Lessons in computing returns – III Compounded returns.
by J Victor on August 1st, 2010Hi there,
Let’s catch up with compound interest in this article..
BASICS FIRST.
The formula for compound return is as follows:
 ^{· }FV = P ( 1+ r) ^{n }
 Where FV is the future value
 P is the money invested
 r is the rate of return
 n is the number of years for which the amount is deposited.
Situation1.
You invest Rs 50,000 today and it grows to Rs 100,000 in five years. The fiveyear return is 100 per cent; but what is its annual return?
To calculate this, you need the formula on compound interest. Using Rs 50,000 as principal, Rs 100,000 as future value and five as the number of years, let’s find out the annual rate.
 FV = P (1+r) ^{n}
 Therefore, r = (FV/P) ^{1/n} – 1
 Here, the first step is to calculate 1/n = 1/5 = 0.20
 Now, r = (50000/ 100000 ) ^{.2} ^{0} 1
 r = 2 ^{.20} 1
 2 ^{.20} = 1.1487
 1.1487 1 = 0.1487
 Therefore r as a percentage would be (0.1487 * 100 ) = 14.87 %
This 14.87 per cent is the compound return, and is the only relevant return when you analyze an investment.
If you divide the 100 percent by the number of years, you get the answer as 20%.This is the simple return.
The 100 per cent is referred to as holding period return. The holding period return keep on changing with the period of holding.
That brings us to the first moral of computing long term return. compounded returns is the best measure for long term return.
You can also use the rule 72 discussed elsewhere and arrive at the approximate rate of return since in this question, the investment has doubled in 5 years.
Situation 2.
Suppose you want to make an estimate of future rate of return of a stock. One way of doing so, is to look at the past rate of return as an indicator of the future. Here’s how the return is computed in this case.
Consider a stock, A Ltd, whose return during each of the last five years has been 10 per cent, 20 per cent, 15 per cent, minus 30 per cent and 20 per cent per annum. Hence its simple average is 7 per cent per annum. Consider another stock, B Ltd, whose return during the last five years has been 10 per cent, 15 per cent, 20 per cent, 10 per cent and minus 20 per cent. Its simple average return too is 7 per cent per annum. So should we say that they are identical performers? Surprisingly, the answer is ‘No’. Here’s why.
If the stock price of A Ltd began at Rs 100, it would have grown to
 Rs 110 ( 100 * 110%) in the first year
 Rs 132 (110 * 120% ) in the second year
 Rs 151.80 ( 132 * 115% ) in the third year
 Rs 106.26 (151.80 * 70%) in the forth year (the company grew at 30%)
 Rs 127.51 (106.26 * 120%) in the final year.
Rs 100 growing to Rs 127.51 is a compounded rate (CARG) of 4.98 per cent using the compound interest rate formula.
Similarly Y Ltd, which began at Rs 100 at the beginning of the first year, would have sequentially grown to Rs 110, Rs 126.5, Rs 151.8, Rs 166.98 and Rs 133.54 at the end of each of the five years. Rs 100 growing to Rs 133.58 is a compounded rate of 5.96 per cent.
See the difference in the compounded rate. Yet the simple average of the growth rate was same.
Clearly, Rs 100 growing to Rs 127.51 is not the same as Rs 100 growing to Rs 133.58. So, compounded annual growth is considered the right measure of return;
The simple average is used for purposes of year on year measurement or short term measurement of returns.
Till my next post …
……. have a nice day !!
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2 Responses to “Lessons in computing returns – III Compounded returns.”
prashanth
February 4, 2013 at 8:50 pm
hi victor i have a major doubt , you were talking about inflation and how it affects the return on investments.i have seen many finance companies who borrow bulk from major banks and lend it to public at higher rates. like for example say a company like magma fincorp ltd or tata capital borrow huge funds approximately at around 6.5% and lend it to public and around 11 to 12% after broker commision.how does this make a business sense because the margin is around 5 to 6% infrastructure costssalaries which is very thin. keeping the inflation rate at around 8% actual profits will be in the negative, isn;t it. can u explian this?
prashanth
February 4, 2013 at 8:52 pm
also why would a bank lend money at 6% when the inflation rate is around 8%.