Untitled-29

Cost of Capital^41

If you can invest the amount at 5% per annum compounded annually what will be the
amount you would require today to land up with the same position?

Solution

Here i = 0.05, A = 7000, and n = 20. Putting it in the formula we get:

Using the shortcut from the table we get:













+

+ -

= 20

20

0. 05 ( 1 0. 05 )

[( 1 0. 05 ) 1 ]

PresentValue 7000

PV = 7000 x 12.4622 = Rs 87,235.4

We looked at the present value of an annuity of Rs 1 for 20 years at 5% interest in the
Present Value Annuity Factor Table given at the end of this book (i.e. find the value of
Present Value Annuity Factor n,i)and found the figure to be 12.4622 (try finding the
figure yourself) and then substituted the figure here to get the answer. Another way of
doing it would be to use a scientific calculator and calculate the value that comes out to
be the same.

Let us see how we use Microsoft Excel to do the same. Insert the values as given in
the example. Here r = I = 0.05, Nper is the number of periods = 20, Pmt is the periodic
annuity = 7000 in this case. Fv is the future value = 0 in this case as it is an annuity and
Type is a value representing the timing of the payment = 0 in this case as the first
investment is done at the end of the period 1. Putting these values we get the following
screen.

Can you find the answer? Yes, it is Rs 87,235.47 a difference of Rs 0.07 from the
answer we got using the table above.

A variation on this would be that the payment made at the start of the period instead of
the end of the period. This means that you earn extra interest for one year. The formula
is slightly different in that the whole value is multiplied by (1+i) resulting in the following
formula: