + (45,000 / (1.07)^2) + (50,000 x (1.07)^3) = 103,484.

Bond B works out to: (0 / (1.07)) + (30,000 / (1.07)^2) + (95,000 / (1.07)^3) = 103,752

Bond B is better when you discount the cash flows to the present, but only marginally so.

What happens if we use 12% for the discounting?  Net Present Value (NPV) of Bond A works out to 93,784 and of Bond B works out to 91,535.  Bond A looks better! A change in the discounting factor could impact these calculations!  In this case, Bond B’s cashflows are backended and an increase in the discounting rate tends to decrease the values of cash flows which are farther in the future. Intuitively, you can understand why it is so. If inflation is higher, for example, your appetite for accepting the same promised return in future would be considerably diminished. Decision on which discounting factor to apply is critical in such situations – we may revisit this at a later point in time.

That’s a lot of math!  It is very important to understand how compounding works, and the impact of time on the value of money.  Hence the diversion in this issue.  A revision course in sixth and seventh standard math will help!

Bye.  Till we meet next.

Dinesh Gopalan
Fidelity India Finance
Bangalore
mobile: 9845257313