**Installment Financial Sharing (IFS): A Financial Subsystem of Rastin PLS
Banking**

**Bijan Bidabad**

*B.A., M.Sc.,
Ph.D., Post-Doc.*

**Professor**

Economics and Chief Islamic Banking
Advisor

Bank Melli, Iran

E-mail:[email protected]

**Abstract**

Installment Financial Sharing (IFS) is a
subsystem of Rastin Profit and Loss Sharing (PLS) Banking System, and the guidelines, instructions, organization, workflow and electronic mechanism
of Rastin PLS Banking have been put forward for this subsystem as well. Profit
in this financial sharing method is based upon the yield of the real sector, and bank as an intermediary of funds, receives a commission as like
as an agent, and provides capital management and financial services to financer (depositor) and participates in
investment project of the entrepreneur on
behalf of the depositor. In installment Financial Sharing, the contribution of the depositor is paid back by installments
and ownership of the project is finally transferred to entrepreneur.Financial
innovations of "*Mughasatah* Certificate"
and "*Musharakah* *Mughasatah* Certificate" and
"Rental *Mughasatah* Certificate" are used in this subsystem.
The financer (depositor) of sharing
project receives a certificate, which is
negotiable in Rastin Certificate Market via the internet.

**Keywords:*** **Mughasatah,
Installment, Sharing, Rastin PLS Banking, Islamic banking, Usury-free banking*

**1. Introduction and Objective**

Rastin PLS banking was designed to
implement usury-free Islamic banking. The base system of this type of banking
actually provides the necessary structure and organization
for financial participation. But it was necessary to paste some new financial
subsystems to the base system to satisfy the needs of the banking clients.
Installment Financial Sharing (IFS) was designed to fulfill Rastin PLS Banking
System to complete some of its shortcomings. IFS[1]
provides the background for depositor participation in the investment project
in which entrepreneur desires to preserve
his own ownership, and depositor wishes to obtain periodic income (monthly,
seasonal, or yearly). IFS is a subsystem of Rastin PLS Banking System, its
guidelines, instructions, organization,
workflow, electronic mechanism and contracts are highly similar to Rastin PLS
Banking, and the latter characteristics have been described in detailed PLS
banking documents.[2]

In IFS, the bank is a firm that works on behalf of the depositor, and allocates his deposit to entrepreneur and divides
the profit or loss of the entrepreneur's investment between the depositor and the entrepreneur according to the
signed contract and receives a commission
for providing financial management services.

**2. Installment Financial Sharing (IFS)**

In this subsystem, the interest rate of installments and rents are in accordance with investment real return, and the bank
is intermediary of funds, and receives a commission
as an attorney or agent and provides
financial and capital management services for his clients. In IFS, the return
of principal capital and yield of conducting activities are paid to depositors periodically, and the ownership of the investment project will be transferred to the
entrepreneur after the payment of the last installment.
Accordingly, bank allocates the capital (deposit) of the depositor in IFS projects based on the will of
the depositor and finally divide the
profit among depositor and entrepreneur and pay
back the principal and profit of investment to the depositor by installment and transfer the ownership of the
project to entrepreneur. Profit and loss will be divided between them according
to their agreement in the contract based on the Rastin PLS banking
instructions, after deduction of bank commission.

Bank deals with depositor through *Joalah*
contract and goes through three new contracts of “*Mughasatah*”, “Rental *Mughasatah*”
and “*Musharakah Mughasatah*” with entrepreneur
and according to depositor desire, will provide the conditions for his
financial participation within the entrepreneur's project.

An entrepreneur is a legal or
real entity who receives deposited funds of depositor via the bank and
according to the agreement will invest in the pre-agreed project. Depositor
provides part of the fund for the entrepreneur's project, and entrepreneur provides the bank with appropriate
guarantees to cover the fulfillment of his obligations. “Trustee” is a unit
that supervises the process of IFS on behalf of the
bank in order to make sure about the goodness of fulfillment of the project operations.

There are several financial innovations
in IFS such as "Mughasatah Certificate", "Rental Mughasatah
Certificate", and "Musharakah* *Mughasatah Certificate",
which provide new preparations for investment projects. These certificates are
digitally negotiable on the internet in
Rastin Certificate Market (RCM)[3] of
the bank. The certificate holder (depositor) can transact his certificate over
the internet; hence, they are negotiable
at the international level.

By applying to Rastin PLS bank branch,
the entrepreneur proposes an IFS project
proposal to the bank. In addition to
informing the entrepreneur about the conditions and regulations concerning IFS
(according to written instructions), the necessary documents, information, and
analysis about the project, including economic, technical and financial
justification and other related information of the project will be received
from the entrepreneur. According to
available previous records of entrepreneur activities, the assessment unit will
assess the entrepreneur's capability and
ability according to written instructions and will report to the PLS department. If the assessment is positive,
according to the related instructions, the quality and quantity of needed
collaterals or guarantees will be defined,
and after signing a contract, the needed
funds will be paid to entrepreneur. All documents including the detail of
sharing subject, budgeting, time schedule, funds and the way of fund consuming,
implementation of the project and its
phases, quality control method, reporting and fulfillment
of the project and its installments will
be provided by the entrepreneur to the
bank assessment unit. Reports provided by the bank trustee unit will be the
basis for all entrepreneur activities evaluations.

By applying to information portal
(website) of Rastin Certificate Market (RCM), depositor becomes familiar with the rules and conditions and selects his
desired entrepreneur's investment proposal. By signing and registering the
contract, and after the payment, the system automatically issues the
certificate. After each financial period and at the end of the contract, under
the supervision of the bank's trustee, entrepreneur calculates the share of
principal and profit of the project and passes it to depositor via bank.

