The document proposes a new mathematical model for musyarakah (joint venture) contracts in Islamic banking. The model allows for two different profit sharing rates between the bank and customer. This addresses limitations in previous models that used a single rate, which could be unfair to one party. The document applies the new model to a sample musyarakah product over 6 months with changing profit rates. The results show the new model distributing profits fairly between the bank and customer compared to previous models. This could encourage banks to offer more musyarakah products and promote equity-based contracts in Islamic finance.

1. THE APPLICATION OF NEW MUSYARAKAH
MODEL IN
ISLAMIC BANKING PRODUCTS
Maheran Mohd Jaffar
Mathematics Department
Fakulti Sains Teknologi & Matematik
Universiti Teknologi MARA
Malaysia
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2. Content
Introduction
Background problem
New Musyarakah model
Application of model in musyarakah product
Results
Discussion
Usefulness/benefits to society
Conclusion
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3. Introduction
Islamic banking
Significant and popular
Competitive alternatives to conventional products
Loan financing contracts
Bai’ bithaman ajil (deferred payment sale), murabahah (Cost
plus profit), wadiah (savings with guarantee), ijarah (leasing)
etc.
Equity fincancing contracts
not popular : mudharabah (profit sharing), musyarakah (joint
venture)
Mudharabah contract
Musyarakah contract
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4. Musyarakah Contract
A joint venture
Very dynamic concept
Not many musyarakah products
The financial institutions love sure profit.
Potential investors love profit sharing products.
Higher risk
Not many scientific research
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5. Percentage of Islamic Financial Concepts Used in
Banking System (Malaysia) in 2007, 2008 and 2009
Percentage (%)
Islamic Concepts 2007 2008 2009
Bai Bithaman Ajil 37.0 33.0 33.4
Ijarah 1.4 2.7 2.8
Ijarah Thumma Al-Bai 30.2 30.4 31.3
Murabahah 11.4 15.2 16.6
Musyarakah & mudharabah 0.5 1.4 1.7
Istisna' 0.9 1.3 1.3
Others 18.5 16.1 12.9
Total 100 100 100
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6. Background Problem
Islamic banks
are pesimistic in packaging their products.
prefer the sure profit
need to improvise and offer new products to attract
fund managers
Not many scientific research
Need better understanding on the flow of
money
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7. New Musyarakah Model
A new mathematical model for joint venture
Both parties can put in initial capital.
Provides two profit sharing rates.
Investment can be calculated at any time
Total investment and profit for the two parties.
Transparent, fair, and justified profit sharing
model.
Risks are shared between investors.
A catalyst to new products
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8. New Musyarakah Model…
Customer Bank
(Capital provider) (Entrepreneur)
Initial investment:
Net Profit:
(1-k)% (1-j)%
j%
k%
Total
investment: + + + +
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9. New Musyarakah Model…
Capital provider’s investment at time t :
Et – capital provider’s : + +
investment at time t
Qt – entrepreneur’s E t = E t −1 + rt kE t −1 + rt (1 − j )Q t −1
investment at time t
rt – rate of profit at time t
k – capital provider profit Entrepreneur’s investment at time t:
sharing ratio
j – entrepreneur profit : + +
sharing ratio
Q t = Q t −1 + rt (1 − k ) E t −1 + rt jQ t −1
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10. Application of Model in
Musyarakah Products
A customer (capital provider)
Initial investment: RM1000
Profit sharing rate: k:(1-k) = 60%:40%
An Islamic bank (entrepreneur): RM500
Initial investment: RM500
Profit sharing rate: (1-j):j = 20%:80%
Tenor: 6 months
Assumed profit rates: 4%, 5%, 6%, 4%, 6%, 7%
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11. Application…
Customer Bank
(1-j):j
k:(1-k) (Entrepreneur)
(Capital provider)
60%:40% 20%:80%
Initial investment: RM1000 RM500
1st month profit is 4% RM40 RM20
40% 20%
60% 80%
Total investment: 1000 + 24 + 4 = 1028 500 + 16 + 16 = 532
2st month profit is 5% RM51.50 RM26.60
40% 20%
60% 80%
Total investment: 1028 + 30.84+ 5.32 = 1064.16 500 + 20.56 + 21.28 = 573.84
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12. Results
Profit from
Profit from Capital
Term Investment + Profit Rate Profit Entreprenueur's
Provider's Investment
Investment
Total Profit
Entrepr Capital Entre
Capital
Year e Provi pre 60:40 20:80
Provider
nueur der nueur
Capital Capital
Entrepre Entrepre
Provi Provide Capital
nueur nueur Entrepre
t der r Provide
nueur
r
% 70 30 10 90
0 1,000.00 500.00 0% 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
1 1,000.00 500.00 4% 40.00 20.00 24.00 16.00 4.00 16.00 28.00 32.00
2 1,028.00 532.00 5% 51.40 26.60 30.84 20.56 5.32 21.28 64.16 73.84
3 1,064.16 573.84 6% 63.85 34.43 38.31 25.54 6.89 27.54 109.36 126.92
4 1109.36 626.92 4% 44.37 25.08 26.62 17.75 5.02 20.06 141.00 164.74
5 1141.00 664.74 6% 68.46 39.88 41.08 27.83 7.98 31.91 190.95 224.03
6 1190.05 724.03 7% 83.30 50.68 49.98 33.32 10.14 40.55 250.17 297.89
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TOT
1250.17 797.89 351.39 196.67 210.83 140.55 39.33 157.34 250.17 297.89
AL -

13. Discussion
Customer
RM250.17
Profit calculated using new model
RM351.39 + RM196.67 =RM548.06 Bank
RM297.89
BUT if use only 1 profit sharing rate Customer
60%:40% then RM548.06 RM328.84
customer gains bigger profit Bank
unfair to the bank RM219.22
banks will not offer musyarakah
product.
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14. Discussion…
If profit sharing rates k:(1-k) => 60%:40% and
(1-j):j => 40%:60% or k = j
Unfair to bank.
Bank involvement in the joint venture is far greater compared to
customer.
The values for k and j can never be the same.
two profit sharing rates are essential.
gives credit for the expertise, time, and effort of the joint
venture.
Transparent – calculation of any time
Can calculate the total investment and profit
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15. Usefulness/Benefits to Society
Catalyst to innovation and research in the area of
Islamic finance
A catalyst to new products innovation & research in
finance/investment
Linkages and collaborations between academicians &
industries
Dynamic activities in implementing musyarakah concept
Public have choices of investing instead of taking loans
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16. Conclusion
Justified and fair profit sharing model
The risk are shared between both parties
Encourage opportunity for entrepreneur to invest
Able to package more musyarakah products in Islamic
banking/investment
An alternative or a complement to the existing products
offered by Islamic banks
Initiate new joint venture investment and financing
products
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17. THANK YOU
Funded by the Fundamental Research Grant Scheme (FRGS),
FRGS 600-RMI/FRGS 5/31Fst(26/2008) from the Ministry of Higher
Education, Malaysia.
Maheran Mohd Jaffar
maheran@tmsk.uitm.edu.my
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