Interest rates determination

Step 3 Calculate the present value of the expected future cash flows found in Step 1 by the appropriate interest rate or interest rates determined in Step 2. 

The money used in a project must be returned by the project with interest whether it comes from debt or equity. The recent swings in the cost of money have brought to everyone s attention the complexity of setting return and interest rates for feasibility studies. If a project is ready to be built and the loans have been negotiated, the interest rate can be determined accurately. Establishing the interest rate for a feasibility study on a project that will not be built for one or more years in the future is difficult and becomes a policy decision that should be set by management. The same rate should be used on all studies to keep the yardstick the same length. 

When formulating a silicone adhesive, sealant, or coating, based on hydrosilylation addition cure, one must consider the following properties of the uncured product pot life, dispensing technique, rheology, extrusion rate, cure performance. These characteristics directly affect the processing properties of the polymer base or crosslinker parts. The degree of cure conversion at the temperature of interest is determined by properties such as tack free time, cure profile and cure time. Once... 

It is interesting to note that the hydrolysis of certain Schiff bases in weakly acidic solutions shows a similar mechanism (22). N-protonated substituted benzylidene-t-butylamines react with hydroxide ions to amino alcohols in the rate-determining step, and at lower pH the rate is almost entirely determined by attack of water on the protonated Schiff bases as a consequence of the rapidly decreasing concentration of hydroxide ions. 

During the next fifty years the interest in derivatives of divalent carbon was mainly confined to methylene (CHg) and substituted methylenes obtained by decomposition of the corresponding diazo compounds this phase has been fully reviewed by Huisgen. The first convincing evidence for the formation of dichlorocarbene from chloroform was presented by Hine in 1950. Kinetic studies of the basic hydrolysis of chloroform in aqueous dioxane led to the suggestion that the rate-determining step was loss of chloride ion from the tri-chloromethyl anion which is formed in a rapid pre-equilibrium with hydroxide ions ... 

The selection of the discount factor depends on the financial policy of the business, but is usually 2-3 per cent above the current interest rates. Use of discounting methods will determine whether the project cost will produce a better return than by simply investing the capital involved at the highest compound interest rate or, if the capital cost has to be borrowed, whether the rate of return is much higher than the cost of borrowing. 

It was of interest to determine whether glycosides of 6-deoxy-D-xylo-hex-5-enopyranose were susceptible to enzyme hydrolysis by / -glucosi-dase. Since aromatic glucosides are hydrolyzed by this enzyme at a much faster rate than aliphatic glycosides, phenyl 6-deoxy-/ -D-rt/Zo-hex-5-enopyranoside (18) was prepared (20). Phenyl / -D-glucopyranoside was converted to the 6-tosylate by selective esterification and then, by conventional procedures, transformed to phenyl 2,3,4-tri-0-acetyl-6-deoxy-... 

The silver(II) oxidation of dithionate " is of interest because this reductant is rather inert and oxidation is often preceded by rate-determining disproportiona-... 

Johans et al. derived a model for diffusion-controlled electrodeposition at liquid-liquid interface taking into account the development of diffusion fields in both phases [91]. The current transients exhibited rising portions followed by planar diffusion-controlled decay. These features are very similar to those commonly observed in three-dimensional nucleation of metals onto solid electrodes [173-175]. The authors reduced aqueous ammonium tetrachloropalladate by butylferrocene in DCE. The experimental transients were in good agreement with the theoretical ones. The nucleation rate was considered to depend exponentially on the applied potential and a one-electron step was found to be rate determining. The results were taken to confirm the absence of preferential nucleation sites at the liquid-liquid interface. Other nucleation work at the liquid-liquid interface has described the formation of two-dimensional metallic films with rather interesting fractal shapes [176]. 

Kinetics of chemical reactions at liquid interfaces has often proven difficult to study because they include processes that occur on a variety of time scales [1]. The reactions depend on diffusion of reactants to the interface prior to reaction and diffusion of products away from the interface after the reaction. As a result, relatively little information about the interface dependent kinetic step can be gleaned because this step is usually faster than diffusion. This often leads to diffusion controlled interfacial rates. While often not the rate-determining step in interfacial chemical reactions, the dynamics at the interface still play an important and interesting role in interfacial chemical processes. Chemists interested in interfacial kinetics have devised a variety of complex reaction vessels to eliminate diffusion effects systematically and access the interfacial kinetics. However, deconvolution of two slow bulk diffusion processes to access the desired the fast interfacial kinetics, especially ultrafast processes, is generally not an effective way to measure the fast interfacial dynamics. Thus, methodology to probe the interface specifically has been developed. 