According to the written instructions
and related formulas, the amount of installments, rent or periodic yield and
commission share of the bank will be
calculated by the accounting/auditing
unit. The share of entrepreneur and depositor will be defined by considering
the kind of IFS financing and the method of installment
payment and rent (profit or loss). In the case
of discontinuance of the project, the
occurred losses will be calculated according to the compiled instructions. The
structure and organization of Rastin PLS
banking are also applied to the subsystem
of IFS.

**3. Mughasatah Contracts**

In order to perform IFS
operations,
a new contract by the title** ***"Mughasatah"
*is defined:

**Mughasatah**

*"Mughasatah"** *is defined as a
contract in which the *moghsit*
(depositor) will provide a part or total amount of funds and by providing the
remainder, *ghasit* (entrepreneur)
will invest and pay back the borrowed
amount to *moghsit* (depositor) in
periodic installments and finally becomes
the owner of the project. This procedure uses "Mughasatah
Certificate" as its financial instrument. This contract is used for those
projects that can be finished after a period. *Moghsit* (depositor) has the right to receive the installments until he is paid off, and the
entrepreneur becomes the owner of the project. If the project is to be
concluded to receive rent at compromising contract time, the
procedure in these types of projects
works by issuing "Rental Mughasatah Certificate".

**Rental Mughasatah**

For finitude projects, "Rental
*Mughasatah"*, the entrepreneur can be a real person or
legal entity. *Moghsit* (depositor)
has the right to receive installments
plus the rent until the end of the project,
and the entrepreneur will own total project after then. The rent will be
defined in the contract to be paid by installment,
or calculated as a share of the finished project as assessed at the beginning
of the contract. It is not necessary to pre-fix
the amount of rent for all periods, but this must be cited in the contract.
"Rental *Mughasatah"* is a kind of contract in which *moghsit*
(depositor) provides a part or total fund for project and *ghasit* (entrepreneur) will finance the
remainder and invest the funds in the *moghsatah*
(project) and pays rent to the *moghsit*
(depositor). Then, the share of the depositor from the assessed (valuated) value of the constructed project is
calculated according to the amount of his fund and the period of his
participation and will be paid by installment
to the depositor in addition to rent payment. In
the end, the ownership of the project will be transferred to the entrepreneur. The amount of periodic rent might
be different according to the signed contract.

**Musharakah Mughasatah**

The entrepreneur of prolong (endless)
projects should be a legal entity. In
this case, also the depositor has the right to receive back his own share, plus a
share of the yields of the project until the contract terminates. Then, the
entrepreneur will become the owner of the constructed project. In this case,
bank issues *"Musharakah* *Mughasatah Certificate"*. "*Musharakah*
*Mughasatah"* is a contract, in which depositor provides a part or
total amount of resources needed for project financing and entrepreneur
provides the remainder, then, the share of the depositor from the valuated (assessed) of constructed project and
its yields (productivity) is calculated according to the amount of his share
and the period of his participation and will be paid by installment to depositor.

**Mughasatah Certificate**

*"*Mughasatah Certificate" is
an anonym document issued by Rastin PLS
bank with a nominal price for real financial participation (sharing) for a
certain period. The bearer of this paper receives periodic payments relative to
his share and the period of participation. Payments will be paid at the end of each period. In the end, the entrepreneur will own the
project.

**Rental Mughasatah Certificate**

"Rental Mughasatah
Certificate" is an anonym
document with the defined nominal price
for a defined period of time (rental tenure) issued by Rastin PLS bank
which conducts Rastin PLS activity. The
owners of these certificates have right on the results of the sharing project
which is proportional to the nominal value of the certificate and the duration
of holding certificate until the end and receive periodic rent and installment of the valuation of the project at
the end of each period. At the end of the contract,
the entrepreneur will become the owner of the project.

**Musharakah Mughasatah Certificate**

*"Musharakah
*Mughasatah
Certificate" is an anonym
document with a defined nominal price for
a defined period of time (*Musharakah* tenure) issued by Rastin PLS bank which conducts PLS activities. The owner of
this certificate has right on the result of the sharing project proportional to
the nominal value of the certificate and the duration of holding the
certificate until the end of the contract,
and receive periodic installment plus
income (positive/negative) yields of the project at the end of each period. In the end, the entrepreneur will become the
owner of the project.

All *Mughasatah* certificates are
kinds of Rastin Certificates[4]
and obtain rent, or yield plus installment
until the end of the contract, and after the settlement of the contract, the entrepreneur becomes the owner of
the project. The settlement of the project differs from finitude and endless (productive) projects. The settlement is
after the payout of the last installment for *"*Mughasatah
Certificate". In "Rental Mughasatah Certificate", after the
payment of last installment and rent, the
contract is settled. In *"Musharakah *Mughasatah Certificate",
when the last payment of installments and
profit or loss (yield) is paid, the settlement takes place.

**4. The Amortisation Date of the Share of
Moghsit (Depositor) **

This is the time when depositor has
received all installments (including
principal, rent, or the yield of investment) from the *ghasit* (entrepreneur)
and had no more share in the project that
belongs to the entrepreneur thereafter. This calculating is in connection with
the duration of project after its construction
period and the share of each party (regarding the tenure of their participation), the amount of share of
depositors, the paid-in capital of
entrepreneur, and the value added of the
project (and dismantled value of the project at the end of its useful life – if
applicable).

Amortization date
calculations of all *Mughasatah* contracts are similar. However, this
point of time can be agreed upon by the bank on behalf of depositor and
entrepreneur when the contract is signed.

