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Comments on Discounting of in Project Evaluation


The article by Dr. Anas Zarqa has been addressed to an issue which is crucial not only because of its importance in the field of applied economics but also because this is likely to be one of the main questions that development economists would be worried about if the proposition of Interest-Free Economy is put in practice.

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The paper has been primarily addressed to the following two issues:

  • Discounting in Islam.
  • Role of Islamic Values in Project Evaluation.

Whereas the subject of the “Role of Islamic Values” has been touched only in brief, the detailed discussion has been offered to answer the following questions about “discounting” in Islamic perspective.

  • Is discounting allowed in Islam?
  • Does zero interest on loans imply zero discount rate?
  • If discounting is acceptable, what should be the discount rate?
  • If a discount rate is established, does not this mean admitting interest through the window after kicking it out of the main door?

The author’s answers to these questions, in brief are:

  • Yes:
    • “The opportunity and willingness to engage in real investment and assume risk and the fact that the expected value of net productivity of investment is positive together justify discounting”.
  • No.
  • The (risky) rate of return on equity should be the discount rate.
  • No:
    • “Because discounting is based on the (risky) rate of return on capital which is accepted as a legitimate source of income in Islam.”

I must appreciate the efforts of Dr. Zarqa in giving an elaborate discussion of discount rate that would not conflict with Islamic Economic principles. I would, however, like to raise a few points that render Dr. Zarqa’s paper, in a sense, quite confusing from the point of view of its contribution to the theory of Islamic Economics.

The reader, who is keen to look for “the concept of Discounting in Islam” in a paper entitled “Economics of Project Evaluation in Islamic Perspective”, is completely lost when the author treats the price of capital and the rate of discount to be the same and then revolves most of his discussion to justify that the (risky) rate of return on equity rather than interest rate is the correct measure of the price of capital. The discount rate and the price of capital can be assumed to be the same only in the conditions of general equilibrium in the economy. As soon as we deviate from the conditions of equilibrium in the economy we are again in dark as to what should be the discount rate. The developing countries, to which most of the users of Dr. Zarqa’s paper belong, generally face a situation of excess demand of capital in the economy resulting from various economic and noneconomic factors. In such situations, the discount rate will significantly diverge from the price of capital. For illustration, see the following diagram.

The availability of capital at KO is showing a situation of excess demand in the capital market. In this situation, the expected rate of return on capital (e) is higher than the discount rate (d) Dr. Zarqa’s formula, to use expected rate of return as a discounting factor, will lead to an'underestimation of future benefits. The efforts that Dr. Zarqa has spent in proving that under realistic assumptions interest rate and rate of return on capital converge (a fact already established in modern economics) would have been more fruitful if he had indicated that under realistic assumptions the discount rate (MRS between future and present consumption) and the rate of return on capital converge in an Islamic perspective (if he really believes that expected rate of return should be a discount factor).

I think it is this digression from the discussion of discount rate to the discussion of price of capital, that has led the author to justify the use of the return on equity as a discount rate on the ground that economists have found cost of capital:

(Earnings per Share)

Price per Share

As an appropriate discount factor in the investment decisions in the private sector. The economics of project evaluation from the point of view of a development economist is something entirely different from the investment decisions in the private sector corporate financing particularly when it is a question of the selection of an appropriate discount rate. Though the author refers to Samuelson to conclude that the “rate of return on capital in a private industry of similar riskiness” can be used as a discount rate for public investment, he does not explicitly realise that Samuelson’s approximation for discount rate can have relevance only for Western economies under very restrictive assumptions about the sources of financing and the equilibrium conditions in the economy.

Another confusion arises from the author’s assertion that “the opportunity and willingness to engage in real investment and assume risk — justifies compounding and discounting”. This assertion implicitly assumes not only that all savers save for the purpose of investment but also that they are willing to take risk of losing their savings. In a society, particularly a developing one a large number of savers would not like to take any risk on their savings as the motives are to build-up support for old age, dowry for daughters’ marriages, finances for children’s education and hedge against accidents and uncertainties (in the absence of proper insurance programmes. These savings can be mobilized for financing the investments in public sector projects (or even in private sector) by borrowing these funds as loans with a guaranteed return of the principal. In an Islamic economy, these loans are not entitled to returns (profits) nor will they bear any interest. I think this is exactly what Dr. Zarqa meant when he raised the question, “Does not this zero interest on loans imply the use of zero discount rate and the disregard of the time dimension of costs and benefits”, but Dr. Zarqa does not seem to have answered this question. Obviously, the expected rate of return on equity cannot be applied to this source.

Though the title of the paper is “An Islamic Perspective on the Economics of Discounting in Project Evaluation” the author concen trated his efforts on determining a discount rate for the allocation of capital in an Islamic economy despite that he had himself pointed out in the beginning of his paper.

“Project Evaluation is related to, but different from the question of the allocation of capital.”

With such emphasis, the paper on “An Islamic Perspective on the Economics of Discounting in Project Evaluation" was expected to have been addressed in quite a broader perspective, covering:

  • The economic behaviour of Muslim consumers (and investors).
  • The objective function of the society with specific reference to arguments of the welfare function in an Islamic economy.

Only passing remarks have been made on arguments of the welfare function of Islamic economy and nothing has been mentioned about the consumption behaviour of Muslims (which is constrained not only by economic injunctions but also by religious injunctions such as "Pay Zakah and Khairat' and “do not be extravagant”. Unless the welfare function of an Islamic economy and the behaviour of a Muslim consumer is clearly distinguished from the existing concepts, the question, “Is discounting allowed in Islam?” does not arise at all. Once this perspective is clear, only then we can go to the next question that whether “price (cost) of capital" can be used as a discount rate or we need to devise some other measures to indicate the discount rate. That the (risky) rate of return on equity and not the interest rate is the appropriate measure of the “price of capital" is only a secondary question.

Dr. M. Fahim Khan


Consider a project undertaken either by a private investor or a public authority and which is expected to yield a stream of benefits b{ over the next T years. Such a stream can be reduced to a single number, the present value, PV, of the project, by the well known formula

co b{

  1. Is the concept of discounting and compounding based on un- Islamic values? If acceptable, does not this amount to admitting interest through the window after kicking it out of the main door?
  2. If discounting is acceptable, while interest is prohibited, what should a Muslim firm or public authority use as discount factor in lieu of the rate of interest?”

The questions are clear. The author’s answers to these questions are equally clear. His answer to 1 is No and his answer to 2 is “the rate of return on equity.” Let us begin by considering the author’s arguments underlying his answer to question 1.

As I understand it, the author sees a justification for discounting in that a sum of money earns an uncertain rate of return. Thus, he writes: “. . . . the opportunity and willingness to engage in real investment and assume risks and the fact that the expected value of NPI (net productivity of investment) is positive together justify discounting and compounding.”

"Only equity funds that share in the risk inherent in investment can obtain a stochastic rate of return. This fundamental Islamic rule is quite in harmony with the concept of a stochastic opportunity cost of investment, which is the basis of discounting. Discounting is thus an entirely legitimate concept in an Islamic economy with a zero rate of interest on loans.

As long as that other project, whether actual or potential, is a Halal investment, the process of discounting is entirely Halal.  Also he writes,

“... In an uncertain world — the.only world we know — interest rate and equity rate diverge, with the latter and not the former being the discounting factor.”

I reporduce all these arguments in some detail because despite reading and re-reading, I do not see how they justify discounting. Simple examples might illuminate my difficulties. I have one hundred dollars with which I propose to buy a machine. Now let us consider two hypothetical regimes. Under the first, the machine gives me a three- year stream of certain benefits of $ (75, 60, 40). Under the second regime, it gives me an uncertain stream with the above figures being expected values of the probability distribution of the returns in each year. Now the question is whether, under either regime, I should discount or not to determine whether I should buy the machine. As I understnd the author, under the first regime we should not discount but that under the second regime we should. I agree that uncertainty is of the essence but from my own ongoing and at present superficial study, it seems to me that it is precisely because of the uncertanity, that discounting should not be used.

For a substantiation of this statement, let us assume that I borrowed one hundred dollars to begin with. This gives the classical situation of a mudarabah, Qirad or Muqarada studied in detail by A. L. Udovitch. In such a contract, it is precisely the uncertainty that is responsible for the institution of a profit-sharing scheme agreed to by all the parties in advance. I quote Udovitch in some detail (pages 190—192).

Any proportional division of prof it agreed upon between an investor and an agent is acceptable in a commenda contract. The only requirement, and one which is a sine qua non of a valid commenda contract, is that division of profit between the parties be strictly proportional. Most of the cases discussed in the legal texts are introduced by the formulaic phrase: “If a man handed over to another money in the form of a commenda on the basis of half the profit."

Any violation of the proportional division rule renders the commenda in valid. One violation frequently discussed in the sources is when one of the parties stipulates a specific sum of money from the profit instead of, or in addition to, his proportional share of the profits. Such an arrangement could conceivably lead to an inequitable situation in which one party would get all the profit and the other none, and is therefore invalid. In certain circumstances it would also come perilously dose to a usurious transaction.

Finally, goods are inadmissible as investment. To quote from Udovitch again (pages 180-181).

“There are two general considerations underlying the rejection of goods and commodities for investment in a commenda. The first is the opposition to risk and injustified enrichment which permeates the entire Islamic law of obligations; and the second, its coro/lory, is the strict requirement in Islamic law that the object of any contract be determined (ma'lum) i.e. clearly known and defined."

In explaining the ineligibility of commodities for the formation of a commenda, Kasani says:

"The commenda in goods leads to uncertainty concerning the amount of the profit at the time of division. This is so because the value of the goods is known only by estimation, chance, and conjecture, and will differ with the difference of those who do the estimating. And uncertainty in turn leads to dispute, and dispute leads to discord.”

Starting from the Koranic prohibition of a certain game of hazard (Maysir,), Islamic Law insists that there must be no doubt concerning the obligations by the parties to a contract. The object of the contract, in particular, must be determined (Wlum, 'known'; opposite majhul, ‘unknown ’). This requirement is particularly strict as regards objects which can be measured or weighed, which are subject to the prohibition of riba; no undetermined quantity fjuzaf) is permissible here.

Schacht draws attention to the prohibitions on exchange of animal for meat, of wheat for flour; of dried dates for fresh dates on the tree (the so called muzabana), a similar contract concerning corn (the so called muhaka/a).

Udovitch establishes that identical principles apply to partnerships. We shall not go into these here but refer the reader to relevant chapters in his book on the: (1) Hanafi Mufawada partnership, (2) Hanafi Limited investment partnership (/nan), and (3) Maliki partnership.

In the light of all these passages and in the light of author’s own insistence on the importance of uncertainty in investment, the question which occurs to me is what justification is there for the usage of any positive discount rate? To put the matter in another way, what justification is there to agree to compounding at any given rate or to regard the rate of profit to be any given number (say the rate of return on equity assuming it were known). It is precisely because of this uncertainty of the rate of return, that profit-sharing (at a rate determined between the parties) is advocated.

However, in all the passages quoted above there is an implicit assumption that only two time periods are involved. The investor gives the money to an agent for a specified time period and the latter then returns the principal to this investor along with his share of the profit (or loss). However, in project evaluation we are typically concerned with a stream of returns as in Formula. The question which occurs is whether shares of profit, not necessarily all equal, can be agreed upon for each year. The following passage from Sarakhsi Mabsut (22:105) and Shaybani Mudaraba (112a-112b) shed some light on this.

