Internal return rate

Internal Return Rate. Another rate criterion, the internal return rate (IRR) or discounted cash flow rate of return (DCERR), is a popular ranking criterion for profitabiUty. The IRR is the annual discounting rate that makes the algebraic sum of the discounted annual cash flows equal to zero or, more simply, it is the total return rate at the poiat of vanishing profitabiUty. This is determined iteratively. 

The internal return rate (IRR), a fixed point on the diagram, caimot be viewed as a measure of profitabihty, which should vary with the cost of capital (discount rate). Because the curvature of the total return curve caimot be predicted from the single IRR point, there is no way that the IRR can be correlated with profitabihty at meaningful discount rates. Even both end points, ie, the IRR and the total return at zero discount rate, are not enough to predict the curvature of the total return curve. 

Internal return rate. The internal return rate (IRR), also known as the discounted cash flow return rate, is the iteratively calculated discounting rate that would make the sum of the annual cash flows, discounted to the present, equal to zero. As shown in Figure 2, the IRR for Project Chem-A is 38.3%/yr. 

Internal reflection, 24 111-112 Beer s law expression for, 24 113 Internal resistance, batteries, 3 410 Internal return rate (IRR), 9 544-545 Internal sizing, in paper manufacture, 18 109-113... 

NPV (6 years) Internal return rate Payback period Saved CO2 eq. emissions... 

One economic evaluation method that is used is based on the internal return rate (IRR), which is considered suitable for an initial estimate of economic feasibility of industrial processes (Di Lucdo et al, 2002). This method is based on evaluating the discount rate that causes the present value of the cash flow, projected for the plant life, to be equal to the invested capital. The basic idea for the IRR evaluation is to obtain a single value that synthesizes the merits of the project for its lifetime. This value is not determined by market interest rates, and hence it is labelled internal return rate. The IRR is intrinsic to the project and does not depend on anything but the project cash flow. 

The method is based on the calculation of the so-called net present value (NPV) of the investment and it requires an estimation of the effect of the discount rate (DR) on this value. The DR when NPV = 0 is the expected internal return rate (IRR). 

Fig. 3. Profitabihty diagram for Venture A. (a) Simple diagram. NRR is net return rate IRR, the internal rate of return, is a given fixed point, (b) Three NRR cutoff lines for Venture A where B, C, and D represent NRR values of 15, 10, and 5%/yr, respectively. For example, at a discount rate of 10% per year, the NRR cutoff for Venture A could be as high as 10.74% per year for marginal acceptance (point X). Acceptable levels are to the left of NRR cutoff...

Neopentyl (2,2-dimethylpropyl) systems are resistant to nucleo diilic substitution reactions. They are primary and do not form caibocation intermediates, but the /-butyl substituent efiTectively hinders back-side attack. The rate of reaction of neopent>i bromide with iodide ion is 470 times slower than that of n-butyl bromide. Usually, tiie ner rentyl system reacts with rearrangement to the /-pentyl system, aldiough use of good nucleophiles in polar aprotic solvents permits direct displacement to occur. Entry 2 shows that such a reaction with azide ion as the nucleophile proceeds with complete inversion of configuration. The primary beiuyl system in entry 3 exhibits high, but not complete, inversiotL This is attributed to racemization of the reactant by ionization and internal return. 

The kinetic method of determining relative acidity suffers from one serious complication, however. This complication has to do with the fate of the ion pair that is formed immediately on removal of the proton. If the ion pair separates and difiuses into the solution rapidly, so that each deprotonation results in exchange, the exchange rate is an accurate measure of the rate of deprotonation. Under many conditions of solvent and base, however, an ion pair may return to reactants at a rate exceeding protonation of the carbanion by the solvent. This phenomenon is called internal return ... 

The differences in rate for the two positions of naphthalene show clearly that an additional-elimination mechanism may be ruled out. On the other hand, the magnitude of the above isotope effect is smaller than would be expected for a reaction involving rate-determining abstraction of hydrogen, so a mechanism involving significant internal return had been proposed, equilibria (239) and (240), p. 266. In this base-catalysed (B-SE2) reaction both k and k 2 must be fast in view of the reaction path symmetry. If diffusion away of the labelled solvent molecule BH is not rapid compared with the return reaction kLt a considerable fraction of ArLi reacts with BH rather than BH, the former possibility leading to no nett isotope effect. Since the diffusion process is unlikely to have an isotope effect then the overall observed effect will be less than that for the step k. ... 

