A1, rate of 20% would lead to
A1, A2 and A3 be discounted at 10% per annum, the present values are A1 / (1 + r) 1, A2 / (1 + r) 2 and A3 / (1 + r) 3
Substituting data given, the workout at 1000, 2000 and 1000 respectively. Sum of these present values is Rs 4,000, which is the same as the supply price of the capital asset (machine, in our illustration). The rate of discount, 10%, is thus the marginal efficiency of capital (MEC).
If the discount rate be 5% instead of 10%, the present values of the annuities would work out at Rs 1,048, Rs 2,195 and Rs 1,150. The sum of these values is Rs 4,393, which is higher than supply price of Rs 4,000. According to the definition, discount rate of 5% here can’t be taken as MEC. The reason is obvious.
The rate does not equate the sum of the present values of the annuities to the suppiy price of the capital asset. In like manner, a discount rate of 20% would lead to a sum of the present values as low as Rs 3,368 (917 + 1681 + 770). Even this rate can’t be taken as MEC.
To demonstrate further, let MEC be 20% when the cost of the capital investment is Rs 4,000. Annuities after 1, 2, and 3 years then have to be Rs 1,200, Rs 2,880 and Rs 1,728 so that the sum of the discounted annuities (PVs) may be just equal to Rs 4,000.
Further, let MEC be 5%. The values of annuities must then be Rs 1,050, Rs 2,205 and Rs 1,158 respectively after 1, 2 and 3 years so that the sum of the discounted annuities may be Rs 4,000.
The purpose of all these illustrations is to impress upon the reader the following realities about MEC, rate of discount and the annuities:
1. Every rate of discount can’t serve as MEC.
2. For a higher MEC, annuities too must be higher so that, their discounted values may sum up to the given cost of the capital investment.
3. For a lower MEC, annuities too must be lower so that their discounted values may sum up to the given cost of the capital investment.
Expressions like [1/(1 + r)1], [1/(1 + r)2], [1/(1 + r)3],…, [1/(1 + r)n] multipling annuities A1 A2, A3 …, An respectively reduce them equal to their respective present values P1 P2, P3 …, Pn and are therefore known as discounting factors. Here, 1/ (1 + r)n is the discounting factor for the year, n at the discount rate of ‘r’.
Supply price of capital asset is the cost of its replacement, Cr. It is possible to find MEC that equates the sum of the discounted annuities (sum of the present values) to the supply price of the capital asset.
The values of the discounting factor for different years at different values of V can thus be calculated. Such values are also available in tabular form in logarithmic or statistical tables for ready reference. Table 5.1 lists the discounting factors corresponding to different rates of interest and to different time periods.