A Bit About Time Value of Money

Ever wondered how the value of money grows when invested and falls when not invested? Here comes the concept of time value of money. A rupee today is more valuable than a rupee a year after. This is so because, in such an inflationary period a rupee today represents a greater real purchasing power than a rupee a year after. Also rupee earned today can be employed productively to generate positive returns. 
Let us see this by a simple illustration - 

Assuming a 5% interest rate, Rs. 100 invested today will be worth Rs. 105 in one year (Rs100 multiplied by 1.05).  Conversely, Rs100 received one year from now is only worth Rs. 95.24 today (Rs100 divided by 1.05), assuming a 5% interest rate.
This is how your money grows when invested and degrades when not invested. Now when it is invested, see the difference of earning between interest earned on simple interest method and that earned on compound interest method.

To make it simpler see the diagram

The money earned in future has less value (which is interest factor ) as compared to the money earned today (which can be invested to earn interest on it.

Example:
Mr. Sharukh Khan invested Rs.1000 for Three years in a savings account that pays 10% interest p.a. Mr. Khan Reinvests the 22 interest earned. What would be the total amount after three years?

Compound Interest					Simple Interest
Principal	1000
Interest	10%
	Year	Interest	Corpus		Interest	Corpus
	1	100	1100		100	1100
	2	110	1210		100	1200
	3	121	1331		100	1300

Here you clearly see the difference of earnings. Compounding maximizes your return by making interest portion also participate in growth of money.
Now what about the constant cash flow you receive will change. Here comes the concept of annuity.
An Annuity is a stream of Constant Cash Flow (payment or receipt) occurring at regular intervals of time.

E.g. EMI payment, Payment of life insurance premium
Two types of annuity
1. Deferred annuity / Ordinary Annuity / Regular Annuity - When Cash Flows occur at the end of each Period.
2. Annuity due - When the Cash Flow occur at the beginning of each period.
Example-
1. Deferred Annuity
Mr. Gates deposited Rs. 1000 annually at the end of the year in a bank for 5 years & earns a compound Interest rate of 10% p.a. What will be the value of the deposit after 5 Years ?

N	5
I	0.1
Amount invested	1000
	year	Interest	Value
	1	100	1000
	2	210	2100
	3	331	3310
	4	464.1	4641
	5	610.51	6105.1

2. Annuity due-
Mr. Gates deposited Rs. 1000 annually at the beginning of the year in a bank for 5 years & earns a compound Interest rate of 10% p.a. What will be the value of the deposit after 5 Years?

N	5
I	0.1
Amount invested	1000
	year	Interest	Value
	0	100	1100
	1	210	2310
	2	331	3641
	3	464.1	5105.1
	4	610.51	6715.61

This concludes that it is always better if you receive your annuity at the beginning of the year so as to maximize your returns.
Here arise some concepts-

Present value - It is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money.

Future value is the value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today.

E.g. You have to lend Rs 1,00,000 to one of your friends and He is offering you following choices .
Choice 1 : He will pay you Rs 18,000 per year for next 10 yrs .
Choice 2 : He will pay you 13,000 per year for next 15 yrs .
Choice 3 : He will pay you Rs 8,000 per year for whole life .

Which One should you choose?
You have to see that which choice has the highest worth if you calculate its Value today . So how do you calculate the Net Present Value in this case , where you have Rs X receivable every year for n years . Here you also have to consider present rate of returns which you can assume at 8% .

So We have 3 variables
X : Amount received per year
n : Number of years
r : Present rate of return
NPV = X * [(1+r)^n - 1]/[r * (1+r)^n]
Calculating through this formula , we get the NPV of the choices as
1. 120781
2. 111273
3. 100000

Net Present Value of the last choice is simple , how much money do you put in bank today that will fetch you 8,000 per year forever ? If X is the amount than at 8% interest you get 8,000 , so

8% of X = 8,000
.08 * X = 8,000
X = 8,000 * (1/.08)
X = 1,00,000

If you see the total amount received in all the cases you will realise that the choices with lesser NPV will give you have higher Total amount .

For Case 1 : NPV = 120781 , Total amount received = 1,80,000
For Case 2 : NPV = 111273 , Total amount received = 1,95,000
For Case 3 : NPV = 100000 , Total amount received = Infinite (The amount is paid forever)

The present value of the 3^rd option is less so it is better option. So we see the lowest present value for our future cash flows gives us maximum return of money.

Future value -
You can afford to put Rs. 10,000 in a savings account today that pays 6% interest compounded annually.   How much will you have 5 years from now if you make no withdrawals?
PV = 10,000
i = .06
n = 5
FV = 10,000 (1 + .06)⁵ =  10,000 (1.338) = 13,382  

End of Year	1	2	3	4	5
Principal	10,000	10,600	11,236	11,910	12,624
Interest	600	636	674	714	757
Total	10,600	11,236	11,910	12,624	13,382

Thus we conclude that Rs. 13382 received after 5 years is equivalent to Rs. 10000 invested today.

Thus to conclude time value of money has greater significance to determine how much your money is worth. So before investing do the necessary calculation and achieve the maximum from your portfolio.