Investing Basics

Lessons in computing returns – V The Rule of 72

Hi ,

So we were playing some  games with percentages in the last few posts.

In this article, let me introduce a short cut – an approximately 500 year old formulae to help you in your calculations- Rule 72.

For those who love math and accountancy, the rule 72 may not be new. Luca Pacioli (1445–1514) , in his book ‘summa de arithematica’ discusses the rule when he talks about the estimation of the doubling time of an investment. However, it’s not Pacioli who invented this rule.

RULE 72

The rule is very simple – Divide 72 by the Interest Rate. What do you get?

You get the number of years it would take for your investment to Double. Practical, very simple. The Rule of 72 is not absolutely precise, but it gives you a practical estimate that you can work out in your head.

Example 1.

You go into a bank that offers 9.50% annual interest on your FD. How many years will it take for your capital to double?

It’s Simple- Divide 72 by 9.50. Roughly 7 and half years.

Example 2.

At what rate should you invest to double your money in 5 years?

Divide 72 / 5 . The answer is 14.40%. so if you can manage to get 14.40% return on your investment, your money doubles in 5 years.

Example 3.

The rate of interest you pay for your credit cards is 24%. Your credit card liability is Rs 25,000. What happens if you keep paying your minimum due for 3 years?

In 3 years (72/24), you end up paying Rs 25,000 as interest alone. You’ll still have the Rs 25,000 liability remaining.

Example 4

You read from papers that the country’s GDP grows at 7% a year. How long would it take the economy to double it’s growth?

The answer is (72/7) 10 and 3 months approximately.

Example 5.

The inflation rates are at 9%. What the effect of it on your money?

Your money will lose half its value in 8 years ( 72/9)

Example 6

At 8% interest your money would double in (72/8) 9 years. If you decide to remain invested for 27 years, a small deposit of Rs 50,000 would become Rs 400,000!

Not only in years, can you apply this rule in any time frame.

So that’s Rule 72. Nice little mathematical formula that helps you to take financial decisions. The rule is not perfect and it does not account for taxes.

Till my next post …..

……..Have a nice day!

3 Comments

Lessons in computing returns – IV Returns from shares.

Hi there,

In the case of shares, there are two types of returns you expect –

  • Dividends
  • Capital appreciation

How would you compute returns in such cases? let’s discuss with two examples.

Example 1

You invest in 1000 shares of AB Ltd for Rs 100,000 a year back.  At the year end, the shares are quoted at Rs 150 and the company also pays you a dividend of Rs 2 per share. That is, you get Rs 2000 as dividend, and at the same time, you investment is now Rs 150,000. You sell the share.

How would you compute your overall return from this investment?

The gain you made is as follows –

  • Appreciation in market price – Rs 50
  • Dividend received – Rs 2
  • Total gain – Rs 52
  • Return = Rs 52 / Rs 100 = 52%

Example 2

You invest in 1000 shares of AB Ltd for Rs 100,000. You hold on to it for 3 years. The dividends paid during these 3 years are follows- Rs 2, Rs 2.50 and Rs 3. The market prices at the end of each year are – Rs 90, Rs 95 and Rs 110.

How would you compute your yearly return from this investment?

  • The cost per share at the point of investment was Rs 100
  • Fist year return would be – fall in market price Rs 10, dividend paid Rs 2
  • Therefore, net loss = Rs 8
  • Return = -8 / 100 * 100 = loss of 8%

Second year

  • The cost of share at the end of first year = Rs 90
  • Year end price = Rs 95 , dividend paid = Rs 2.50
  • Therefore , net gain = Rs 7.50 ( 95-90 + 2.50)
  • Return = 7.50 / 90 * 100 = 8.33%

Third year

  • The cost of share at the end of second year = Rs 95
  • Year end price = Rs 110 , dividend paid = Rs 3
  • Therefore , net gain = Rs 18 ( Rs 110-95 + 3)
  • Return = Rs 18/ 95 * 100 = 18.94%

Overall return from investment would be = (-8%) + 8.33% + 18.94% = 19.27%

So, while computing yearly returns from investment, you should consider capital appreciation or depreciation (although it’s notional) and also the dividends received.

Bye for now,

Have a nice day !!

0 Comments

Lessons in computing returns – III Compounded returns.

Hi 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 five-year 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 !!

2 Comments

Lessons in computing returns – II Simple returns

SIMPLE RETURNS:

Simple returns are used for evaluating short term returns.

BASICS FIRST:

The formula for computing simple returns is

Simple Return = FV  / P  - 1

Where,

  • FV is the amount received on maturity date and
  • P is the amount invested

Example 1

You deposit Rs 10,000 in a bank for a year and gets Rs 11000 in return. The simple return would be –

  • 11,000 / 10,000 – 1 = 0.1 or 10%

Example 2

You purchased 200 shares of ABC Company at 50 per share. You paid Rs 300 as commission to your broker. On a later date, you sell the stock for Rs 75 and pay a commission of Rs 450 to the broker. What is the simple return on investment?

Total cost of the share = number of shares x rate + commission paid = Rs 10,300

Sale proceeds = number of shares x rate – commission paid =Rs  14550

So, the simple return will be as follows:

  • 14550 / 10300 -1
  • 1.41 – 1 = .41 or 41%

Example 3

You purchased 200 shares of DEF Company at 50 per share. You paid Rs 300 as commission to your broker. On a later date the company declares dividend of Rs 2 per share. You sell the stock for Rs 75 and pay a commission of Rs 450 to the broker. What is the simple return on investment?

The simple return will be as follows:

Total cost = 10,300

Total returns = 14,550 + 400 = 14, 950

Simple returns would be

  • 14950 / 10,300 – 1
  • 1.45 – 1 = 0.45 or 45%

That’s about simple returns. Remember, simple returns are useful only for short term investments.

Till my next post…

….. Have a nice day !!

2 Comments