Proteins may be covalently attached to the latex particle by a reaction of the chloromethyl group with a-amino groups of lysine residues. We studied this process (17) using bovine serum albumin as a model protein - the reaction is of considerable interest because latex-bound antigens or antibodies may be used for highly sensitive immunoassays. The temperature dependence of the rate of protein attachment to the latex particle was unusually small - this rate increased only by 27% when the temperature was raised from 25°C to 35°C. This suggests that non-covalent protein adsorption on the polymer is rate determining. On the other hand. the rate of chloride release increases in this temperature interval by a factor of 17 and while the protein is bound to the latex particle by only 2 bonds at 25°C, 22 bonds are formed at 35°C. 

Economic analysis can determine the discounted profitability criteria in terms of payback period (PBP), net present value (NPV), and rate of return (ROR) from discounted cash flow diagram, in which each of the annual cash flow is discounted to time zero for the LHS system. PBP is the time required, after the construction, to recover the fixed capital investment. NPV shows the cumulative discounted cash value at the end of useful life. Positive values of NPV and shorter PBP are preferred. ROR is the interest rate at which all the cash flows must be discounted to obtain zero NPV. If ROR is greater than the internal discount rate, then the LHS system is considered feasible (Turton et al., 2003). 

The maximum amount your roommate would pay would be determined by his alternate sources of financing. If he could get a loan from a bank it would be at an interest rate of 8% or more. A loan from a finance agency would cost more. At 8% interest compounded annually 13,500 would be worth 23,100 after 7 years. To request that he pay you 23,100 on his twenty-fifth birthday in return for giving him 13,500 now would certainly be fair-especially if he let you use the car and if an ironclad Hen could be placed on his inheritance. 

The federal government requires that the nominal interest rate be stated by each lender. Example 10-8 shows how to determine an equivalent yearly interest rate when the period of compounding is less than a year. 

In the life insurance annuity a person contributes equal amounts over a number of years, and then at a given age (assuming he has not died previously) he receives a lump sum of money or some other form of payment. To determine how this compares with other forms of investment, the investor must determine at what interest rate his money would need to be invested in order to earn that lump sum in the same period of time. The first payment would earn compound interest for n periods. The second payment, which is made at the end of the first period, would earn interest for (n - 1) periods. The general rule is that each payment earns interest for one less period than the proceeding one. This can be expressed as... 

After the net present value has been determined, what does it mean Is 800,000 a good, average, or poor value If the net present value is positive we know the plant is making more profit than if the capital were invested at the interest rate used. But how much higher—1%—2%—10% The only way of knowing is to determine the interest rate that gives a net present value of zero. This interest rate is known as the rate of return. Some companies use the rate of return to determine the optimum investment. The project with the largest return is considered the best. This is also known as the yield on investment method. 

Where the calculation of the net present value was straightforward, die determination of the rate of return requires a trial-and-error procedure. An interest rate is chosen and then the net present value is determined. If it is not zero, another interest rate is chosen and the net present value is recalculated. This is continued until a zero net present value is obtained. 

In Example 10-17 the net present value for plant 1 is zero at an interest rate of 20%. So this is the rate of return. The return for plant 2 is 23.5%. This indicates that plant 2 is superior to plant 1. This method gives a single answer that does not require the advance choice of an interest rate. This means, for Example 10-17, that the Net Present Value method would give a different answer than the Rate of Return method if an interest rate of 5% were used to determine the former. 

This method can be generalized. Two alternatives can be compared by determining the rate of return of the difference between the cash flows of each plant. The cash flow for any period of time is the income minus the expenses. This will give the crossover interest rate above which one plant is best and below which the other is best. 

Whenever two or more rates of return are obtained, the net present value should be determined over a range of reasonable interest rates. Table 10-10 gives these for Example 10-20. 

Upon decreasing the bond sales in Example 10-20 by 100,000, two interest rates greater than zero would be obtained for which the net present value is zero. This would indicate that as long as the interest rate is not between die two values the project should be accepted. Other examples could be constructed where only if the interest rate is between the limits should it be accepted. There also could be more than two points, or no points, where the net present value is zero. If there are incomes and expenses over 8 years the equation that determines the rate of return has 8 roots. Theoretically all, some, or none of these could be positive. 

Some writers claim that an advantage of the Rate of Return method is that no interest rate needs to be chosen. It has already been illustrated that this is not true. The difference in the two measures is when, not whether, a reasonable interest rate is chosen. With the Rate of Return method it does not need to be chosen until after the rate of return is obtained. If it is too high and two processes are both found acceptable, then the net present value must be calculated to determine which is best. In doing this the interest rates for proceeds and outlays may be different. 

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. 

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