• Many farm decisions involve time.
• A farmer has to decide whether to purchase new farm machinery with 10 years of life or a second hand one which may have only five years of life.
• Several other decisions involving time and initial capital investment could be judiciously taken by compounding or discounting.

a) Future value of a present sum:

• The future value of money refers to the value of an investment at a specified date in the future.
• This concept assumes that investment will earn interest which is reinvested at the end of each time period to also earn interest.
• The procedure for determining the future value of present sum is called compounding.
• The formula to find the future value of present sum in given below

FV = P (1 + i)n

where,

FV = Future value;

P = the present sum,

i = the interest rate,

n = the number of years.

Example:

Assume you have invested Rs. 100 in a savings account which earns 8% interest compounded annually and would like to know the future value of this investment after 3 years.

• In the example, a present sum of Rs. 100 has a future value of Rs. 125.97 when invested at 8 per cent interest for 3 years.
• Interest is compounded when accumulated interest also earns future interest.

b) Present value of future sum:

• Present value of future sum refers to the current value of sum of money to be received in the future.
• The procedure to find the present value of future sum is called discounting.
• The equation for finding the present value of future sum is

PV = FV/ (1+ i)n

where,

PV = Present value

FV = Future sum

i = rate of interest

n = number of years.

Examples

Example: A farmer wants to purchase a tractor. The alternatives are,

1. Purchase a new tractor for Rs. 25000/- that will last 10 years.
2. Purchase an old tractor for Rs. 15000/- and replace it after 5 years with another old tractor worth Rs. 15000/-. This means that he shall have to invest Rs. 15000/- now and lay aside an amount which will become Rs. 15000/- within 5 years to replace the old tractor.

A) Farmer with unlimited capital has the opportunity of lending the money at usual interest rate, say 5%.

PV= 15000/(1+0.05)5 = Rs. 11,760

His comparison is Rs. 25000/- for new tractor and Rs. 15000/- plus Rs.11,760/- (Rs. 26760/-) for old tractor. The new tractor is profitable for the farmer with unlimited capital.

B) Farmer with limited capital has an opportunity of investing money in poultry and can make a return of 15 % within the year. His discounting rate will be 15% i.e., opportunity cost of not using money in bank and investing in poultry.

PV= 15000/(1+0.15)5

= Rs. 7,455

His comparison is Rs. 25000/- for new tractor and Rs. 15000/- plus Rs. 7455/- (Rs. 22455/-) for old tractor. The old tractor is profitable for farmer with limited capital.