**5. Dividing the Value of Project at the End of Construction Period**

Allotment of profit of the project
between *moghsit*s (depositors) and *ghasit* (entrepreneur)
is one of the important issues of *Mughasatah*. Traditionally, this type
of apportionment bases on mutual
agreement, but in Installment Financial Sharing (IFS) this apportionment cannot
be left to the bank; therefore, it was
necessary to compile necessary rules for carrying it out accordingly. But, when
installment enters the process of apportionment,
conventionally it involves interest rate, which is not acceptable because of *Reba*.
Hence, we should find a rational usury-free solution for it. Here we should
answer two questions: first, how much are the values of work and capital in
this project? Second, what rate of yield should be applied for the installment of the share of the depositor to be non-usury?

Before entering this discussion, we
should pay attention that *Mughasatah* activity is economically a
production process that creates value-added
and therefore, we can answer the above questions from this viewpoint. In simple
words, according to Neoclassical theory[5], a firm is a unit in which products are produced
by using factors of production (labor and
capital). Mathematically, the production function of the firm is a relation of
the labor and capital in the process of
production. Now consider the process of a *Mughasatah* in which *ghasit*
uses the factors of production of
depositor as capital (K) and contributed
capital of the entrepreneur (B) from one
hand, and his factor of production (entrepreneur's labor work (L)) for the production
of the project. The value of production
function (Q) mathematically is a function of factors of production and can be
described as follows:

Q = f (K + B, L) (1)

The above function does not have a fixed
production factor, and the amount of
production is defined by variable factors of production (labor and capital). The production structure is
defined in such a period that investment does not change, and fixed cost does
not enter the calculations. The applied technology, the know-how of entrepreneur in applying capital and labor in *Mughasatah* is defined as in the
above function. Usually, the production
function is defined as a single-valued continuous increasing function for
non-negative values within the regarded domain and is usually regularly
strictly quasi-concave. The contribution
of depositor and entrepreneur are defined within a period. In this period,
factors and the defined amount of production have
three constraints: First, it should be short
enough so that the *ghasit* cannot change the production factors.
Second, it should be short enough that the production function cannot be
changed due to the improvement of
technology. Third, it should be long enough to cover all the process of *Mughasatah*.
The marginal productivity of capital (K
of *moghsit* plus B of *ghasit*) and *ghasit's* labor work (L)
are noted as^{ }MP_{K+B} and
MP_{L}, and can be defined as follows:

The law of marginal decreasing return
explains that by increasing one factor of production, marginal production
increases at first, but after a while, marginal production starts to decrease.
That is to say, the more we use one of the production
factors, after a while, the less will be marginal production[6]. This law has distinct effects on the
apportionment of the yields of *Mughasatah* that can be understood from
dividing profit relationship that we will explain.

Economies of scale show the way of
increasing production through the proportional
increase of all factors of production. If *Mughasatah *value increases
proportional to the increase of labor and
capital (deposit plus contributed capital of the entrepreneur), the return to scale in the domain of the related factors of production is constant. The return
to scale is positive if the proportional
increase of labor, capital would increase
the production more, and it is negative if the proportional
increase of labor, capital results in
less increase in production. Return to scale is defined by the concept of
homogeneity of the production function. A
production function is homogeneous of degree j if:

In which by an increase of t times of labor
and capital (sum of deposits and paid in capital) for amounts of 0<j<1,
j=1, j>1, the return to scale will be (t^{j})
increasing, constant and decreasing respectively. A linear production function
can result from several linear production
activities simultaneously[7].
Linear production functions are homogeneous of degree one and therefore, have a
constant return to scale. Homogeneity in
production function means that if we increase/decrease all factors of
production proportionally, production will also increase/decrease
proportionally. If production increases/decreases proportionally as an increase/decrease of factors of production, the
production function is homogeneous of degree one. If the ratio of the
production increase is less than the increase in
factors of production, homogeneity has a less than one degree and otherwise has a degree of more than one. In these three
cases, the return to scale is constant, increasing, and decreasing
respectively. This condition mathematically is understandable from relation
(3).

The degree one homogeneity condition in *Mughasatah*
function is quite meaningful; therefore, according to Euler theorem of the
income distribution[8],
we can use this condition to divide the yields of *Mughasatah* contract
between depositors and entrepreneur. In other words, in homogeneity condition, if
all factors of production increase/decrease proportionally, production will
also increase/decrease proportionally. In this case, since the average
productivities of factors of production are unchanged, production productivity
will not change. Euler theorem explains that in a homogeneous function of
degree j, the following relation exists:

Where, f_{L}
and f_{K+B} are marginal productivities of labor (work of entrepreneur) and capital (deposit + paid in
capital) respectively. By replacing (1) in relation (4), with the assumption of
homogeneity of degree one (j=1), we obtain the following relation:

By this theorem,
we can understand that total value of *Mughasatah* is equal to the sum of
multiplication of marginal productivities of labor
(f_{L}) by L and multiplication
of marginal productivity of total capital of depositor and entrepreneur (f_{K+B})
by total capital of *moghsit* and *ghasit* (K+B). In other words, if
we want to divide the result of *Mughasatah* based on marginal
productivities of labor work of
entrepreneur and his contributed capital plus the capital of depositor, the total value of *Mughasatah* are
distributed. Euler theorem has a basic role in marginal productivity theory of
distribution, and accordingly, each part of the *Mughasatah* will receive
his share from the results of *Mughasatah*. It should be mentioned that
homogeneity of degree one causes the profit function of *Mughasatah* to be
also homogeneous of degree one. In other words, if we consider π as *Mughasatah*
profit, we will have:

That is to say, if the labor-work of entrepreneur and the capital of
depositor plus the contributed capital of entrepreneur increase proportionally
(by t), *Mughasatah* profit will also increase proportionally (by t). By
applying above analysis, we can distribute the profits of each part of *Mughasatah*
based on productivity ratio of capital (including the capital of depositor and the contributed capital of entrepreneur) and labor work of entrepreneur from the value added of *Mughasatah*
activity according to the following formula. In the following formula, the
capital value means the deposit of depositor; contributed capital is the total
fund and asset (cash and noncash) brought by the entrepreneur into the project; and value added is the total profit
or value-added obtained by the work of
entrepreneur, through financial participation; and total value added is the
value created by using all factors of production in *Mughasatah* activity, and the project value is the assessed
(valuated) value of *Mughasatah*
project. In other words, we have:

K+B+L=Q=C+V
(7)

which means that sum of
value added (V) and cost (C) is equal to *Mughasatah* value (Q) and is
equal to the total value of labor work (L) and deposit (K) and contributed
capital (B).
This is because:

π=V
(8)

That is value added is equal to the
profit of *Mughasatah* activity. Moreover, the assessed value of the
project is equal to the total value added
plus cost:

C+V=Q (9)

Accordingly, the value added emanated by
the labor work of entrepreneur in *Mughasatah*
will be equal to the assessed value of the project minus the value of deposit
minus contributed capital of the entrepreneur:

L=Q-K-B (10)

Therefore,
the profit share ratios of *moghsit* from the created value added (R_{K})
plus profit share ratio of *ghasit* from the value added (R_{B})
will be equal to the ratio of the value of *moghsit* capital, plus the
contributed capital of *ghasit* to the total value of project (Q); and
also, the profit share ratio of *ghasit* emanated from his labor work in the created value-added will be equal to the ratio of
assessed value added of the project to
the total value of project. In other words:

The
profit shares of *moghsit* and *ghasit* are calculated by multiplying
their profit share ratios by the assessed value added of the project. Or:

Accordingly,
each part of the *Mughasatah* (*moghsit* and *ghasit*) will
share the created value added based on their productivity ratios. In other
words, if we add up the above relations, we will reach the following relation in which the value added is equal to
the labor work yield, plus capital yield,
plus the value added of contributed capital:

This
distribution is in accordance with Euler
theorem of marginal income distribution into capital and labor in which each party (labor work, deposit, and contributed capital)
receives according to his productivity. Therefore, the amount of ownership of *moghsit*
in principal and profit will be:

which means that the dividend of *moghsit* (P_{K})
at the time of assessing the project (at the end of construction period) is
equal to the *moghsit*'s capital value (deposit) and his profit. The dividends of *ghasit*
(P_{L})_{ }at the end of the construction
period will be equal to the total profit of *ghasit* plus the value of his
contributed capital:

Adding
these two relations show that after the end of the construction period, the dividend
of *ghasit* plus the dividend of *moghsit*
is equal to the total value of deposit plus contributed capital of the entrepreneur, plus profits of *ghasit*
and *moghsit*:

In
other words, the total payments to *ghasit* and *moghsit* are equal
to total deposit and contributed capital of entrepreneur and *Mughasatah*
profit:

**6. Accounting Procedure for Apportionment**

In simpler words, ratios of the
dividends of each part of the project from the value
added of the *Mughasatah* activity at the end of construction period is
calculated on the basis of the yield of capital (deposit) and contributed
capital (of entrepreneur) and labor work
(of entrepreneur) on the basis of
following formulas. In following relations, capital value is the amount of
depositor's deposit and contributed
capital is the contribution of entrepreneur and labor
value is the labor work of entrepreneur
resulted from his activity. On the other hand, value-added
is the produced value in excess of the original
capital of depositor plus the contributed capital of the entrepreneur, which is cleared by assessing the
project value. In other words, the market value of the project at the end of
the construction period minus depositor’s capital and contributed capital of
the entrepreneur is the project value added at the end of the construction period.

Therefore,
the markup cost of the project is equal
to the capital value of depositor plus
contributed capital of the entrepreneur:

C = K
+ B
(21)

Value-added
plus markup cost is equal to the value of labor
work plus the value of the contributed
capital plus value of the depositor's capital:

K + B
+ L = C + V
(22)

The
assessed value of the project is equal to the value
added plus markup production cost:

C + V
= Q
(23)

Alternatively,
the assessed value of the project is equal to the value of labor work
productivity, plus the value of paid-in capital plus depositor's capital
(deposit) value:

K + B
+ L = Q (24)

Accordingly,
the yield of the depositor of the created
value-added will be equal to the ratio of
depositor capital to the assessed value
of the project at the end of the construction
period. The ratio of the yield of the entrepreneur from the project from the
created value-added will be equal to the
total of the ratios of his contribution (paid in capital and work) to the
assessed (valuated) value added:

R_{K}
= K/Q (25)

R_{B}
= B/Q
(26)

R_{L}
= V/Q (27)

The
dividends of depositor and entrepreneur from value added are calculated by
multiplying their yield ratios by project value added at the end of the construction period. In other words, the
dividend of depositor from value added is equal to depositor yield ratio
multiplied by created value added:

π_{K}
= R_{K} × V
(28)

Entrepreneur’s contributed capital dividend from value added
is equal to his
contributed capital yield ratio multiplied by value added:

π_{B}
= R_{B} × V
(29)

Entrepreneur’s labor work dividend from value added is equal to his labor work yield ratio multiplied by value
added:

π_{L}
= R_{L} × V
(30)

In other words,
depositor’s dividend from value added is equal
to his capital yield from value added. And Entrepreneur’s contributed capital dividend from
value added is equal to his paid in capital yield from value added. And Entrepreneur’s
labor work dividend from value added
is equal to his labor work yield from
value added.

The share of depositor from the assessed value of the project is calculated by
adding his share from value-added and his
deposit. The share of the entrepreneur
from the assessed value of the project is
calculated by adding up his contributed capital share from value-added and his labor work contribution from value-added,
plus his contributed capital. In other words:

P_{K} =
π_{K} + K (31)

P_{B+L} =
π_{B} + π_{L} + B (32)

Sum of the last two
relations shows that after distribution: The share of depositor from the
project plus the share of entrepreneur from the project is equal to value added
plus the deposit of the depositor plus
entrepreneur’s contributed capital.

P_{K} + P_{B+L}
= V + K + B (33)

If we add up the
above relations, we reach to the following relation in which: depositor's
capital yield + entrepreneur’s capital yield + entrepreneur’s labor yield is equal to the value added of *Mughasatah*. This
economically is adapted to Euler income distribution of value added to labor and capital according to their
productivity (yield).

**7. Calculation of Mughasatah Installment in
Finitude Projects**

"Mughasatah
Certificate" is issued for finitude projects through *Mughasatah*
contract. In this process, depositor provides funds, and entrepreneur mixes it with his own contributed capital and
executes the project. At the end of the construction
period, the bank assesses the project and based on duration and amortization date of depositor’s sources, the installment method to pay depositor back is
defined. In this case, the calculation of installments
includes two parts. One is the installments
for paying back the principal capital of depositor, and the other is the return
or yield of his capital.

Parameters used to
calculate the installments for finitude
projects contracts are the amount of
deposit (K), the entrepreneur’s
contributed capital (B), construction period (M), and operational life of the
project after construction (T).

Figure 1.

Considering figure
1, the entrepreneur, together with his contributed capital (B), receives the deposit of depositor (K) at the beginning
of the construction period and starts
construction according to the contract. The
construction period is M. At the end of the construction period, and the start
of the utilization of the project; bank
assesses (valuate) the value of the project (Q) at market price. If the project
were sold at this time, the shares of depositor and entrepreneur would be
calculated by the following relations:

P_{K} =
π_{K} + K (34)

P_{B+L} =
π_{B} + π_{L} + B
(35)

That is the claims
of depositors and entrepreneur from the project are obtained by the above
relations. Now, the entrepreneur buys the share of the depositor in installment and
becomes the owner of parts of the project gradually, and finally by paying back
all installments, becomes the owner of the whole project. Now suppose that
the useful lifetime of the project from the beginning
of exploitation is T periods (years). If we want to show the shares of
depositor and entrepreneur through the figure 1, it means that from time T_{1}=M to T_{2}=M+N the
ownership belongs to depositors and from T_{2}=M+N to T_{3}=T+M
the entrepreneur will be the owner of the
project. T_{2} is the
time that participation concludes. If the entrepreneur pays back the share of
depositor until T_{2},
he will gain the total ownership from T_{2
}to T_{3}._{ }^{}

Now suppose the
entrepreneur obtains the possession
of the project from time T_{1}=M
and pays back depositor’s share by installment.
In this case, we need to calculate the amount of
his installments. Here, we should
consider a few issues. First, when the
final date of amortization of depositor’s
share is? Second, what the preferential rate or capital time-yield of depositor’s deposit (which is in possession of the entrepreneur) is?

To calculate the amortization
period (N), we use the following relation:

To obtain the time-yield rate (r)
of depositor's deposit, we use the ratio of the total
yield of the project which is equal to the value added (V) of the project to total capital resources used (deposit
and contributed capital of entrepreneur).
The time-yield rate of the project at the
beginning and during the construction period is indefinite and will be assessed
afterward at the end of construction period by assessing the value of the project; and therefore, it is not *Riba* (usury) to be prefixed at the beginning. That is:

r = π_{K}/(K×M)
(37)

And r is the time-yield rate of
depositor's deposit. Considering the fact that the construction period might be longer than one period (year),
inserting M in the denominator, will estimate the time-yield rate of capital for each period (such as a year). This return rate (r) is calculated only
for the deposit of depositor that is obtained practically in the process of construction, and it is not
interest rate and is capital return rate. This rate suggests that if depositor
and entrepreneur wanted to invest in a similar project by using depositor’s
deposits, the entrepreneur should pay depositor at a capital rate of return (r). Therefore, the capital yield rate of
the depositor in the next periods will be calculated by this rate of
return (r).

If the entrepreneur had to pay
back all the share of the depositor at
time T_{2},_{ }he should
pay the amount of P_{K
}(1+N×r). If the entrepreneur wants
to pay back depositor’s principal and profit by equal installments, his monthly payments would be equal to:

I_{t} = P_{K}
(1+0.5×N×r)/N t=1,…,N (38)

In which, t shows periods of 1 to N. It
is clear that:

The 0.5 multiplier in the above relations is because the installment payment starts from the beginning.

Entrepreneur and depositors can unambiguously agree to change the
schedule of the installment from equal
payments via the bank.

**8. Calculation of Rental Mughasatah
Installment in Finitude Projects**

"Rental Mughasatah Certificate" is issued for finitude
projects by Rental *Mughasatah* contract. In this process, depositor
provides funds for the entrepreneur, and
he mixes depositor’s deposit with his own contributed capital and carries out the project. Bank assesses the
project at the end of the construction
period and according to the preliminary
agreement; the project will be in possession of
the entrepreneur as a rented property
until the amortization date of
depositor's share. According to the assessed value of the project and the amortization date, the bank calculates the amount of rent and installment. Bank (on behalf of the depositor) and entrepreneur
will agree upon the rent. The defined installment
consists of two parts: one for the principal deposit, and other for the
periodic rent which entrepreneur should pay to the depositor. The difference between *Mughasatah* and Rental *Mughasatah*
is fixing the rent from the beginning in Rental *Mughasatah*.

