TIME VALUE OF MONEY
A farm manager has to take decisions over varying horizons of time. Two
aspects of such decisions are important, i.e., i) differences in profitability growing
out of time alone and ii) differences in the desirability of investments due to risk
and uncertainty factors. Time has a very significant influence on costs and returns.
There are many decisions where this time comparison principle finds application,
such as: soil conservation programmes which bear fruits over a long time; putting
land under an orchard which may not give returns for 5-10 years; and so on. Two
aspects of the problem are considered under such situations: a) growth of a cash
outlay over time and b) discounting of future income.
Growth of a Cash Outlay or Compounding Present Costs
The cash outlay grows over time due to the compounding of interest charges or
opportunity costs involved in using the capital; if Rs.100 are put in a saving account with an
annual interest at 12 per cent compounded, it will increase to Rs.125.44 by the end of second
year. In symbolic terms, you now have the amount earned at the end of the first year. P + Pi,
plus the interest that amount earned during the second year (P + Pi) i which could be expressed
as: (P + Pi) + (P + Pi) i (or) P (1 + i) + Pi (1 + i) which after factorising (1 + i), results in
Compounding the Present Value
(Amount in Rs.)
Year Beginnin Interest Earned by Beginning Amount
g Amount the End of Year + Interest
1 100.00 100.00(0.12)=12.00 112.00
2 112.00 112.00(0.12)=13.44 125.44
3 125.44 125.44(0.12)=15.05 140.49
4 140.49 140.49(0.12)=16.86 157.35
5 157.35 157.35(0.12)=18.88 176.23
(P + Pi) (1 + i). Factorizing P from the left term gives: P (1 + i) (1 + i) = P (1 + i)2. In general, the
compounded value, F (future value), of a present sum (P) invested at an annual interest rate (i)
for ‘n’ years is given by F = P (1 + i)n .This procedure is called compounding.
Discounting Future Revenues
Costs incurred at one point of time cannot be compared with validity to revenues
forthcoming at a later date. The future value of the present sum is estimated
through: F = P(1 + i) n . Dividing both sides of this equation by (1 + i) n , the following
equation is obtained:
A farm manager has to take decisions over varying horizons of time. Two
aspects of such decisions are important, i.e., i) differences in profitability growing
out of time alone and ii) differences in the desirability of investments due to risk
and uncertainty factors. Time has a very significant influence on costs and returns.
There are many decisions where this time comparison principle finds application,
such as: soil conservation programmes which bear fruits over a long time; putting
land under an orchard which may not give returns for 5-10 years; and so on. Two
aspects of the problem are considered under such situations: a) growth of a cash
outlay over time and b) discounting of future income.
Growth of a Cash Outlay or Compounding Present Costs
The cash outlay grows over time due to the compounding of interest charges or
opportunity costs involved in using the capital; if Rs.100 are put in a saving account with an
annual interest at 12 per cent compounded, it will increase to Rs.125.44 by the end of second
year. In symbolic terms, you now have the amount earned at the end of the first year. P + Pi,
plus the interest that amount earned during the second year (P + Pi) i which could be expressed
as: (P + Pi) + (P + Pi) i (or) P (1 + i) + Pi (1 + i) which after factorising (1 + i), results in
Compounding the Present Value
(Amount in Rs.)
Year Beginnin Interest Earned by Beginning Amount
g Amount the End of Year + Interest
1 100.00 100.00(0.12)=12.00 112.00
2 112.00 112.00(0.12)=13.44 125.44
3 125.44 125.44(0.12)=15.05 140.49
4 140.49 140.49(0.12)=16.86 157.35
5 157.35 157.35(0.12)=18.88 176.23
(P + Pi) (1 + i). Factorizing P from the left term gives: P (1 + i) (1 + i) = P (1 + i)2. In general, the
compounded value, F (future value), of a present sum (P) invested at an annual interest rate (i)
for ‘n’ years is given by F = P (1 + i)n .This procedure is called compounding.
Discounting Future Revenues
Costs incurred at one point of time cannot be compared with validity to revenues
forthcoming at a later date. The future value of the present sum is estimated
through: F = P(1 + i) n . Dividing both sides of this equation by (1 + i) n , the following
equation is obtained:
