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Cost
of Capital in an Islamic Financial System
By
prohibiting interest, Islamic injunctions do not imply that the
opportunity cost of capital represented by interest rate in a
conventional system is zero. In an Islamic framework, the incentive
for the firm to invest will solely depend on prospective
profitability. A profit maximizing firm will continue investing
until the marginal productivity of capital becomes equal to the
opportunity cost of capital; therefore, "cost of capital"
in the Islamic system can be represented by the rate of return on
alternate opportunities for investment of comparable risk.5
It has also been demonstrated that there is a rate of return in
Islamic capital markets serving opportunity cost of capital, and
this rate of return is also closely related to the rate of return in
the real sector of the economy.6
In
the Islamic financial system, determination of prospective
profitability and the rate of return on investments of the same risk
class plays a pivotal role in determining the relative cost of
capital.
Tobin's
q theory of investment suggests the use of information in asset
markets, especially the stock market, in knowing the profitability
of investment. The theory relates investment to the ratio of market
to replacement value of capital and suggests that when the stock
market functions properly, the future profitability of investment
will be solely summarized by q.7 It
is a simple arbitrage argument. If the market valuation of capital
held by a firm exceeds the cost of capital on the open market, then
the firm can increase its value by investing.8
Tobin argues that if q exceeds unity, the value of capital
investment would exceed its costs, and the firm would have incentive
to invest.
A
recent model presented by Mirakhor utilizes this concept of q in
deriving the cost of equity capital of a firm in the Islamic
financial system.9 In its simple form
the model states:
r
= ( Y / V ) (1 - d + dq )
where:
r = Firm's cost of
capital or shareholder's required rate of return.
Y = Value of expected
earnings for the next year.
V = Present value of the
firm's stock of capital. Since there is no debt financing in the
Islamic system, it is equal to value of the firm.
d = Sum of fraction of
expected earnings retained by the firm and the expected rate of
stock financing expressed as ratio of firm's expected earnings.
q = Firm's q ratio.
The model implies that a firm's cost of capital (r) is a function of
a firm's q ratio and the firm's market value (V), stream of expected
future earnings (Y), ratio of retained earnings, and new stock
financing. The q ratio can be simply derived by dividing the value
of the firm (V) determined by the market price of the firm's stock
by the replacement costs of firm's assets such as equipment, land,
receivables, and marketable securities. The cost of capital will
fluctuate with the fluctuations in the q ratio, thus signaling the
prospects of an investment project. For example, we are interested
in finding the cost of capital for a firm with future expected
earnings for next year (Y) of $1,000,000 and equity value of
$10,000,000 (since there is no debt financing, value of the firm is
equal to equity value).
Based
on the historical data, it is known that the firm finances future
projects through retained earnings and new equity issues amounting
to 20 percent of its earnings (d = .20). If the firm's q ratio is 1,
its cost of capital will be 10 percent as the following shows:
1
= $1,000,000/$10,000,000 ( 1 - .2 + (.2 . 1) )
The
figure below gives a graphical representation of cost of capital for
the same firm with varying q ratios. It is obvious from the graph
that cost of capital has a linear relationship with q. A firm with q
lower than 1 will have a cost of capital lower than the return on
equity (10 percent in this case) whereas, firms with q greater than
1 will require higher cost of capital.
A
firm's market value reflects the profitability of existing capital.
The q ratio is an indication of how much this market value can
increase by additional investment, also known as marginal q.
Marginal q - the ratio of market value of an additional unit of
capital (shadow price of capital) to its replacement cost - is the
critical determinant of the firm's investment decision making but is
not observable since the shadow price of capital is not observable.
Instead, what is observable (in principle) is the average q - ratio
of the market value of existing capital to its replacement cost.
Hayashi
rigorously proved a relationship of average q with marginal q-based
information in stock market valuation.10
A relationship of equality between average and marginal q will hold
provided conditions of perfect competition in product market and
linear function of homogenous technology of production and
adjustment costs are satisfied. For competitive firms
(price-takers), this relationship is strong because the unobservable
shadow price is directly linked to the stock market valuation of
existing capital. If one of these conditions is violated, then the
average q is no longer equal to the marginal q; however, a
relationship may still exist. For example, in firms with
monopolistic position (price-makers), average q is higher than
marginal q by what is legitimately called the monopoly rent, and it
is marginal q that is relevant for investment. Several empirical
studies have utilized average q as a proxy for marginal q.
Pricing
assets using q has several advantages over other methods.11
First, the market value of the firm is an indicator of future
profitability as perceived by investors' expectations rather than
the past performance of the firm. Second, since market value is
subject to adjustment by variations in expected profits, q
incorporates an automatic adjustment for risk independent of any
methodology employed by capital markets to determine risk premium.
The value of q should be equal to unity only if profits are high
enough to compensate for shareholders risks. Finally, as compared to
other asset pricing models (capital assets, arbitrage, or option
pricing models), a model based on q is subject to less measurement
errors.
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