Present Value Approach
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Present Value Approach
A problem arises here before any investment decision can be taken. Supply price is the current cost of the asset, i.e., the cost which is to be incurred presently. Prospective yield is the future return on the asset. In other words, prospective yield is an ex-post may not be wise to compare the current cost with the future income. A comparison of the two will involve assuming that the value of one rupee five years hence is equivalent to its value today. It is essential, therefore, that we compare the current cost of the asset with the current value of the future income.
The current value of the future income will always be less than the future value of the future income, just as the present value of Rs. 100 in future will be less. In other words, we ought to know the present value of the future income, i.e., we ought to discount the future income.
Discounting requires the use of compound interest calculations in reverse that is, we known the amount and we have to find the principal amount. First, we explain the calculation of compound interest with the help of an example, then we will see how these calculations can be used ‘in reverse’ to get discounting of the future value.
Application of Compounding. Suppose, an individual has an initial amount, P0 to lend at the market rate of interest, i. If the individual lends his initial amount, P0 at the market rate of interest, i, he will have P1 at the end of one year, where P1 equals the intial amount (P0) plus the interest earned during the year iP0. In algebraic terms:
P1 = P0 + iP0 = P0 (1 + i)1
If the individual lends the amount P1 at the end of the first year for another year he will receive back at the end of the second year amount P2.
P2 = P1 + iP1 = P1 (1 + i)2
Since P1equals P0 (1 + i) in equation (1), we obtain, by substitution
P2 = P0 + (1 + i) (1 + i) = P0 ( + i)2
Thus, in general, if an individual lends and initial amount P0 for n years at the market rate of interest I, he will receive Pn amount at the end of n years,
Pn = P0 (1 + i)n
Table illustrates the total accumulation from an initial mount of Rs. 100 with interest at 5 per cent per annum.
The current value of the future income will always be less than the future value of the future income, just as the present value of Rs. 100 in future will be less. In other words, we ought to know the present value of the future income, i.e., we ought to discount the future income.
Discounting requires the use of compound interest calculations in reverse that is, we known the amount and we have to find the principal amount. First, we explain the calculation of compound interest with the help of an example, then we will see how these calculations can be used ‘in reverse’ to get discounting of the future value.
Application of Compounding. Suppose, an individual has an initial amount, P0 to lend at the market rate of interest, i. If the individual lends his initial amount, P0 at the market rate of interest, i, he will have P1 at the end of one year, where P1 equals the intial amount (P0) plus the interest earned during the year iP0. In algebraic terms:
P1 = P0 + iP0 = P0 (1 + i)1
If the individual lends the amount P1 at the end of the first year for another year he will receive back at the end of the second year amount P2.
P2 = P1 + iP1 = P1 (1 + i)2
Since P1equals P0 (1 + i) in equation (1), we obtain, by substitution
P2 = P0 + (1 + i) (1 + i) = P0 ( + i)2
Thus, in general, if an individual lends and initial amount P0 for n years at the market rate of interest I, he will receive Pn amount at the end of n years,
Pn = P0 (1 + i)n
Table illustrates the total accumulation from an initial mount of Rs. 100 with interest at 5 per cent per annum.
| Value of Rs. 100 a the end of year |
With i = 5 per cent |
or in general |
| 1 2 3 : : : |
Rs. 105 Rs. 110.25 Rs. 115.75 - - - Rs. 100 x (1.05)n |
Rs. 100 (1 +i) Rs. 100 (1+i)2 Rs. 100 (1 + i)3 - - - Rs. 100 (1 + i)n |
Application of Discounting. Now, with the help of equation (3) we can find of out the present value of income to be received after a certain period of time. Suppose that the individual is to receive Pn amount in n years and that he market rate of interest is i. Solving equation (3) for P0 the present value of future income equals Pn divided by (1+ i)n. In equation form :
P0 shown present value of Pn receivable in n years when the market rate of interest is i and is called the discounted present value.
Thus, in vernal, if an individual is to receive Pn amount in n years, he must discount the future income by applying equation (4) in order to determine its present value.
Similarly, we can find out the present value of any series of incomes receivable at future dates. We may calculate the present value of the income stream by discounting each portion of that series.
Thus, the present value of the income stream is the sum of the present values of each of its components. Using the symbol PV, to denote the discounted present value and R1, R2...Rn to show income stream receivable at the end of 1,2,...,n yeas, we can generalize the previous result into n periods.
PV = R1/(1+ i) + R2/ (1 + i)2... + Rn / (1 + i)n
The terms R1/ (1 + i), R2 / (1+ i)2,... + Rn / (1 + i)n
stream receivable at the end of the first year, second year and nth year reservedly .
This is a very useful equation. It is used for judging whether an investment project should be undertaken. If the cost of the machine is less than its present value, the investment project should be undertaken. If the cost of the machine is just equal tot h3e present value of the return, the investment is a matter of indifference. If the cost of the machine is greater than the present value of the return, the investment should not be undertaken
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