Bonds cash flows

The approach used by Fisher et al. (1995) is a smoothed cubic spline that approximates the forward ciuve. The number of nodes to use is recommended as approximately one-third of the number of bonds used in the sample, spaced apart so that there is an equal number of bonds maturing between adjacent nodes. This is different to the theoretical approach, which is to have node points at every interval where there is a bond cash flow however, in practice using the smaller number of nodes as proposed by Fisher et al. produces essentially an identical forward rate curve, but with fewer calculations required. The resulting forward rate curve is the cubic spline that minimises the function (5.17) ... 

A repeat of the above procedure, with the additional step, after the shift in the yield curve, of recalculating the bond cash flows based on a new inflation forecast. This produces a duration measure that is a function of the level of nominal yields. This measure is in effect an inflation duration, or the sensitivity to changes in market inflation expectations, which is a different measure to the real yield duration ... 

As described above, inflation-linked bonds allow to save investors from changes in the general level of prices. However, the indexation is not perfect creating a lag between the index prices and the adjustment to the bond cash flows. According to Deacon and Derry (2004) at the end of a bond s life there is no inflation protection, matched with an equal period before the issue in which the inflation compensation is paid. Figure 6.11 shows an example of indexation lag according to Deacon and Derry (2004). 

Z-spread is the spread over the zero-swap curve hy which the bond cash flows can be discounted to get the current market price... 

Carleton and Cooper (1976) describes an approach to estimating tetm structure that assumes default-free bond cash flows, payable on specified discrete dates, to each of which a set of unrelated discount factors are applied. These discount factors are estimated as regression coefficients, with the bond cash flows beir the independent variables and the bond price at each payment date the dependent variable. This type of simple linear regression produces a discrete discount fimction, not a continuous one. The forward-rate curves estimated from this fimction are accordir ly very ja ed. 

C, = the bond cash flow at time t P = the bonds fair price C = the annual coupon payment rm = the redemption yield n = the number of years to maturity... 

To provide precise protection against inflation, interest payments for a given period would need to be corrected for actual inflation over the same period. Lags, however, exist between the movements in the price index and the adjustment to the bond cash flows. According to Deacon and Derry (1998), such lags are unavoidable for two reasons. First, inflation statistics for one month are usually not known until well into the following month and are published some time after that. This causes a lag of at least one month, as shown in FIGURE 12.3. Second, in some markets the size of a coupon payment must be known before the start of the coupon period in... 

Index-Linked Bond Cash Flows and Yields... 

Yield has been defined in previous chapters as the discount rate that equates the sum of the present values of all a bonds cash flows to its observed market price. A vanilla bond, such as a U.S. Treasury, has m future cash flows—the coupon payments—each having a value C, equal to one-half the coupon rate applied to the face value. C , is the principal payment. The sum total of the bond s discounted cash flows is given by equation... 

The remaining bond cash flows are 5,125, on both July 21, 1994, and January 21, 1995, and 105.25, on July 21, 1995-January 21, 1995, however, is a Saturday, so the cash flow will not actually be received until Monday, January 23. The number of days between the value date. May 11, 1994, and the receipt of each cash flow is July 21, 1994 71 days... 

The discount rate used to derive the present value of a bonds cash flows is the interest rate that the bondholders require as compensation for the risk of lending their money to the issuer. The yield investors require on a bond depends on a number of political and economic factors, including what... 

As noted in Chapter 2, a Treasury bond can be seen as a bundle of individual zero-coupon securities, each maturing on one of the bonds cash flow payment dates. In this view, the Treasury s price is the sum of the present values of all the constituent zero-coupon bond yields. Assume that the spot rates for the relevant maturities—ri,r2,r, --rfj—can be observed. If a bond pays a semiannual coupon computed at an annual rate of C from period 1 to period N, its present value can be derived using equation (17.7). 

Put simply, the Z-spread is the basis point spread that would need to be added to the implied spot yield curve such that the discounted cash flows of the bond are equal to its present value (its current market price). Each bond cash flow is discounted by the relevant spot rate for its maturity term. How does this differ from the conventional asset-swap spread Essentially, in its use of zero-coupon rates when assigning a value to a bond. Each cash flow is discounted using its own particular zero-coupon rate. The bond s price at any time can be taken to be the market s value... 