Effective parameters in calculations of Rental *Mughasatah* are
the amount of deposit of depositors (K), contributed capital of entrepreneur (B), construction period (M), and
operating lifetime of the project after construction (T), the agreed rent
according to the signed contract (S).

Consider the previous diagram in
figure 1. The entrepreneur, with his own contributed capital (B) and deposits
of depositors (K), starts the construction of the project. Construction takes M
periods. At the end of construction, when the project becomes operational, the
bank assesses (valuates), the market
value of the project (Q). As in the previous case, if the project were to sell, the share of entrepreneur and depositor
would be as (34) and (35) which means their claims at the
end of construction period would be defined according to these relations. Now,
the entrepreneur buys depositor's share by installments,
and by paying each installment, his own
share increases until he becomes the owner of the total project. During this period, in addition to paying installment for the principal, the entrepreneur
has to pay rent to depositors according
to the pre-agreed contract. The forecasted operating lifetime of the project
after the construction period is (T)
(e.g., years). If we want to show time ownership of depositor and entrepreneur
in the graph, it means that from time T_{1}=M
until* *T_{2}=M+N,
ownership belongs to depositors, and from time T_{2}=M+N until* *T_{3}=T+M, the
entrepreneur will be the owner. T_{2}
is the expiration date of the contract
with the depositor. If the entrepreneur pays back depositor's shares at
this time, he will become the owner of the project from then after.

Now consider a case
in which the entrepreneur takes possession
of the project from the beginning and starts to pay back the principal capital
of depositor and its rent for using the property. Then, we have to calculate
his installment and rent. First, we have to define T_{2, }which is the amortization date for depositor’s claim. To
obtain amortization date (N), we use the
previous relation of (36) which means that the entrepreneur should pay back
depositor's claim on the assessed value
of the project in N periods (years). Since the value of the project is not
defined at the beginning of the project and can be assessed at the end of
construction date of the project, the share of depositors cannot be calculated
at the beginning.

If they had agreed to pay back the share of the depositor at time T_{2}, he had to pay^{ }P_{K}^{.}
Since he wants to pay this amount in N equal installments,
his periodic installment will be P_{K}
/N. His installment plus his rent is
extracted as in the following relation:

I_{t} = S_{t} + P_{K}
/N t=1,…,N (40)^{
}

In which, S_{t }is the amount of rent for periods of t=1,…,N. Rent installments can be unequal for all these
periods according to the agreed contract.

The total amount of payment to
depositors for principal and rent will be equal to:

By the agreement of entrepreneur and bank on behalf of the depositor, N can be defined without using the
above method. Rent can be defined as a percent
of the value of the project at the time of signing the contract. In other
words, the entrepreneur and bank (on behalf of the depositor), can define the
rent as a percent of the value of the
project when it is constructed and becomes operational. In this case, periodic
(annual) rent is calculated by the following relation:

S_{t} = s × (P_{K}/N) * * (42)

S_{t }is periodic rent, and s is the ratio of the share of total
rent from the assessed value of the project. "s" is a condition of
the contract. In this case, rent has an exact
legal justification for using the
benefits of a rental property. Depositor leaves rental property to be in possession of the
entrepreneur, and he is legally the one who has rented the object. The
amount of rent can be variable, and this
is not against Civil Law. It is necessary to mention that the assessed value of
the project at the beginning of the project is unknown and will be determined (valuated) by the bank at the end of the construction period at market prices.

**9. Calculation of Rental Mughasatah Installment in Endless Projects**

If the project is endless, calculation of the shares of depositor and
entrepreneur at the end of the construction
period is the same as for finitude
projects. Now, if the project is defined as an endless (productive) project in
the contract, the depositor will also
have a periodic share in the productivity of the project during the exploitation
period plus periodic installment. In this
case, the depositor is not just lessors, but he participates in the profit and
loss of the project.

"*Musharakah
*Mughasatah Certificate" is issued for the endless project through "*Musharakah Mughasatah*"
contract. In this process, depositor
provides fund and entrepreneur mixes it
with his own resources and starts constructing the project. At the end of the construction period, the bank assesses the
project and according to the amortization,
period duration calculates the installments
and adds it to depositor’s share from the value added for every period
according to entrepreneur’s financial reports. According to the signed
contract, the project will be monitored by the bank's
trustee until depositor’s claim is amortized.
In addition, in this case, payments to the depositor
by entrepreneur consist of two parts: installment
concerning the return of the principal deposit of depositor, and his share from periodic value added of the project. The
difference between "*Musharakah
Mughasatah*" and the previous case of "Rental *Mughasatah*",
is that in "*Musharakah
Mughasatah*", periodic value added is
calculated and depositor’s share is added to the assessed depositor's share
value of the project.

Effective parameters used in fixing contract and calculations are the amount of depositor's deposit (K), contributed
capital of entrepreneur (B), construction
period (M), and
operational lifetime of the project after
construction period (T).

In this case, the amount of installment for the principal deposit of depositor is similar to the case of the finitude project contract. The amortization period for depositor’s share
is similarly obtained as in the previous case by (36). To calculate the amount
of each installment, if the entrepreneur had to pay back the whole share of
the depositor at the time T_{2}, he had to pay the amount of P_{K}.^{ }In this case, the amount of periodic installment for the assessed value of the
project (P_{K})
will be P_{K}/N. The productivity of the project is as the share
of depositor from the value added by the project from the end of construction
period T_{1}=M up to the date
of amortization of depositors’ claim T_{2}=M+N
which should be paid him annually. The total
share of depositor from his principal deposit plus the assessed value of the
project and his value added (due to project productivity) share will be paid by
the entrepreneur. At every time period (t=1,…,N),
depositor receives his value-added share
in that period (V_{t}^{K}) in addition to the installment for his principal deposit plus his
share from the assessed value of the project. Therefore, the total amount of year
on year installment will be:

I_{t} = V_{t}^{K}
+ P_{K}/N t=1,…,N * *(43)

In which, t shows the periods from 1 to
N. It is clear that:

Keeping in mind that capital time-yield
rate for the deposit (r) is not considered for endless projects. But instead,
the entrepreneur has to pay his periodic
share value added up to the end of the amortization
period.

