Corporate Finance

Time Value of Money 
 45

An Illustration

Suppose you are pursuing an MBA program: the second year fee is Rs 45,000, and is not expected to change.
The interest rate is 10 percent.

Present Value = [45000/(1.10)] = Rs 40909

Now, try discounting Rs 1,000 available 5 years from now at 8 percent.

Present Value = [1000/(1 + 0.18)^5 ] = Rs 681

The value of [1/(1 + r)n] for various combinations of r and n is given in the Present Value Interest Factor
Table (Table A.3 at the end of this book). A section of the same is reproduced in Exhibit 2.2.

Exhibit 2.2 Present value interest factor

PV of Re 1 to be received after n years = [1/(1 + r)n]

Interest rate r (percent)
Year (n)8 9 10 11 12

1 0.926 0.917 0.909 0.901 0.893

2 0.857 0.842 0.826 0.812 0.797

3 0.794 0.772 0.751 0.731 0.712

4 0.735 0.708 0.683 0.659 0.636

5 0.681 0.650 0.621 0.593 0.567

For given ‘t’: higher the discount rate, lower is the present value; and for a given ‘r’, longer the time
period, lower the present value. Given three terms out of PV, FV, r and a, the fourth could be found out
using equation 1. For example:
Rs 5,000 invested in a savings scheme grows to Rs 10,000 in 6 years.

The implicit interest rate, r = (10000/5000)1/6 – 1 = 0.122 = 12.2 percent

Future Value of a Series

So far, we found the present or future value of a single amount at some interest rate and time period. Consider
the following situation:
You invest Rs 500 today, Rs 1,000 at the end of the 1st year, and Rs 1,500 at the end of the 2nd year.
You have to find the future value at the end of the 2nd year; assuming 8 percent interest. The future value of
this series is nothing but the sum of the future values of each cash flow:

Future Value = FV of Rs 500 + FV of Rs 1000 + 1500

Note that 1500 itself is the future value of cash flow occurring at the end of the 2nd year.

FV = 500 (1.08)^2 + 1000(1.08) + 1500

= 500 × FVIF8, 2 + 1000 × FVIV8, 1 + 1500

= Rs 3163