Basics of Discounting

Before we try to understand the concept of discounting, we need to be clear of our understanding of the basics of Simple Interest ( SI) and Compound Interest (CI). 

1.        Simple Interest –

If I have a sum of Rs. 100 and I invest it in a bank @10% p.a. SI, the amount that I get in a year’s time will be calculated using the formula :

SI = P*R*T/100

Where:

P = Principal or Original Amount Invested

R = Rate of Interest

T= Time period for which investment is made

Putting figures into the equation :

SI = 100*10*1/100

SI = Rs. 10

Total Amount received after one year = P + SI

                                                         =100 + 10

                                                         =Rs. 110

SI assumes that the interest received (i.e.  Rs. 10) is not re-invested. That means if the interest is paid half yearly, then the interest that will be earned for the period of 1^st January till 30^th June (Rs. 5) will not be re-invested for the next 6 months. It means the principal (Rs. 100) will remain same for the entire year. Interest earned for the period 1^st July till 31^st December will be Rs. 5 only.

1.        Compound Interest –

Now imagine a situation where a student deposits Rs. 100 in his account on 1^st January and receives 10% p.a. SI, which is credited in his account on 31st December of each year. If the interest is paid half yearly, the interest earned for the period 1^st January to 30^th June (i.e. Rs. 5) will be reinvested for the next 6 months. That means, form 1^st January till 30^th June the Principal would be Rs. 100, whereas, for the period of 1^st July till 31^st December the principal would be Rs. 105 i.e. (100 + 5). That means, now he is earning interest not only on original principal (Rs. 100) but also on Interest earned during the year  (Rs. 5). This is known as compounding effect and is given by the formula :

A= P*(1+r/100)^t

Where :

A = Amount received on maturity

P = Amount invested

R = Rate of interest

T = time for period which is P is invested

Putting figures in the equation we get:

A= 100*(1+10/2/100)^1*2

A= Rs. 110.25

Please note that while compounding, the rate of interest remains same for the entire time period. Also, since interest is paid half yearly, the rate is halved whereas the time is doubled in the above formula.

1.      Discounting – Now that we have learned the basic concept of SI and CI, let us move a bit further to understand the concept of discounting. For that lets re –write the CI formula. 

A= P*(1+r/100)^t

We can say that “A” is the amount I will receive in future if I deposit “P” amount today at “r” rate of interest for “t” time period.

If I Know my future value (A) & I want to know how much should I invest today to get that, I just need to re – arrange my formula as:

P = A/(1+r/100)^t

The above formula is the backbone of the concept of discounting. The factor

1/ (1+r/100)^t  is known as discounting factor and “r” is known as discounting rate.

Thus, we can say discounting is reverse of compounding. In compounding we calculate the Future value keeping the interest rate constant, whereas in discounting we calculate the Present value keeping the interest rate constant.

A question  that might cross your mind is how do we know the future value? Well, in discounting that might not be necessarily the known value. But we definitely know the future cash flows. For example, in case of a bond, we know the quantum and timing of the interest that will be received. Also, we know that on maturity the face value of the bond will be paid. So we can discount today all the interest that will be received during the life of bond as well as the maturity value. What we get is the Present value of the bond. We compare that present value with the value at which bond is trading and determine whether the bond is fairly priced, overvalued or undervalued? Accordingly we take the decisions. 

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