Principal repayment

To obtain the price of an inflation-linked bond, it is necessary to determine the value of coupon payments and principal repayment. Inflation-linked bonds can be structured with a different cash flow indexation. As noted above, duration, tax treatment and reinvestment risk, are the main factors that affect the instrument design. For instance, index-aimuity bmids that give to the investor a fixed annuity payment and a variable element to compensate the inflation have the shortest duration and the highest reinvestment risk of aU inflation-linked bonds. Conversely, inflation-linked zero-coupon bonds have the highest duration of all inflation-linked bonds and do not have reinvestment risk. In addition, also the tax treatment affects the cash flow structure. In some bond markets, the inflation adjustment on the principal is treated as current income for tax purpose, while in other markets it is not. 

Determining the value of coupon payments and principal repayment ... 

After having determined the binomial inflation rate tree, we calculate the value of coupon payments and principal repayment. Each coupon is linked to the inflation rate in the binomial inflation rate tree and the value is obtained as the present value of coupon payments. 

In the same way, the value of the principal repayment is given at maturity as the par value linked to the inflation rate (Figure 6.9). Consequently, the principal is discounted at time 0. For instance, at higher node fs, the pricing is given by (6.18) ... 

Determining the Value of an Option-Free Bond The fair value of an option-free bond is the sum of the present values of aU its cash flows in terms of coupon payments and principal repayment. The bond value is given by Equation (9.5) ... 

The pricing of a floating-rate note at issue does not differ from a conventional bond. In fact, it is the present value of coupon payments and principal repayment and is given by (10.3) ... 

Yield to call This method calculates the yield for the next available call date. The yield to call is determined assuming the coupon payment until the call date and the principal repayment at the call date. For instance, the yield to first call is the rate of return calculated assuming cash flow payments until first call date. When interest rates are less than the ones at issue, the yield to call is useful because most probably the bond will be called at next call date ... 

To calculate the value of these bonds, it is preferable to use the binomial tree model. The value of a straight bond is determined as the present values of expected cash flows in terms of coupon payments and principal repayment. For bonds with embedded options, since the main variable that drives their values is the interest rate, the binomial tree is the most suitable pricing model. 

Sinking fund is a debt instrument that requires the issuer to redeem a part of the outstanding principal each year over the bond s life. The provision assures that the bond is periodically repaid, avoiding the large principal repayment at maturity. This characteristic decreases the yield compared to a conventional bond. The issuer can redeem the bond with two main methods ... 

Cash flow is simply the cash that is expected to be received in the future from owning a financial asset. For a fixed-income security, it does not matter whether the cash flow is interest income or repayment of principal. A security s cash flows represent the sum of each period s expected cash flow. Even if we disregard default, the cash flows for some fixed-income securities are simple to forecast accurately. Noncallable benchmark government securities possess this feature since they have known cash flows. For benchmark government securities, the cash flows consist of the coupon interest payments every year up to and including the maturity date and the principal repayment at the maturity date. 

Income earned from reinvestment of the bond s interim cash flows (i.e., coupon payments and principal repayments). 

The source of dollar return called reinvestment income represents the interest earned from reinvesting the bond s interim cash flows (interest and/or principal payments) until the bond is removed from the investor s portfolio. With the exception of zero-coupon bonds, fixed income securities deliver coupon payments that can be reinvested. Moreover, amortizing securities (e.g., mortgage-backed and asset-backed securities) make periodic principal repayments which can also be invested. 

Although it is commonly quoted by market participants, the cash flow yield suffers from limitations similar to the yield to maturity. These shortcomings include (1) the projected cash flows assume that the prepayment speed will be realized (2) the projected cash flows are assumed to be reinvested at the cash flow yield and (3) the mortgage-backed or asset-backed security is assumed to be held until the final payoff of all the loans in the pool based on some prepayment assumption. If the cash flows are reinvested at rate lower than the cash flow yield (i.e., reinvestment risk) or if actual prepayments differ from those projected, then the cash flow yield will not be realized. Mortgage-backed and asset-backed securities are particularly sensitive to reinvestment risk since payments are usually monthly and include principal repayments as well as interest. 

The two most common types of embedded options are call (or prepay) options and put options. As interest rates in the market decline, the issuer may call or prepay the debt obligation prior to the scheduled principal repayment date. The other type of option is a put option. This option gives the investor the right to require the issuer to purchase the bond at a specified price. Below we will examine the price/yield relationship for bonds with both types of embedded options (calls and puts) and implications for price volatility. 

Market valne transactions aggressively nse ramp-up periods to acquire assets when accumulating the collateral pool. There is typically a liquidity facility, which is in place prior to the closing of the transaction, to help bridge the acquisition of assets. The principal repayment of liabilities are extinguished when the nnderlying assets are sold (traded) out of the portfolio, rather than when they matnre. 

Interest indexation. Interest-indexed bonds have been issued in Australia, although not since 1987. They pay a coupon fixed rate at a real—inflation-adjusted—interest rate. They also pay a principal adjustment (equal to the percentage change in the CPI from the issue date times the principal amount) every period. The inflation adjustment is thus fully paid out as it occurs, and no adjustment to the principal repayment at maturity is needed. 

Capital indexation. Capital-indexed bonds have been issued in the United States, Australia, Canada, New Zealand, and the United Kingdom. Their coupon rates are specified in real terms, meaning that the coupon paid guarantees the real amount. For example, if the coupon is stated as 2 percent, what the buyer really gets is 2 percent after adjustment for inflation. Each period, this rate is applied to the inflation-adjusted principal amount to produce the coupon payment amount. At maturity, the principal repayment is the product of the bond s nominal value times the cumulative change in the index since issuance. Compared with interest-indexed bonds of similar maturity, these bonds have longer durations and lower reinvestment risk. 

The principal repayment is computed as in expression (12.4). Note that the redemption value of a TIPS is guaranteed by the Treasury to be a minimum of 100 percent of the face value. 

Consider a TIPS issued on January 15, 1998, with coupon of 3.625 percent and a maturity date of January 15, 2008. The base CPI-U level for the bond is the one registered in October 1997. Say this is 150.30. Assume that the CPI for October 2007, the relevant computing level for the January 2008 cash flows, is 160.5. Using these values, the final coupon payment and principal repayment per 100 face value will be ... 

The principal repayment and the interest payment in any month during the mortgage term can be calculated using equations (14.5) and (l4.6), respectively. 

All classes of a single CMO receive an equal share of the interest payments it is the principal repayments received that differ. Consider an issue with a nominal value of 100 million, 60 million of which is allocated to the class A tranche, 25 million to the class B, and the rest to class C. Holders of class A bonds receive all the principal repayments until the bonds retire, after which class B holders get all the repayments, and so on. The class A bonds thus have the shortest maturity and the highest credit rating, and the class C bonds the longest and usually the lowest. A level of uncertainty is still associated with the maturity of each bond, but it is lower than that associated with a pass-through security. CMOs are discussed in more depth below. 

The principal-repayment profile and expected amortization of the underlying loans... 

C , = the coupon payment plus the principal repayment mi = the number of days from the value date to maturity fii = the number of interest periods from the value date until C, = mj 182 or 183... 

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