Time Value of Money

This is to start a series of tutorials, with the aim to help the reader build a strong understanding of the complex financial world. To start, let's try to understand the time value concept of money.

Prerequisites :

Concept of compounding

Given two examples of future income, how can one tell, which of the two is better ?

Say, you won a lottery, but given the choice of,

Option A : Receiving $ 100 after 2 years
or
Option B : Receiving $ 110 after 4 years

We also have following assumptions -

1. There is no risk of whether or not you will receive the amount.
2. No inflation for the given time period.

Given that, your task is to choose the better option. Let's see.

Suppose you have a Bank that gives an interest rate of 1 % per annum. We'll compute, how much invested today, would fetch you $ 100 after 2 years, and $ 110 after 4 years [For the formula, see Concept of compounding].

For option A : 100 / (1.01) ** 2 = $ 98.03

For option B : 110 / (1.01) ** 4 = $ 105.70

As you can see, if you choose option B (i.e., receiving $ 110 after 4 years), it's equivalent to having 105.70 dollars in your hand today, and is definitely better than having $ 98.03 (Option A).

Now, instead of 1 %, what if the interest rate in your bank is 10 % per annum. Let's again compute how much each of these are worth today.

Option A : 100 / (1.1) ** 2 = $ 82.64

Option B : 110 / (1.1) ** 4 = $ 75.13

Definitely, option A is better in such a scenario.

There are two relations that we need understand from this small example and which are extremely important in the study of finance.

1. If the prevailing interest rates are high, it means a future cash flow is less significant today. And the vice versa, that if the prevailing interest rates are low, a future cash flow can be much more significant.

Take option A alone, and note how the present value of the investment diminished when the interest rates rose from 1 % to 10 %. Same is the case with option B.

Mathematically, this is the same inverse relation of Present value and discount rate.

2. A cash flow from the far future is more sensitive to interest rates than a cash flow from the near future.

In the above example, as a result of interest rate change from 1% to 10%, the value of the cash flow after 4 years (Option B), diminished much more than it did for the 2 years option.

This relation is due to the multiplication effect of the time factor in the Present Value formula.

Most of the real world financial instruments, such as bonds, mortgage loans and insurance have to do with a series of such future cash flows. In the next section, we'll cover the Net Present Value of a series of future cash flows.