Profit expected

They suggested that each project should pay an insurance premium i to guarantee the expected profits. The magnitude of b is proportional to the amount of capital to be risked. It is also a function of the degree of risk involved. Working capital and capital for auxiliary facilities are assumed to be risk-free. Thus, the risk rate is applied only to the fraction of the capital investment hkely to be lost it the project is unexpectedly terminated. 

Compute the number of items x to be manufactured that maximizes the expected profit. 

The return on investment is the expected profit divided by the total capital invested. This is the percentage return that an investor may expect to eventually earn on his money. Since the federal corporate income tax rate is around 48% on all profits, it must be stated whether the profit is the before- or after-tax earnings. 

Optimization techniques are procedures to make something better. Some criteria must be established to determine whether something is better. The single criterion that determines the best among a number of alternatives is referred to as the performance index or the objective function. Economically, this is the expected profit for a plant design. It may be expressed as the net present value of the project. 

One-phase optimization Maximize expected profit across one or multiple price scenarios. This approach corresponds to the classical expect value maximization known from decision theory. 

Two-phase optimization Maximize expected profit across multiple price scenarios subject to the constraint that a given minimum profit value is reached. From a practical point of view, this approach seems to be more appropriate in situations where a high variability of profit can be expected and the risk of low profit outcomes shall be minimized. 

The expected profit determines the average profit across all price scenarios weighted with their scenario probability. The expected profit function can be defined as follows ... 

The expected profit across multiple scenarios provides a more realistic picture of the future profit situation compared to one single scenario. However, scenarios are consolidated and averaged in one total number with their probability weights. The planner would have no information about potential worst case profits as a profit basis and might like to sacrifice expected profit opportunities for safety in exchange. This is addressed by the two-phase optimization approach. 

This first phase determines the best minimum profit z from all scenarios. zmm is then fixed as baseline profit z""" for the second phase of the optimization, during which the expected profit zcxp is maximized across all scenarios given the constraint that each scenario profit zo reaches the minimum scenario profit z""M". 

Fig. 102 shows the numerical results. The results of the first period are indexed at 100 in order to compare the results of the subsequent periods compared the first period. Results of the one-phase optimization strategy are relatively constant sales quantities and expected profits slightly below the index level of 100. Executing this plan can lead to very positive best-case scenario profits but also to very negative profits, if the worst-case price scenario occurs. 

Less extreme plans can be reached with the two-phase optimization strategy compared to the one-phase optimization approach scenario profits are nearer by and the worst case scenario is comparably better than in the one-phase-optimization strategy. The overall plan in sales, production and procurement is more cautious with lower sales quantities and lower expected profits as the pay-off for better minimum profits. 

Fig. 103 shows all scenario profits in the one-phase and the two-phase optimization case as well as the sales quantity index the two-phase optimization results do not disperse as strong as the one-phase-optimization. Besides, the worst case scenario is comparably better than the worst case scenario of the one-phase-optimization strategy. The plan is more cautious supply quantities are reduced leading to lower expected profits but better minimum profits in the worst case scenario. Although robustness is not measured it get s visible in the numerical tests for the 2-phase optimization approach. 

The first approach adopts the classical Markowitz s MV model to handle randomness in the objective function coefficients of prices, in which the expected profit is maximized while an appended term representing the magnitude of operational risk due to variability or dispersion in price, as measured by variance, is minimized (Eppen, Martin, and Schrage, 1989). The model can be formulated as minimizing risk (i.e., variance) subject to a lower bound constraint on the target profit (i.e., the mean return). 

The model is subject to the same set of constraints as the deterministic model, with 0i as the risk trade-off parameter (or simply termed the risk factor) associated with risk reduction for the expected profit. 0j is varied over the entire range of (0, oo) to generate a set of feasible decisions that have maximum return for a given level of risk, which is equivalent to the efficient frontier portfolios for investment applications. 

Tables 6.3-6.5 show the computational results for Risk Model II over a range of values of risk parameter 02 with respect to different recourse penalty costs, for three representative cases of 0 = 1E — 10, IE — 7, and 1.55E — 5, respectively. An example of the detailed results is presented in Table 6.6 for 02 = 50 of the first case. Figure 6.2 illustrates the corresponding efficient frontier plot for Risk Model II while Figure 6.3 provides the plot of the expected profit for different levels of risk.

Although increasing 02 with fixed value of 0 corresponds to decreasing expected profit, it generally leads to a reduction in expected production shortfalls and surpluses. Therefore, a suitable operating range of 02 values should be selected to achieve a proper trade-off between expected profit and expected production feasibility. Increasing 02 also reduces the expected deviation in the recourse penalty costs under different scenarios. This, in turn, translates to increased solution robustness. In that sense, the selection of 0j and 02 values depends primarily on the policy adopted by the decision maker. 

In general, the coefficients of variation decrease with smaller values of 02. This is definitely desirable since it indicates that for higher expected profits there is diminishing uncertainty in the model, thus signifying model and solution robustness. It is also observed that for values of 02 approximately greater than or equal to 2, the coefficient of variation remain at a static value of 0.5237, thus indicating overall stability and a minimal degree of uncertainty in the model. 

