# Present Value

So far we have been finding out the future value of money, by adding interest.

The reverse process, of finding the present value of a sum of money to be received in future, implies discounting the fund flows to the extent of the interest rate.

The assumption is that a sum of money received today has more value than a similar sum sometime in the future.

We can discount the money by doing the reverse of what we do in compound interest.

We know that A = P (1 + R/100)^{n}.

So Present Value (PV) of a sum A due after n years = A/(1 + R/100)^{n}

**Illustration:**

What is the present value of a property which would be valued at Rs 2 lakh at the end of 2 years, the rate of interest being 5% compound?

(PV) of a sum A due after n years = A/(1 + R/100)^{n}

= 2/(1.05)^{2} = 1.81 lakhs

In the above illustration, the tendency of the student is to discount 2 lakhs by 5% twice. However, this would give the wrong answer.

In the case of simple interest, PV is easier to find, since we need to discount 2 lakh by 5% and multiply by 2.

# Depreciation

Assets depreciate with time. Accountants decrease the value of machinery and other assets by a fixed percentage every year. So if a machine is bought for Rs 1000, its value after one year will be shown in the books as Rs 900, if the rate of depreciation is 10%. In the second year, the value will be shown as Rs 810.

Students will see that the depreciation is being compounded. Hence to calculate the written down value (WDV), we use the formula:

WDV = P(1 â€“ r/100)^{n}, where P is the initial purchase price and n is the number of years.