# FIXED-PROMISED REGULAR-PAYMENT SUKUK

- Fixed-Promised Regular Payments and Zero-Promised Maturity Payment
- Fixed-Promised Regular Payments and Promised Maturity Payment
- VARIABLE-PROMISED PAYMENT SUKUK
- Growing-Promised Regular Payments and Predetermined Maturity Payment
- Declining-Promised Regular Payments and Zero-Promised Maturity Payment
- UNDETERMINED-PROMISED PAYMENT SUKUK
- CONCLUSION

*Sukuk* securities may be designed to have periodical payments to investors. The interval between two consecutive payments (i.e., duration of the period) is fixed for the whole tenure of the security. However, it may vary from one payment per year to one payment per month (e.g., 1, 2, 3, 4, 6, and 12 payments per year are common in different markets). The simplest form of *sukuk* with promised regular payments are those with a fixed number of promised payments. Such a cash-flow pattern might fit three forms of *sukuk* securities: diminishing *musharakah sukuk, bai bithaman ajjal sukuk,* and *ijarah sukuk.*

## Fixed-Promised Regular Payments and Zero-Promised Maturity Payment

The diminishing *musharakah sukuk* payment structure may be to have some promised regular payments at certain times with a zero maturity payment. The number of promised regular payments is fixed and predetermined. The cash-flow pattern of such a security is depicted in Figure 13.2.

The cash flow here is identical to a constant annuity. Thus, in order to evaluate the price of a diminishing *musharakah sukuk,* the present value of the annuity is applicable. This results in Equation 13.2.

Here *P* is the price of the diminishing *musharakah sukuk* security, *R* is the amount of the periodical promised payment, *r* is the discount rate, and *N* is the number of periods remaining to maturity.

FIGURE 13.2 **Fixed-Promised Regular-Payment Cash-Flow Pattern of** **Sukuk**** without Promised Maturity Payment**

FIGURE 13.3 **Cash-Flow Pattern for** **Sukuk**** with Fixed-Promised Regular Payments and Promised Maturity Payment**

## Fixed-Promised Regular Payments and Promised Maturity Payment

*Bai bithaman ajjal sukuk* may generate a cash-flow stream of some fixed-promised and predetermined-promised regular payments and promised maturity payments. *Ijarah sukuk* has fixed and predetermined rental payments (i.e., rewards) and a market-valued maturity payment. However, in practice, the maturity value of the property is fixed and predetermined for both sides of the contract. Therefore, the cash-flow pattern of an *ijarah sukuk* would be similar to that of a *bai bithaman ajjal sukuk.* The cash-flow pattern of such securities is depicted in Figure 13.3.

The valuation of these forms of *sukuk* is similar to that of a conventional bond because of the similarity of cash-flow patterns and the tradability. Thus, *sukuk* can be priced by using Equation 13.3.

Here, *P* is the price of the *sukuk* security, *R* is the amount of the periodical promised payment, M is the amount of the predetermined maturity payment, *r* is the discount rate, and N is the number of periods remaining to maturity.

# VARIABLE-PROMISED PAYMENT SUKUK

Some forms of *sukuk* securities have a variable cash-flow pattern. They can have a growing or declining pattern of promised payments. *Sukuk* with variable-promised regular payments are *bai bithaman ajjal, ijarah,* and diminishing *musharakah.*

## Growing-Promised Regular Payments and Predetermined Maturity Payment

*Bai bithaman ajjal sukuk* may be designed so that the periodical promised payments follow a constant growth model; however, their respective amounts are predetermined. The amount of the maturity payment is fixed and predetermined, while the amount of the promised regular payment in a given period follows a predetermined constant growth model. In *ijarah sukuk,* the maturity payment should be based on the market value (hence, a priori undetermined), while the amount of the promised regular payment (i.e., rental fees) in a given period follows a predetermined constant growth model.

In practice, however, the maturity payment of *ijarah sukuk* is predetermined and mentioned in the contract. Therefore, its cash flow is similar to *bai bithaman ajjal sukuk.* The cash-flow pattern of these *sukuk* securities is depicted in Figure 13.4.

This cash-flow pattern of *sukuk* consists of a growing annuity of promised regular payments and a promised maturity payment. Thus, using the formula for calculating the present value of an annuity, one can formulate the price of a *sukuk* security as shown in Equation 13.4.

Here, *P* is the price of the *sukuk, r* is the discount rate, N is the number of periods to maturity, g is the growth rate of promised regular payments, and *Ri* is the amount of the first promised regular payment. It is assumed that the promised payments are growing at a constant rate of g; thus, R2 = R1(l + g).

FIGURE 13.4 **Growing-Promised Regular-Payment Pattern with Predetermined Promised Maturity Payment**

FIGURE 13.5 **Declining-Promised Payment Cash-Flow Pattern**

## Declining-Promised Regular Payments and Zero-Promised Maturity Payment

In diminishing *musharakah sukuk,* the amount of the promised regular payment in a given period follows a predetermined constant negative growth (i.e., declining) model with growth rate that is a negative number. In other words, the cash flow of regular payments declines to zero at maturity. This cash flow is presented in Figure 13.5.

The same formulation approach used for the valuation of *bai bithaman ajjal sukuk* is applicable for the case of diminishing *musharakah,* with consideration of the negativity of the growth factor. Thus, the price of a diminishing *musharakah sukuk* can be formulated as shown in Equation 13.5.

Here, *P* is the price of the diminishing *musharakah sukuk, r* is the discount rate, N is the number of periods to maturity, g is the negative growth rate of the promised regular payments, and *R* is the amount of the first promised regular payment. It is assumed that the promised regular payments are declining at a constant rate of g; thus, *R2 = R (1 + g) < R.*

# UNDETERMINED-PROMISED PAYMENT SUKUK

*Musharakah* and *mudarabah sukuk* securities distribute undetermined amounts of payments. The amount of a promised payment in such *sukuk* securities is calculated based on the venture's performance in each specific

FIGURE 13.6 **Undetermined-Promised Payment Cash-Flow Pattern**

period. Moreover, the amount of the maturity payment is not predetermined. It is based on the value of the venture at maturity. However, the distribution ratio of payments is fixed and predetermined. The cash-flow pattern of such *sukuk* securities are charted in Figure 13.6. Since the *mudarabah* contract is a debt contract, this type of security is not allowed by *Shari'ah* to be traded at any price other than par value.

The valuation of *musharakah sukuk* requires summation and the discounting of stochastic variables. The value of such *sukuk* can be expressed as shown in Equation 13.6.

Here, *P* is the price of the *musharakah sukuk, M* is the stochastic variable representing the market value of the venture at maturity, *R{* is the stochastic variable representing the amount of the periodical promised payment, *r* is the discount rate, T is the time to maturity, and *d* is the distribution ratio.

# CONCLUSION

This chapter translated the structures of different *sukuk* contracts into their basic payment patterns. This enables us to see the fundamental principles of the payment structures, which can be used to build mathematical models and coherent valuation theories for the industry practices. This is similar to the attempts in the 1930s and 1960s to build valuation models for conventional finance instruments, such as the bonds by Professor J. B. Williams in 1938.

We believe that valuation is a necessary condition for providing objective market advisory services as the *sukuk* market grows bigger in more and more financial centers. Serious students of Islamic finance can use these models to value as well as refine the formulas.