The lack of a substrate isotope effect suggests very extensive internal return and is readily explained in terms of the fact that conversion of the hydrocarbon to the anion would require very little structural reorganisation. Since koba = k 1k 2/(kLl+k 2) and k 2 is deduced as > k2, then kobs = Kk 2, the product of the equilibrium constant and the rate of diffusion away of a solvent molecule, neither of the steps having an appreciable isotope effect. If the diffusion rates are the same for reactions of each compound then the derived logarithms of partial rate factors (above) become pAT differences between benzene and fluorobenzene hydrogens in methanol. However, since the logarithms of the partial rate factors were similar to those obtained with lithium cyclohexylamide, a Bronsted cor-... 

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). 

Hardy effect.248-249 The internal return part of the ionization equilibrium is particularly hard to detect since it is almost completely independent of the concentration of anything in the bulk of the solution outside of the solvent cage. The extent of internal return will depend on the reactivity of the cage walls and their resistance to the escape of either ion. Unless internal return has been eliminated by the use of an extremely reactive cage wall, the measured rate is not that of the ionization but the lesser rate of ion pair dissociation. In the case of the acetolysis of a, a-dimethylallyl chloride (XXXIX), internal return is detectable by virtue of the fact that the chloride ion can return to either of two allylic carbon atoms.248... 

Another detectable example of internal return is afforded by the solvolysis of xo-norborriylbromobenzenesulfonate (XL) it racemizes from 40 to 240% faster than it produces bromobenzenesulfonic acid, yet both reactions are strictly first order. The racemization reaction is kinetically independent of bulk bromobenzenesulfonate concentration but its rate is dependent on the nature of the solvent, pyridine being less effective than alcohol, acetic acid, or aqueous acetone.238 The behavior of 3-phenyl-2-butyl- -toluenesulfonate is similar.250... 

We have examined the competing isomerization and solvolysis reactions of 1-4-(methylphenyl)ethyl pentafluorobenzoate with two goals in mind (1) We wanted to use the increased sensitivity of modern analytical methods to extend oxygen-18 scrambling studies to mostly aqueous solutions, where we have obtained extensive data for nucleophilic substitution reactions of 1-phenylethyl derivatives. (2) We were interested in comparing the first-order rate constant for internal return of a carbocation-carboxylate anion pair with the corresponding second-order rate constant for the bimolecular combination of the same carbocation with a carboxylate anion, in order to examine the effect of aqueous solvation of free carboxylate anions on their reactivity toward addition to carbocations. 

The ion-pair intermediate must undergo internal return to reactant at a rate... 

The rate data were analyzed by assuming Equation 6.17. In this equation kt is the titrametric rate constant for product formation, ks is the solvent-assisted ionization constant, and FkA is the fraction of the aryl-assisted rate constant that gives rise to product (as opposed to the fraction that gives starting material through internal return). 

In the simplest type of bond homolysis, where only one bond breaks, as with a dialkyl peroxide, cage recombination simply regenerates the starting compound and hence is the radical analog of internal return in ionizations.97 Equation 9.38 illustrates this process the bar over the radical pair is the symbol for its caged nature. The effect of the internal return is simply to lower the rate of... 

If a carbanion is thermodynamically accessible, but is subject to rapid quenching by internal return of C02 in the case of decarboxylation, or by a proton in carboxylation, or in a hydrogen/deuterium exchange reaction, then the carbanionic intermediate off the enzyme would give the appearance of greater basicity than its thermodynamic value would predict. The localized character of the carbanion at the 6-position of UMP requires that the proton that is removed by a base in solution initially remains closely associated, and therefore, to a great extent be transferred to the carbanion. This reduces the rate of exchange and creates a discrepancy between kinetic and thermodynamic acidities. 

By examination of the stereochemical consequences of decarboxylation, Cram and Haberfield8 obtained evidence for internal return of carbon dioxide to the carbanion, affecting the stereochemical outcome of these reactions. It is reasonable to consider that the barrier for the combination of the carbanion and carbon dioxide may be comparable to or lower than that for diffusion, in which case the reverse reaction will be a kinetically significant component in the overall rate of reaction. In such a case, a catalyst cannot deal with the direction of the reaction -if it lowers the transition state energy for the forward reaction, conservation of energy demands that it also lower the barrier for the reverse reaction. The energy for addition of the carbanion to carbon dioxide is also inherent. The reaction should occur readily if the reaction partners have reduced entropy. 

We can consider decarboxylation reactions in terms that are analogous to those in proton transfer reactions the reactivity of the carbanion in carboxylation reactions is analogous to internal return observed in proton transfer reactions from Bronsted acids. Kresge61 estimated that the rate constant for protonation of the acetylide anion, a localized carbanion (P A 21), is the same as the diffusional limit (1010 M s1). However, achieving this rate is highly dependent on the extent of localization of the carbanion. Jordan62 has shown that intermediates in thiazolium derivatives are also likely to be localized carbanions, which implies that protonation of these intermediates could occur at rates approaching those of other localized carbanions. 

We have presented evidence that pyrrole-2-carboxylic acid decarboxylates in acid via the addition of water to the carboxyl group, rather than by direct formation of C02.73 This leads to the formation of the conjugate acid of carbonic acid, C(OH)3+, which rapidly dissociates into protonated water and carbon dioxide (Scheme 9). The pKA for protonation of the a-carbon acid of pyrrole is —3.8.74 Although this mechanism of decarboxylation is more complex than the typical dissociative mechanism generating carbon dioxide, the weak carbanion formed will be a poor nucleophile and will not be subject to internal return. However, this leads to a point of interest, in that an enzyme catalyzes the decarboxylation and carboxylation of pyrrole-2-carboxylic acid and pyrrole respectively.75 In the decarboxylation reaction, unlike the case of 2-ketoacids, the enzyme cannot access the potential catalysis available from preventing the internal return from a highly basic carbanion, which could be the reason that the rates of decarboxylation are more comparable to those in solution. Therefore, the enzyme cannot achieve further acceleration of decarboxylation. In the carboxylation of pyrrole, the absence of a reactive carbanion will also make the reaction more difficult however, in this case it occurs more readily than with other aromatic acid decarboxylases. 

When R—X is enantiomerically enriched exo-2-norbornyl 4-bromobenzenesulfonate (brosylate), 1 in Fig. 4.5, and SOH is aqueous ethanol, for example, solvolysis is accompanied by racemisation. However, the rate of racemisation is faster than the rate of product formation, and starting material isolated before completion of the solvolysis is partially racemised [14]. The most economical interpretation of these results (and much other evidence, see Chapter 7) is that R+ X- includes the achiral nonclassical carbenium ion (3 in Fig. 4.5), and the ion pair undergoes internal return faster than nucleophilic capture. In other words, k- > k2 in Scheme 4.4, the precise value of the ratio k- lk2 depending upon the particular solvent, and the greater this ratio, the closer the initial reversible process approaches a pre-equilibrium. 

In contrast, when R—X in Scheme 4.4 is enantiomerically enriched endo-2-norbornyl brosylate (2 in Fig. 4.5) under the same reaction conditions, solvolysis is still accompanied by racemisation, but the rate of racemisation is identical with that of product formation [14]. The achiral carbocation in this reaction, therefore, is captured by solvent much faster than it can undergo internal return, i.e. k2 i in Scheme 4.4. In this case, therefore, the initial ionisation is the rate-determining step. 

A detailed and elegant study of the SnI solvolysis reactions of several substituted 1-phenylethyl tosylates in 50% aqueous TEE has enabled the rates of (1) separation of the carbocation-ion pair to the free carbocation, (2) internal return with the scrambling of oxygen isotopes in the leaving group, (3) racemization of the chiral substrate that formed the carbocation-ion pair, and (4) attack by solvent to be determined.122... 

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