Reference rate future values

The future worth (FW) method is comparable to the present worth method except that the comparison between the project s estimated expenditures and benefits occurs at a reference time called the future (t = F). As in present worth analysis, in future worth analysis a project is acceptable at a particular interest rate if the future value of the revenues and other benefits exceeds the future value of the expenses. Likewise, the preferred alternative, given equal future benefits, would be the alternative with the lowest future costs. 

An economic analysis generally involves more imcertain-ties than a thermodynamic analysis. In the above discussion, it has been assumed that each variable in the eco-norrric analysis is known with certainty. However, many values used in the calcirlation are uncertain. A sensitivity artalysis determines by how much a reasonable range of uncertainty assiuned for each uncertain variable affects the frrral decision. Sensitivity studies are recommended to irrvestigate the effect of major assmnptions about values referring to future years (e.g., cost of money, inflation rate, and escalation rate of fuels) on the results of an economic analysis. 

Because the future values for the reference index are not known, it is not possible to calculate the redemption yield of an FRN. On the coupon-reset dates, the note will be priced precisely at par. Between these dates, it will trade very close to par, because of the way the coupon resets. If market rates rise between reset dates, the note will trade slightly below par if rates fall, it will trade slightly above par. This makes FRNs behavior very similar to that of money market instruments traded on a yield basis, although, of course, the notes have much longer maturities. FRNs can thus be viewed either as money market instruments or as alternatives to conventional bonds. Similarly, they can be analyzed using two approaches. 

If a chemical composition or a product quality variable cannot be measured on-line, it may be possible to predict it from measured process variables, such as flow rates, temperatures, and pressures. When the predictions are used for feedback control, this strategy is referred to as inferential control (see Chapter 16). On-line prediction of future values of controlled variables based on a dynamic model is a key element of a widely used, advanced control strategy model predictive control (see Chapter 20). 

What we have calculated is the present value (at a particular reference date) of a future sum of money, using a specified discount rate. In any discounting calculation, it is important to quote the reference date and the discount rate. 

Whether the presence of scar and/or the amount of scar is predictive of SCD is yet to be determined. In a study of 48 patients with CAD who were referred for EP study, infarct size was compared with LVEF, with respect to their correlation with induciblity on EP study (91). They found that patients with sustained, mono-morphic VT had larger infarcts than patients who did not have inducible arrhythmias, and patients with polymorphic VT or VF had intermediate infarct masses. Infarct mass and surface area were better predictors of inducibility of monomorphic VT than LVEF. The study was limited by its small sample size, but demonstrates that scar burden on MRI may correspond to inducibility on EP study. However, while inducibility on EP study is helpful in risk stratification of SCD, as discussed earlier even patients with a negative EP study have a high rate of future SCD. Thus, the true value of delayed enhancement MRI would be to demonstrate risk stratification beyond that of conventional methods. 

The interest rate required to induce the investor to permit his or her money to be used is referred to as the opportunity cost of capital. The value today (e.g., 95.23) of money promised for delivery sometime in the future (e.g., 100), evaluated at the opportunity cost of capital (e.g.,... 

We will refer to the present value of 1 to be received in period t as the forward discount factor. In our calculations involving swaps, we will compute the forward discount factor for a period using the forward rates. These are the same forward rates that are used to compute the floating-rate payments—those obtained from the EURIBOR futures contract. We must make just one more adjustment. We must adjust the forward rates used in the formula for the number of days in the period (i.e., the quarter in our illustrations) in the same way that we made this adjustment to obtain the payments. Specifically, the forward rate for a period, which we will refer to as the period forward rate, is computed using the following equation ... 

Two sets of experiments have been carried out. In the first set of experiments, the background fluidization velocity was kept constant, while the amount of secondary gas added or extracted via the membranes was varied. In the second set of experiments, the amount of secondary gas added/ extracted via the membranes was varied, while simultaneously the background fluidization velocity was adjusted so that the outlet flow rate remained constant (see Table 4.7). Measurement 1 is the reference case, without in- or outflow via the membranes. Although the fluxes of gas through permselective membranes are much smaller than the cases used in this study, these values were chosen to emphasize the efiect of permeation and to anticipate future improvements in membrane performance. On the other hand, the selected permeation cases are much more realistic for the nonselective porous membranes. 

When thinking about capital costs, it is important to think about a concept sometimes referred to as the present value of money or the opportunity cost of money. This fluctuates based upon inflation and interest rates. Let s think about it with a very simple example. Imagine that if you spent 100, you could build a plant that could generate 120 beyond cost in ten years. You might consider a profit of 20 to be attractive. This is a 20% return on your initial 100. However, you need to remember that because you spent the 100, it was not available for other investments. Had you been able to invest the money in a bond paying 7.2% interest, at the end of ten years, you would have 200. So by investing in a plant and making 20, you have lost the opportunity to make 100 profit in a bond. You have effectively lost 80 in opportunity cost. This example is oversimplified and needs to reflect current interest rates as well as risks both with alternative investments and with investments for the project, but serves to illustrate that a dollar in the present is more valuable than a dollar in the future. This needs to be factored into a detailed cost estimate. 

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