Note Trial solutions for 0 < 0.000001 are not considered since improvement in expected profit is not anticipated based on trends in computed values. 

Operational risk factor 82 Optimal objective value Expected variation in profit V(z0)(E + 8) Expected total unmet demand/ production shortfall Expected total excess production/ production surplus Expected recourse penalty costs Es Expected variation in recourse penalty costs Vs Expected profit E[z0] f = E[ o] - Es c. a... 

Figure 6.3 Risk Model II plot of expected profit for different levels of risk as represented by the economic risk factor 0n and the operational risk factor 02.

From Table 6.7 and the corresponding efficient frontier plot in Figure 6.4, similar trends to Risk Model II (and also the expected value models) are observed in which decreasing values of 0 correspond to higher expected profit until a certain constant profit value is attained ( 81 770). The converse is also true in which a constant profit of 59330 is reached in the initially declining expected profit for increasing values of 0i. 

In his influential study of almost a thousand inventions in four different industries, Schmookler (1966) argued that expected profitability of inventive activity, which depends to an important extent on market size, determines the pace and direction of industrial innovation. 

Removing profit would lead to the right conclusion, analytically, but what advice does it give decision makers If economic profits are indeed positive, but the decision on whether or not to permit firms to develop and introduce a new product is based on AWP less above-normal profits, more products will be judged to be effective than if AWP had been used. But if firms are in fact reimbursed at AWP, their expected profit from investment in R D will rise. The products firms are thus induced to develop because of the excess profits may not be efficient, and, from the standpoint of economic efficiency, they should not be produced. Yet the price signals will be telling firms to invest. Some method will need to be found to resolve this conflict. Efficient decisions based on correct cost-effectiveness analysis may well conflict with the price signals that may follow for implementation of those decisions. This is an issue for both country U and country T. 

This situation would represent an improvement over the preceding case. More products that are efficient to introduce would be introduced, and the overall rate of use would increase close to Q (Reinhardt, Chapter 2). Since overall expected profits would be set at the breakeven level, there should be less of an incentive for firms to overinvest in them. However, it would be unlikely that things would turn out exactly right. 

The project portfolio enables an overview on the ongoing research activities. Numerous economic and technical parameters have been proposed to provide a meaningful picture. Examples are attractiveness, strategic fit, innovation, gross/net present value, expected profits, R D expenditures, development stage, probability of success, technology fit, and realization time. Most of these parameters cannot be determined quantitatively, at least during the early phases of a project. 

In the standard economic model of the firm, business decisions are generally explained by their effects on expected profitability. Let us examine some ways in which innovative activity and expected profitability interact ... 

If the goal of the buy-out price is to mimic what would have happened under best-case competitive market conditions, then the price should be based on expected profits rather than sales or costs. Ganslandt, Maskus, and Wong (2001) used cost data to calculate the buy-out, which rewards effort rather than success. Gross sales are certainly an element of pharmaceutical appropriation, but the relevant market metrics are the net present value (NPV) of the cash flow or the NPV of the profit stream. The purpose of the buy-out price should be to restore the expected profits, and more particularly, the lost R D cost recovery. 

Once the list is culled, a decision must be made on how to score each criterion. This can be as simple as a qualitative judgment of effectiveness (+), ineffectiveness (—), or indifference ( ), or a simple subjective score (say, 1 to 10). Some criteria lend themselves to a more quantitative evaluation of a relevant statistic, such as expected profit, volume, sales, and so on. Once the choices are made, each altemative solution can then be rated according to the list of criteria. 

Imagine that every time the widget entreprenem hires a new employee, a transaction cost C is incurred. The hiring of a successful employee results in the employer realizing a marginal value V per time unit, but the probability of success in hiring is assumed to be probability p on each hire. Thus the expected profit P per time period to the employer may be written as follows ... 

To define the economic performance of a manufacturing venture, an analyst must predict various sources and sinks of money throughout the lifetime of a project. In fact the investors invest a huge amount of money when they begin to build the chemical plant, but they will earn money from sales only when the plant is finished and operating. Owing to inflation and devaluation, future money is different from present money [13,15], Therefore, a future income needs to be discounted to its present value in order to evaluate the expected profitability of a chemical plant. Of course, when dealing with future events, nobody can be absolutely positive about prices, inflation rates, etc. Therefore many assumptions need to be... 

Two other measures that can be used to evaluate the profitability of a product are the return on investment and the payback period. The return on investment (ROZ) is the expected profit divided by the total capital invested, expressed as a percentage return. It must be clearly stated whether the profit is based on pre-tax or after-tax earnings. The after-tax ROI is compared with the earnings that could be achieved by an alternative investment, e.g. capital bonds. An after-tax ROI of at least 15-20% is usually expected (or 30-40% pre-tax ROI), assuming that the project is not particularly risky ... 

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