If we name the periodic value added of the project for periods of t=1,…,N_{ }as Vt
which can be positive, negative, or zero, it should be divided proportionally
according to the shares of depositors and entrepreneur. The dividend is paid to
"*Musharakah *Mughasatah Certificate" holder at the end of each
period. Therefore, at the end of each financial period and calculating profit
and loss, the share of "*Musharakah *Mughasatah Certificate"
holder from the project yield (

* * (45)

Considering the above explanation, total shares of depositor for his installment and periodic value added will be
equal to V_{t}^{K}+P_{K}/N.
P_{K}/N is depositor’s share for his capital contribution from the
assessed value of the project, and V_{t}^{K} is his share from the periodic value added of the project which will be paid to the depositor ("*Musharakah* *Mughasatah*
Certificate" holders).

**10. Considerations for Installment Financial Sharing (IFS)**

Since in *Mughasatah*, the deposit of depositor and contributed
capital of entrepreneur mix together, they have mutual rights. The entrepreneur
can insure the share of the depositor to cover the probable risk. If the
assessed value of the project was less than its cost, it is possible to use
"loss insurance" to cover the probable loss. Therefore, the
entrepreneur insures depositor’s loss.
This insurance is obligatory for all three kinds of *Mughasatah* (*Mughasatah*,
Rental *Mughasatah,* and *Musharakah* *Mughasatah*). In this
case, according to the signed contract,
the project will be sold by auction under the supervision of the bank's trustee, and the contract will be settled, and the bank receives no commission. This process is only applicable in
"*Mughasatah*" and is not applicable in Rental *Mughasatah*
and *Musharakah* *Mughasatah*.

Installment Financial Sharing (IFS) operational mechanism^{[9]}, organization^{[10]}, and instructions comply with Rastin PLS
banking instructions. These instructions include:

§ Checking
capability of the entrepreneur

§ Guarantees,
collaterals and paid in capital

§ Providing
economic, technical and financial justification proposal

§ Documents and evidence necessary for project evaluation

§ Bank yields

§ Supervision
standards and regulations

§ Entrepreneur
reporting

§ Accounting and
auditing

§ Timing and cost
changing

§ Inflation
effects on income, cost and net outcome of the project

§ Failure because
of entrepreneur’s delay and timing change

§ New sharing (capitalization during the
operation)

§ Settlement with
entrepreneur

§ Arbitration

§ Force majeure

§ Compilation of
PLS banking contracts

§ General
conditions of PLS contracts

§ Trustee
competency

§ Depositor
dispensing and immature settlement

§ Replacing *Pazireh* Certificates with
shares in (productive) endless projects

§ Insurance
coverage

§ Certificates
transaction

§ Future
certificate issuance

§ Future
certificate purchase and sale order

§ Types of
guarantees and collaterals for the goodness
of carrying activities and playing commitments in compliance with general PLS
instruction

§ Banks receipts

§ Commodity
checking and control

§ Raw material and
final goods standards

§ Delivering final
goods and termination

§ Insurance
instruction in *Joalah* Financial Sharing (JFS)

§ Delay in payment
and abstaining from fulfilling obligations

§ Entrepreneur's
company corporate governance

§ Professional behavior of trustee and appraiser

§ Entrepreneur's
company information disclosure

**11. Conclusion**

Real
establishment of usury-free Islamic banking can remove many world economic
problems such as crises[11]. To reach this
goal, Rastin Banking with Islamic and ethic
essence was designed and developed. Rastin Banking should be developed to fulfill the needs of clients and to become a
good substitute for conventional banking. In this regards, Installment Financial Sharing (IFS) was designed. IFS is a
fully new financial innovation and works under Rastin PLS Banking. It provides
the background for depositor participation in the investment project in which entrepreneur desires to preserve his own
ownership, and depositor wishes to obtain periodic income (monthly, seasonal,
or yearly). These two needs are important desires of banks clients in both realms of borrowing and lending. IFS fill this
gap in profit and loss sharing mechanism.

**References**

Bidabad, Bijan. (2014). New Operational Islamic
Banking System, Volume One, Theoretical Foundations, *LAP Lambert Academic Publishing,* OmniScriptum GmbH & Co. KG,
ISBN: 978-3-659-54463-7.

Bidabad, Bijan. (2014). New Operational Islamic
Banking System, Volume Two, Applicational Issues, *LAP Lambert Academic Publishing,* OmniScriptum GmbH & Co. KG,
ISBN: 978-3-659-55210-6.

