Required Rate of Return in an Islamic Economy
An implication of the main assumption (i) mentioned earlier is that the Islamic idea of intertemporal consumption-investment decision is opposed to the very basis of intertemporal allocation of income to consumption as given by the consumption theory of interest. The new approach in Islamic economics would be to allocate income inter- temporally among savings in real investment.
Therefore, in an Islamic economy the choice to the investor is not between today’s and tomorrow’s consumption, but rather between today’s investment returns and tomorrow’s investment returns. This is the same thing as lagged investment intertemp orally considered. Private and social rates of time preference as explained by the consumption theory of interest, are therefore, untenable in the Islamic economy. They are instead replaced by the marginal efficiencies of capital, privately owned or socially owned, as the case may be.
We have shown in the Technical Appendix at the end of this paper that in the Islamic framework of investment-consumption decision, the marginal efficiency of investment, *r’, is given by the result,
T+1 -0 +r).
- (1+r) denotes the slope of the income line at the point of tangency of this line with the investment possibility curve. Since r is directly related to real investment, so it is in fact the marginal efficiency of investment.
Because r is inversely related to the investment level, therefore, as investment increases due to transfer of funds from potential consumption to investment, it is made more and more attractive by a declining r. Figure 1 shows that under such conditions the returns-line indicated by T'P' shifts upwards but tilts downwards. Consequently, the optimal locus of points of tangency of the capital budgetline with the investment possibility curve shifts upwards as indicated by RR'.
In Figure 1, Y1 and Y2 denote the incomes available in time periods 1 and 2, respectively, for investment. The income allocation line is initially given by TP, with optimal investment allocation at R on the investment possibility curve, VF. Now the slope of TP is —(1+r). As r declines, TP shifts to T'P' in a downward tilting fashion, and R moves up to R'.
Initially an investment of AF today would give a return of HR tomorrow. After the change in income, an investment of FP > AF resulting from the declining r, gives a net increase in return of R'G' > RH. Thus, the locus RR' moves upwards as shown.
So much for the private rate of return. Let us now turn to the social rate of return in an Islamic economy. In an Islamic economy individual preferences that make up the social preferences are essentially altruistic in nature, and are formed under given codes of the Shari'ah that establish the relation of the individual with the state.
We claim, therefore, that the marginal efficiency of social investment is a weighted average of the marginal efficiency of private investments. This result can be established simply by taking an example. Consider an Islamic government tenders contracts to private firms for the construction of a railway line. This is a social project, and in the private sector it would involve such agents as steel manufactures to fabricate the railway tracks, the mining sector to pass railway tracks through mountainous tunnels, civil engineering firms to design the layout and build bridges, the training and educational sector to provide the manpower need and others. Now, if a given proportion of the total investment in these sectors goes to meet the needs of the railway construction project, then it would readily follow that the social rate of return on this project would be a weighted average of the sectoral (private) rates of return, with finer breakdowns as applicable.
In a diagram it could be shown that the social rate of return is to be determined by the slope of the tangent at the common point of the social indifference curve and the socially desirable investment possibility curve. This is also the point where the marginal social productivity of investment would be a well-defined function of the marginal social productivity of private investment. The notion of the social time preference rate of the modern economy is, therefore, again replaced by the marginal efficiency of social investment.
We can now summarize the results of this section for an Islamic economy:
- In both the cases, of private and social investment, the intertemporal choice of investment is based on the marginal efficiency of investment.
- The social marginal efficiency of investment is a weighted average of the private marginal efficiencies of capital.
The main areas of analysis of the rate of capitalization in valuation models in an Islamic economy, that we intended to undertake, have been covered. In the next section we simply bring together the quantitative results to establish the Islamic capitalization rate in its quantitative structural form.
The Capitalization Rate for Islamic Valuation Models
The capitalization rate for capital valuation models in an Islamic economy, denoted by p, is now given by,
p = r + aP where,
r denotes the required rate of return identified as the marginal efficiency of investment, private or social, as the case may be;
P denotes the percentage share in risk-bearing by the mudarabah firm;
a denotes a suitable percentage, possibly representing the relative cost of production or investment for the mudarabah firm.
Source: Fiscal Policy and Resource Allocation in Islam, Ziauddin Ahmed, Munawar Iqbal and M. Fahim Khan. Republished with permission.