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 !!

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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 !!

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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 !!

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Lessons in computing returns – I Percentages

Hi there,

Most of the financial calculations are expressed in percentages. Not only profits, there are many other places where this knowledge can be very useful. Let’s catch up with it:

PERCENTAGE POINTS

A percentage point = 1%

Example

You go to a bank to open a fixed deposit account. The bank says, interest rates have gone up from 8% to 10%. How much is the increase? Is it a 2% rise?

The answer is No. An 8% to 10% rise is 25% rise in interest rates. This is how we calculate it:

  • 10 / 8  = 1.25
  • 1.25 * 100 = 125% or 25 % increase in interest rates.

Another way to ay it correctly is – you can say that the interest rates have increased by ‘2 percentage points’.

In financial markets, Instead of percentage points, the term used is ‘basis points’. 1 basis point is equal to 1 / 100th of a percentage point.

  • 1 basis point = 1/ 100th of a percentage point
  • So, 100 basis points = 1 percentage points.

Next time , when the Reserve bank revises the interest rate by ’25 basis points’ , understand that what the bank means Is that it has revised the interest rates by 0.25%

Here are some questions for you to try out-

  1. A bank is offering a 30% increase in the interest rates on fixed deposit. The old rate is 6%. What is the new rate?
  2. You see an advertisement in paper saying that loan rates have slashed from 12% to 10%. What is the actual drop in loan rates?
  3. The RBI increases rates by 25 basis points. If the old interest rate was 6%, what is the new rate?
  4. A bank cuts interest rates by 125 basis points for the 2rd consecutive month. If the interest is 8 % now, what was the interest 2 months back?
  5. The fixed deposit interest rate has gone up from 8% to 10%. What is the rate of increase in percentage and in percentage points?

Answers:

  • 1. The old rate is 6%. The increase is 30%. So, the increase in rate is 6* 30% = 1.8%. The new rate would be 7.8%
  • 2. The loan rates have been slashed fro 12 % to 10%. The decrease in rate is 2 percentage points or 200 basis points or 16.66%
  • 3. The new interest rate would be 6.25%
  • 4. The present interest rate is 8%. So, last month the interest rate was 9.25% therefore, 2 months back, the interest rate was 10.50%.
  • 5.  Increase in terms of percentage points = 2 and increase in terms of percentage is 25%

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