The key to the discounted cash flow methods is the determination of a proper interest rate. For this, two factors must be known. One is how much does it cost to obtain money The second is what is a reasonable amount of profit to expect from a plant The first depends on the source of money. This can be corporation earnings, the sale of stock, the issuance of bonds, the selling of assets, or borrowing from some outside source. The second depends on economic conditions. 

Sources of finance for company acquisitions as mentioned above can be from reserves or maybe taken a senior or subordinated debt. Alternatively a bond may be issued with various characteristics offering an annuity, a balloon payment or a combination of the two. A variety of convertible structures have been utilized for this purpose as asset sales and the use of the target s balance sheet. There has also been a place for royalty transactions where the future-value of product cash flows are securitized to provide capital in the near term to achieve a company acquisition. 

Figure 6-1 shows the concept of cash flow for an overall industrial operation based on a support system serving as the source of capital or the sink for capital receipts. Input to the capital sink can be in the form of loans, stock issues, bond releases, and other funding sources including the net cash flow returned to the... 

The assumptions of this study are premised on the commitment to a multi trillion dollar, centralized H2 production and delivery system in the U.S. over a thirty-year time period. Therefore, it is believed that the capital structure assumptions of 30% equity capital and 70% debt are more realistic for the assumed scale of capital investments. In addition, there are cash flow benefits to financing capital budgeting projects with debt capital rather than equity capital because interest on debt is tax deductible whereas dividends payments are not. The 7% interest rate for 30-year coupon bonds is a reasonable assumption for the assumed scale of investments, particularly so if a national H2 plan is adopted with government regulation and guaranteed bond issues. 

Internal Rate of Return (IRR). This is a measure of how much improvement in cash flow results from the investment (project cost) as measured by a percent return. This is roughly equivalent to the interest rate that an investment would earn if invested in a bank or in bonds. A company usually has a measurement called a hurdle rate that defines the minimum acceptable rate that a profit-adding project must have before it is approved for expenditure. In many companies, this rate is the rate it... 

The asset swap is an agreement that allows investors to exchange or swap future cash flows generated by an asset, usually fixed rates to floating rates. It is essentially a combination of a fixed coupon bond and an IRS. We define it thus ... 

The zero-coupon curve is used in the asset-swap analysis, in which the curve is derived from the swap curve. Then, the asset-swap spread is the spread that allows us to receive the equivalence between the present value of cash flows and the current market price of the bond. 

As shown in Eigures 1.4 and 1.5, with this swap structuring, the asset-swap spread for HERIM is 39.5 bp and for TKAAV is 39.1 bp. These represent the spreads that will be received if each bond is purchased as an asset-swap package. In other words, the ASW spread provides a measure of the difference between the market price of the bond and the value of the cash flows evaluated using zero-coupon rates. 

Z-spread is an alternative spread measure to the ASW spread. This type of spread uses the zero-coupon yield curve to calculate the spread, in which in this case is assimilated to the interest-rate swap curve. Z-spread represents the spread needful in order to obtain the equivalence between the present value of the bond s cash flows and its current market price. However, conversely to the ASW spread, the Z-spread is a constant measme. 

A credit default swap (CDS) price provides fundamental credit risk information of a specific reference entity or asset. As explained before, asset swaps are used to transform the cash flows of a corporate bond for interest rate hedging purpose. Since the asset swaps are priced at a spread over the interbank rate, the ASW spread is the credit risk of the same one. However, market evidence shows that credit default swaps trade at a different level to asset swaps due to technical... 

We assume we have constructed a market curve of Libor discount factors where Df(t) is the price today of 1 to be paid at time t. From the perspective of the asset swap seller, it sells the bond for par plus accrued interest. The net up-front payment has a value 100 F where P is the market price of the bond. If we assume both parties to the swap are interbank credit quality, we can price the cash flows off the Libor curve. 

This is the observation that, due to demand and liquidity reasons, zero-coupon bonds sourced from the principal cash flow of a coupon bond trade at a lower yield than equivalent-maturity zero-coupon bonds sourced from the coupon cash flow of a conventional bond. 

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