Bidabad,
Bijan. Installment Financial Sharing (IFS), a subsystem of Rastin PLS banking,
Planning and Research Department of Bank Melli Iran, Tehran, 2011.

http://www.bidabad.com/doc/detailed-ifs.pdf

Bidabad, Bijan, Fluctuations and
Business Cycles Prevention by New Financial Instruments and Banking Structure
Reform

http://www.bidabad.com/doc/Fluctuations-and-Cycles.pdf

Bidabad, Bijan, Stabilising Business Cycles by PLS Banking and Ethic Economics.

http://www.bidabad.com/doc/pls-business-cycles-en.pdf

Bidabad, Bijan, M. Allahyarifard, The Executive Mechanism of Profit and Loss Sharing (PLS) Banking.

http://www.bidabad.com/doc/PLS-banking-Executive-Mechanism.pdf

Bidabad, Bijan (2018), General Regulatory
Framework in Rastin Profit and Loss Sharing Banking (Part I-Operational
Context). *Journal of Business and Finance
in Emerging Markets*, JBFEM, [S.l.], v. 1, n. 1, p. 11-26, May. ISSN
2580-5568.

https://doi.org/10.32770/jbfem.vol111-26

http://www.bidabad.com/doc/rastin-regulatory-en-I.pdf

Bidabad, Bijan (2018), General
Regulatory Framework in Rastin Profit and Loss Sharing Banking (Part II-Legal
Groundwork). *Journal of Business and
Finance in Emerging Markets*, JBFEM, JBFEM, [S.l.], v. 1, n. 2, p. 109-126,
Nov. ISSN 2580-5568.

https://doi.org/10.32770/jbfem.vol1109-126

http://www.bidabad.com/doc/rastin-regulatory-en-II.pdf

Bidabad, Bijan (2019), General Regulatory Framework in
Rastin Profit and Loss Sharing Banking (Part III-Auxiliary Provisions). *Journal of Business and Finance in Emerging
Markets*, JBFEM, May, Vol 2, No. 1, pp. 51-65. ISSN 2580-5568.

https://doi.org/10.32770/jbfem.vol251-66

http://www.bidabad.com/doc/rastin-regulatory-en-III.pdf

Bidabad, Bijan, Nasaji Safarzadeh Masoud,
Aghabeigi, Jina, Organization of Profit and
Loss Sharing (PLS) Banking in Bank Melli Iran. Planning and Research Department of Bank Melli Iran, Tehran, 2010.

http://www.bidabad.com/doc/PLS-organization.pdf

Bidabad, Bijan, Safaeipour,
Mohammad, The Electronic Market for
Transaction of *Musharakah* (Partnership)/Pazireh (Subscripted)
Certificates. Fifth Conference of E-Commerce,
23-24, November 2008, Ministry of Commerce, Tehran, Iran.

http://www.bidabad.com/doc/charchoobe-bazare-electronic-pls.pdf

Eatwell, J., M. Milgate, P. Newman
(1988). The new Palgrave dictionary of economics. MacMillan.

George J. Stigler (1946), Production and Distribution Theories: The
Formative Period, New York, Macmillan.

Henderson, R., Quandt, P. (1982),
Microeconomic theory, a mathematical approach. Mc-Graw Hill.

Savabi Asl, Farhad; Bidabad, Bijan
and Shahrestani, H., (1993). Estimating Aggregate Investment Function of Iran,
Considering Various Functions, MS. Dissertation, Islamic Azad University,
Tehran.

**Copyrights**

Copyright for this article is retained by the author(s), with
first publication rights granted to the journal.

This is an open-access article distributed under the terms and
conditions of the Creative Commons Attribution
license (http://creativecommons.org/licenses/by/4.0/)

[1] - Bidabad, Bijan.
Installment Financial Sharing (IFS), a subsystem of Rastin PLS banking,
Planning and Research Department of Bank Melli Iran, Tehran, 2011. http://www.bidabad.com/doc/detailed-ifs.pdf

[2] - The Persian and English documents of Rastin Banking
including detailed explanation of this banking method can be accessed through http://www.bidabad.com in full texts.

[3] - Bidabad, Bijan, Safaeipour, Mohammad, The Electronic Market for Transaction of *Musharakah*
(Partnership)/Pazireh (Subscripted) Certificates. Fifth Conference of
E-Commerece, 23-24, November 2008, Ministry of Commerce, Tehran, Iran. http://www.bidabad.com/doc/charchoobe-bazare-electronic-pls.pdf

[4] - Rastin certificates are the name for collection of
certificates designed for Rastin PLS banking and operate under the supervision
of trustee unit of bank and are issued with prefix of certificate.

[5] - For more information, see microeconomic texts, as:
Henderson, R., Quandt, P. (1982), Microeconomic theory, a mathematical
approach. Mc-Graw Hill.

[6] - This is the intersection point of marginal and
average production curves.

[7] - There are many production functions with different
economic and mathematical characteristics. See: Eatwell, J, M. & Milgate, P. Newman
(1988). The new Palgrave dictionary of economics. MacMillan.

Savabi Asl, Farhad; Bidabad, Bijan and
Shahrestani, H., (1993). Estimating Aggregate Investment Function of Iran,
Considering Various Functions, MS. Dissertation, Islamic Azad University,
Tehran.

[8] See: George J. Stigler (1946), Production and Distribution
Theories: The Formative Period, New York, Mac Millan.

^{[9]} Bidabad, Bijan, M. Allahyarifard, The Executive
Mechanism of Profit and Loss Sharing (PLS) Banking. http://www.bidabad.com/doc/PLS-banking-Executive-Mechanism.pdf

[10] Bidabad, Bijan, Nasaji Safarzadeh Masoud, Aghabeigi,
Jina, Organization of Profit and Loss
Sharing (PLS) Banking in Bank Melli Iran. Planning and Research Department of Bank Melli Iran, Tehran, 2010. http://www.bidabad.com/doc/PLS-organization.pdf

[11] - Bidabad, Bijan, Fluctuations and Business Cycles
Prevention by New Financial Instruments and Banking Structure Reform http://www.bidabad.com/doc/Fluctuations-and-Cycles.pdf

Bidabad, Bijan, Stabilizing Business Cycles by PLS Banking and Ethic
Economics. http://www.bidabad.com/doc/pls-business-cycles-en.pdf