A man gives to another one thousand dirhams as a commenda on a half-profit basis, and the agent makes a profit of an additional thousand. The two then divide the profit between themselves, with each taking five hundred dirhams white the capital of the commenda remains as it is in the possession of the agent. If the capital is then immediately destroyed, or if the agent trades with it unsuccessfully, or if it is lost after he trades with it, their division is void; the five hundred that the investor took is to be considered as part of his capital, and the agent owes him the five hundred which he took for himself, which is also to go to the investor as part of his capital. The money which was lost is from the profit; because the profit does not emerge until the capital is delivered to the investor.

Udovitch, in commenting on this passage writes (page 247):

After the investment is restored and the remaining profit divided, the investor is perfectly free to immediately reinvest the original sum with the original agent according to the provisions of their previous agreement. This, however, is viewed as a completely independent and new contract; and, in spite of the identical mise-en-scene, any subsequent financial reverses would not in any way affect or undermine the finality of the earlier division of profits.

In concluding my discussion of question 1, I would like to make two remarks which will serve as counterpoints to some implicit assumptions in the author’s discussion. Firstly, there are influential economists in the West, who argue against a positive rate of time preference especially in projects undertaken by a public authority. Secondly, interest is not indispensable for the functioning of a private ownership economy.

To substantiate my first remark, I shall quote from Ramsey and Harrod. In his seminal and influential study on optimal growth, Ramsey* writes:

... it is assumed that we do not discount later enjoyments in comparison with earlier ones, a practice which is ethically indefensible and arises merely from the weakness of the imagination.

Ramsey is discussing the preferences of an authority planning over time for the whole economy. Harrod goes even further by arguing against time preference on the individual level.

Time preference in this sense is a human infirmity, probably stronger in primitive than in civilized man. On the assumption — that a government is capable of planning what is best for its subject, it will pay no attention to pure time preference, a polite expression for rapacity and the conquest of reason by passion.

Koopmansf puts the issue succinctly by emphasizing that a positive rate of time preference is essentially a problem of values.

Scratch an economist and you find a moralist underneath. What is at issue is clearly an intertemporal distribution problem: that of balancing the consumption levels of successive generations, and of successive stages in the life cycle of a given cohort of contemporaries.

It is important to underscore how influential Ramsey’s arguments have been in the modern theory of growth. There has been a seminal contribution by von Weizsacker to cope with the technical difficulties raised by the Ramsey-Harrod prescription. To get a passing appreciation of Ramsey’s paper on the modern theory of optimal growth, the reader is referred to, for example, Shell.

It is important to be clear about what these authors are saying and what they are not saying. There is no implication in these statements as to whether the rate of interest in a market economy is positive or not. Instead the authors address themselves to whether a planning authority should discount its stream of benefits at a positive rate or not.

For a substantiation of my second remark, I refer the author to my paperf prepared for the conference which purports to show the irrelevance of the rate of interest, assuming it exists, for an ‘optimum’ allocation of resources in an idealized model of a private ownership economy.

I now turn to a brief consideration of the author’s arguments in support of the conclusion that a rate of return on equity should be used. But what is this rate? In an economy with many commodities and even with complete certainty, there are as many such rates as the number of commodities that can be chosen as numeraire. Again, one of these rates is optimal only if the economy satisfies several idealized conditions. But for all of this, the author is again referred to see my paper quoted earlier. In conclusion, I cannot help pointing out that Western economists’ emphasis on a setting with .complete certainty is not because they do not consider settings with uncertainty unimportant but because’they do not know how to handle them. In any case, it is currently a topic of active research. As such, I find the author’s discussion on this issue very confusing.

I have little to say on Section IV of the author’s paper other than that I have great sympathy for general objectives as say spelt out under the phrase al-Adl wal Ehsan as brought out in “An Agenda for Islamic Reform.” An attempt to be more specific leads us to problematic statements such as:

Thus rural sanitary water supply has much higher Islamic priority than rural electrification.

Dr. M. Ali Khan


Source: Fiscal Policy and Resource Allocation in Islam, Ziauddin Ahmed, Munawar Iqbal and M. Fahim Khan. Republished with permission.