All of us must have learnt about compounding and its significance sometime in school. However, recently, we came across an interesting story which explained the power of compounding wonderfully. Here it is…
Once upon a time there was a king known for his generosity and keeping his word. A famous and intelligent prisoner was awaiting his death sentence and was brought in front of the king. The king was playing chess when the prisoner was brought in front of him. Here’s the dialogue that followed.
King: What is your last wish?
Prisoner: Your Majesty, I wish to make provisions for my family to survive after my death.
King: Well! Tell me what you want.
Prisoner: Give me the number of grains of rice on the last square of the chess board, if a single grain was kept on the first square and then doubled on every next square (1 on first, 2 on second, 4 on third, 8 on fourth, 16 on fifth and so on, till the 64th square), and I shall give it to my family before I die.
Prisoner: Give me the number of grains of rice on the last square of the chess board, if a single grain was kept on the first square and then doubled on every next square (1 on first, 2 on second, 4 on third, 8 on fourth, 16 on fifth and so on, till the 64th square), and I shall give it to my family before I die.
King: (thinking what a paltry demand the prisoner had made) Wish granted.
The king then ordered his ministers to have the amount of rice calculated and given to the prisoner. But he was in for a rude surprise. The amount calculated was so large that the king lost his entire kingdom and was indebted to the prisoner all his life.
So, what would the rice be worth today? We at MoneyWorks4me.com thought of playing with numbers and here’s what we found out.
Considering rice to be priced at Rs. 22.5 per kg ($500 per M ton) and every grain of rice to be of 20 mg, the rice that the prisoner got, would be worth a humongous Rs. 41,50,51,742 crore or just above $92 trillion.
With this he could easily buy the GDP of the entire world.
In fact, this figure was arrived at considering very conservative estimates and assuming that the prisoner was given the worst quality of edible rice. If he was given a little better quality of rice, he would have very well been in a position to afford both the global GDP and global market capitalization.
Had the king not underestimated the power of compounding, we would have missed a wonderful story.
Understanding compound growth:
Most of us have learnt about compound interest in our school. It is nothing but the effect of interest getting added to your capital, earning further interest. Take a look at the table below to understand the difference between simple and compound growth.
Thus in simple growth the base on which the investor earns remains the same whereas in compound growth the base increases with the amount earned in every cycle. Thus after five years the earnings in case of simple growth is 5,000 (50% of 10,000), whereas in case of compound growth the earnings are 6,105 (61% of 10000.)
The difference becomes more and more significant with larger periods as Simple growth is linear and compound growth is exponential.
Compounding does its wonders through two tools, compounding rate and the number of compounding cycles.
Compounding Rate:
Compounding rate is the percentage by which the Investment (rice in the above story) grows with every compounding cycle. In the above story the compounding rate was 100 percent. Though it is extremely difficult (impossible over long period) to get a compound growth of 100%, even a modest 15% to 20% rate can do wonders for us. In fact even a difference of 2% can add significantly to your wealth. Take a look at the table below to see the growth of a portfolio of Rs. 10000 growing at the respective rates.
Compounding Cycle:
Compounding cycle is a factor like time (or a square on chess board as in the story) in which the investment grows by the compounding rate. This period may be one day, one month, one quarter or any period. Generally one year is the most frequently used compounding period (CAGR).
For compounding to become attractive, it should be allowed to undergo sufficiently large number of compounding cycles. Just consider that the chess board was 7 x 7 instead of 8 x 8. This would give the prisoner 49 compounding cycles instead of 64 and reduce his worth to Rs. 12,666 crore or around $ 2.8 billion, sufficient to buy just a Mid-cap company. The latter compounding cycles contribute more to your wealth as the base on which your wealth compounds grows larger with each cycle.
When investing in stocks for the long term, we routinely hear the term CAGR which signifies the rate at which your investment grows every year. At MoneyWorks4me.com, we consider that when you invest in stocks, you should earn minimum 15% CAGR. The MRP (intrinsic worth) of a stock that we calculate is based on this assumption. We also say that to reduce your risk, you should always invest in a stock when it is at a 50% discount to its MRP. Doing this will in fact lead to a higher CAGR of greater than 20%. Have a look at the table given below to understand what you would earn if u were able to grow your investment of Rs. 10,000 with a CAGR of 10, 15 or 20 %.
From the above table we can clearly draw two inferences:
- A small percentage increase in the growth rate significantly increases the returns.
- The returns in the latter years are more impressive due to the higher base effect. Thus longer the period, more attractive the gains.
The famous Value Investor Warren Buffet grew Berkshire Hathaway Book value from $19 in 1965 to $95,453 in 2010(45yrears) with a CAGR of 20.2 %.
Over long periods Stocks give a CAGR of more than 15%. SENSEX has given a return of 17.8% CAGR since 1978-79 over a period of 32 years. By understanding and effectively applying the principles of value investing, an investor can definitely achieve a CAGR of above 20% over long periods.
