Expected cash flows change

For securities that fall into the first category, a key factor determining whether the owner of the option (either the issuer of the security or the investor) will exercise the option to alter the security s cash flows is the level of interest rates in the future relative to the security s coupon rate. In order to estimate the cash flows for these types of securities, we must determine how the size and timing of their expected cash flows will change in the future. For example, when estimating the future cash flows of a callable bond, we must account for the fact that when interest... 

There are valuation models that can be used to value bonds with embedded options. These models take into account how changes in yield will affect the expected cash flows. Thus, when V and V+ are the values produced from these valuation models, the resulting duration takes into account both the discounting at different interest rates and how the expected cash flows may change. When duration is calculated in this manner, it is referred to as effective duration or option-adjusted duration or OAS duration. Below we explain how effective duration is calculated based on the lattice model and the Monte Carlo model. 

The prices used in equation (4.4) to calculate convexity can be obtained by either assuming that when the yield changes the expected cash flows either do not change or they do change. In the former case, the resulting convexity is referred to as modified convexity. (Actually, in the industry, convexity is not qualified by the adjective modified. ) In contrast, effective convexity assumes that the cash flows do change when yields change. This is the same distinction made for duration. 

The modified duration of a bond measures its price sensitivity to a change in yield. It is essentially a snapshot of one point in time. It assumes that no change in expected cash flows will result from a change in market interest rates and is thus inappropriate as a measure of the interest rate risk borne by a mortgage-backed bond, whose cash flows are affected by rate changes because of the prepayment effect. 

Effective duration is essentially approximate duration where P and P are obtained using a valuation model—such as a static cash flow model, a binomial model, or a simulation model—that incorporates the eflFect of a change in interest rates on the expected cash flows. The values of P and T, depend on the assumed prepayment rate. Generally analysts assume a higher prepayment rate when the interest rate is at the lower level of the two rates—interest and prepayment. 

It is not expected that significant improvement in collection rates for wholesale deliveries of electricity and natural gas can be achieved during a reasonable forecast period unless a significant change in collection rates and practices of handling cash flows takes place... 

This budget shows expected cash receipts as a result of selling goods or services and planned cash disbursements to pay the bills incurred by the pharmacy. Pharmacies prepare cash budgets to allow them to anticipate changes in cash flows over a period of time. 

The project team must detail all past costs that the project has incurred since its inception (start of EvP) on an annual basis. In addition, an annual project financial information table (ProFIT) data sheet should be presented. This sheet contains the revenue and cost forecasts for the upcoming ten-year period. It computes net present value (NPV) of future cash flows and return on capital employed (ROCE) automatically. At this stage, the team is expected to include detailed production costs data as well as estimates of plant costs (based on an engineering estimate, for example). The ten-year projection should be provided for three scenarios base, optimistic, and pessimistic. These cases are not meant to be simple percentage changes of the sales projections. Instead, the team should try to identify the drivers of the project s success and construct alternatives for the future that lead to different results for the project. The base case should be the most likely case. The optimistic scenario should be based on the positive development of some (not all) key success factors. The pessimistic scenario is usually the minimum feasible case, meaning a situation where the organization would still prusue the project, but some factors do not develop in a positive way. 

The fundamental value of a company, on the other hand, is the net present value of the expected future cash flows, discounted by the cost of capital (DCF). This only alters for the better or the worse if fundamental changes occur, for example if prices change, new technologies are introduced or the company achieves a breakthrough into new markets. 

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 ... 

A fundamental property is that an upward change in a bond s price results in a downward move in the yield and vice versa. This result makes sense because the bond s price is the present value of the expected future cash flows. As the required yield decreases, the present value of the bond s cash flows will increase. The price/yield relationship for an option-free bond is depicted in Exhibit 1.9. This inverse relationship embodies the major risk faced by investors in fixed-income securities—interest rate risk. Interest rate risk is the possibility that the value of a bond or bond portfolio will decline due to an adverse movement in interest rates. 

It is necessary to evaluate the profitability of proposed improvements to a process prior to obtaining approval to inclement changes. For one such process, the capital investment (end of year 0) for the project is 250,000. There is no salvage value. In years 1 and 2, you expect to generate an after-tax revenue from the project of 60,000/yr. In years 3-8, you expect to generate an after-tax revenue of 50,000/yr. Assume that the investments and cash flows are single transactions occurring at the end of the year. Assume an effective annual interest rate of 9%. 

We now evaluate the discounted cash flows for both options assuming the average expected change in demand and exchange rates over the next two periods. 

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