Cash flows yield

Discounted Cash-Flow Rate (DCFR) or Discounted Cash-Flow Yield... 

There are several yield measures commonly quoted by dealers and traders in the bond market. Among the more prominent are current yield, yield to maturity, yield to call, yield to worst, and cash flow yield. In this section, we will demonstrate how to compute various yield measures for a bond given its price. We will also highlight their limitations as measures of potential return. 

A yield can be calculated given the projected cash flows based on an assumed prepayment rate. The yield is the interest rate that will make the present value of the assumed cash flows equal to the clean price plus accrued interest. A yield calculated in this manner is called a cash flow yield. 

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. 

Cash flow yield calculated in this way is essentially a redemption yield calculated assuming a prepayment rate to project the cash flows. As such, it has the same drawbacks as the redemption yield for a plain vanilla bond it assumes that all the cash flows will be reinvested at the same interest rate and that the bond will be held to maturity. In fact, the potential inaccuracy is even greater for a mortgage-backed bond because the frequency of interest payments is higher, which makes the reinvestment risk greater. The final yield of a mortgage-backed bond depends on the performance of the mortgages in the pool—specifically, their prepayment pattern. 

Given the nature of a mortgage-backed bond s cash flows, its exact yield cannot be calculated. Market participants, however, commonly compare an MBS s cash flow yield to the redemption yield of a government bond with a similar duration or a term to maturity similar to the MBS s average life. The usual convention is to quote the spread over the government bond. 

The OAS-derived yield spread is based on the present values of expected cash flows discounted using government bond—derived forward rates. The spread berween the cash flow yield and the government bond yield is based on yields to maturity. The OAS spread is added to the entire yield curve, whereas a yield spread is over a single point on the government bond yield curve. For these reasons, the two spreads are not strictly comparable. 

Applying two important tax credits would improve the early years cash flow and shorten the payback period. A 10% investment tax credit and a 10% energy tax credit applied to the incremental capital costs for the expanders yields nearly 1.0 million additional first-year cash... 

Whatever problems arise, the farmer needs to plan well ahead, and analyse possible scenarios under conversion that encompass changes, including the use of existing resources, the need for investments, possible changes in yields and total productivity, availability of labour and machinery, accessibility to markets and likely output prices and cash flow. 

This discount factor, dnis the amount that would yield one dollar after n years if invested at an interest rate of i The discounted-cash-flow rate of return can be determined by the trial-and-error method illustrated in Table 1, where the annual cash flows are discounted by the appropriate discount factor to a total present value equal to the necessary initial investment. ... 

Add the after-tax income to the depreciation for the year, yielding the cash flow. 

This factor finds the equivalent present value, F, of a single future cash flow, F, occurring at n periods in the future when the interest rate is /% per period. Note that this factor is the reciprocal of the compound amount factor (single payment). For example, what amount would you have to invest now to yield 2829 in nine years if the interest rate were 10% ... 

A more complex exeunple would consider the investment yielding the four-year stream of cash flows illustrated in the discussion on cash flow profiles. What rate of return would equate the — 6000... 

To illustrate, consider a uniform cash flow of 1000 per year beginning at some uncertain time m and continuing for a duration of t years. The delay to initiation is uniformly distributed between 6 months and 1 year. The project duration is gamma distributed with mean of 3 years and standard deviation of 1 year the parameters of the gamma distribution yielding these statistics are a = 3 and b = 9. The nominal interest rate is 10% compounded continuously. It is assumed that the initiation time and project dmation are independent random variables. Our problem is to determine the equivalent present value of these cash flows. (This problem is taken from Park and Sharp-Bette (1990, p. 411)... 

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. 

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. 

From market observation we know that index-linked bonds can experience considerable volatility in prices, similar to conventional bonds, and therefore, there is an element of volatility in the real yield return of these bonds. Traditional economic theory states that the level of real interest rates is cmistant however, in practice they do vary over time. In addition, there are liquidity and supply and demand factors that affect the market prices of index-linked bonds. In this chapter, we present analytical techniques that can be applied to index-linked bonds, the duration and volatility of index-linked bonds and the concept of the real interest rate term structure. Moreover, we show the valuation of inflation-linked bonds with different cash flow structures and embedded options. 

In the traditional approach the duration value is calculated using nominal cash flows, discounted at the nominal yield. A more common approach is to assume a constant average rate of inflation, and adjust cash flows using this inflation rate. The real yield is then used to discount the assumed future cash... 

As above, assuming a constant average inflation rate, which is then used to calculate the value of the bond s coupon and redemption payments. The duration of the cash flow is then calculated by observing the effect of a parallel shift in the zero-coupon yield curve. By assuming a constant inflation rate and constant increase in the cash flow stream, a further assumption is made that the parallel shift in the yield curve is as a result of changes in real yields, not because of changes in inflation expectations. Therefore, this duration measure becomes in effect a real yield duration ... 

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 ... 

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