Time Value of Money, Part-9

If Mr. A is earning 12% rate of return and inflation for the same period happened to be 8%. The real rate of return earned by him is..

Let’s first of all understand the concept of real rate.

Real rate is the adjusted rate. This adjustment can done with any rate say for example an automobile company’s sales has grown by 10% and the price rise during the year is 5%. The real growth in the sales of the company is

Real growth is [(1+0.10)/(1+0.05)]-1 = 4.76%

The equation above which we have used is Fisher’s equation.

In the case of Mr. A the answer is

[(1.12)/(1.08)] – 1 = 3.70%.

Hence we can say that Mr. A has earned 3.70% in terms of purchasing power even though the total rate of 12%.

 The concept of real rate is useful for financial planning while doing the retirement planning especially at the withdrawal stage.

Now let’s take up some of the miscellaneous approaches for time value

First is rule of 72

If Mr. earns 12% rate of return, within how many years his money will get doubles

Equation: 72/r

Where r= rate of interest

Answer: 72/0.12 = 6 years

 Second is rule of 69

Equation: 0.35 + (69/r)

If we find the doubling period using previous question, the same will be

Answer: 0.35 + (69/.12) = 6.1 years.

Rule of 72 and 69 both are the approximation methods however rule of 69 gives better approximation.

Important: Both the methods assume compound interest.

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Time Value of Money, Part-8

Let say Mr. A wants to arrange money for his children forever. Will time value of money be useful to understand such arrangement?

Yes definitely. The concept which we are talking about is ‘Perpetuity’. Let’s understand with an example.

Mr. A has Rs.10 lakh with him and wants to give some money to his children every year at the end of year. If rate of return which he can earn is 10%, what amount of money he can give to his children?

1000000 × 0.10 = Rs.1,00,000 forever, if rate of return is constant at 10%.

 Mr. A wants Rs.1 lakh forever. Rate of return is 12%, what amount of money he is required to invest now?

 This is the question of present value of perpetuity.

PV = 100000/0.12

Answer: Rs.8,33,333

 Mr. A wants Rs.1 lakh forever from today. Rate of return is 12%, what amount of money he is required to invest now?

This is the question of present value of perpetuity due.

PV = (100000/0.12) × 1.12

Answer: Rs.9,33,333

Alternatively you can find the PV of perpetuity in normal way and can add up the required money today. Say 8,33,333+1,00,000 = Rs.9,33,333.

 Mr. A wants Rs.1 lakh forever at an interval of every two years. Rate of return is 12%, what amount of money he is required to invest now?

We require the compound rate for two years. i.e. (1.12)² – 1 = 25.44%

PV = 100000/0.2544

Answer: Rs.3,93,082

Now let’s take up a challenge question

Mr. A requires Rs.2 lakh forever at an interval of every three years. First withdrawal is after 1 year from today. Rate of return is 9% per annum. The amount of money to be invested today for the same is…..

Answer: Keep trying… All the best!

 Note: Answer will be published in the coming posts.