The Variable Choices in Sensitivity Analysis

Published: 2021-06-29 21:30:04
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We will examine as variable X the real equity premium. It is used to measure the return if in the market exists a risk-free return. We choose real equity premium because it plays a very important role to measure the cost of capital and to evaluate the cash flows of a company. The price of risk is the equity risk premium (ERP, where we treat equities as the same thing as the total market) and the quantity of risk is beta in the capital asset pricing model (CAPM). So, the EPR is the price of risk and it’s the difference between the market (broad equity) return and a risk-less return. One factor which could cause variable X to deviate from its expected (or forecasted) value are the expected earnings growth rate. The dividend growth rate is less than economic growth because it shares growth with entrepreneurs and managers. Overall economic growth (e.g., GDP) is not shared lockstep by shareholders in existing enterprises. Current owners only participate in productivity growth. They are diluted in two ways. First, innovation dilutes them because new companies don’t create value generally for public company owners. Second, managers dilute them with stock options and restricted stock (and equity-like cash incentives, for that matter). So you end up with an even more conservative estimate:

Critically analyse the sensitivity of the labour-saving technology investment to variable X.
The sensitivity of the labour-saving technology investment to variable X is high. In Part I the labour cost is in year 1 100$ and in Part II reduces labour cost in 82,5$. That affects the variable cost per unit, the total variable cost, the operating cash flows and the net present value positively. In Part I before the reduction of the labour cost the project NPV was negative and in Part II is positive. The lowest cost affects also the equity premium. The expected value of its future earnings will be higher, discounted at the real bond rate. Moreover, the cost of capital to the private firm , which is equal to a weighted average of the bond rate and the rate of return to private equity, is greater than the cost of capital to the public sector, which is equal to the bond rate. The higher savings will lead to higher earnings, higher price of the bond of the firm, lower equity premium and higher project NPV. From table 1 we can see that when we give prices in equity premium from 3% to 7%, as it gets higher the project NPV reduces and becomes negative whivh means that we donâA¢”šA¬A¢”žA¢t accept the project. So, we donâA¢”šA¬A¢”žA¢t want a very high equity premium.
Table 1
0,08 151205
0,09 134807
0,1 119285
0,11 -26233
0,12 90642
0,13 77418
0,14 -57446
0,15 -71372
0,16 -147443 From the following chart we see that in 3% equity premium the NPV is 151205 and in 4,5% becomes negative -26233 and then after a small growth starts going down and is always negative. So, the equity premium until 5,5% is acceptable.
Chart 1
The first two way table is between unit sales factor and real equity premium. When the unit sales factor is 0,6 the NPV is negative. Aw the unit sales factor gets higher the NPV becomes positive. After 100% of unit sales factor, as shown in table 2, the NPV is positive and becomes higher. The reduction of labour cost and the increase of unit sales factor leads to higher NPV.
Table 2
0,6 0,8 1 1,2 1,4
-189633 -19214 151205 321624 492043
-198377 -39546 119285 278115 436946
-206179 -57768 90642 239052 387462
-213161 -74148 -57446 203878 342891
-219426 -88912 -147443 172117 302631 We examine another two way table, table 3, which is the sales growth factor and the real equity premium. As salew growth factor becomes higher the NPV gets higher and as the real equity premium gets higher the NPV reduces. The best is 7% sales growth factor and 3% real equity premium, which means higher sales growth and lower real equity premium.
Table 3
0,02 0,04 0,05 0,06 0,07
-7279 28857 47756 67231 87296
-24906 8013 25219 42942 61195
-40871 -10808 4896 21065 37710
-55371 -27850 -13484 1302 16518
-80636 -43326 -30152 -16600 -2659
Sensitivity Analysis of the New Product Technology
The decision maker will make decisions consistent with his values, which are those things that are important to him, especially those that are relevant to this decision. The decision maker might set a goal for his decision, which is a specific degree of satisfaction of a given objective. For example, the objective of the decision might be to increase wealth, and the goal might be to make a million dollars. A decision maker might employ decision analysis, which is a structured way of thinking about how the action taken in the current decision would lead to a result. In doing this, one distinguishes three features of the situation: the decision to be made, the chance and unknown events which can affect the result, and the result itself. The most commonly studied and discussed value is economic value, which we assume to be measured in dollars. Given a stream of cash flows over time, we use the NPV to describe the current value of future cash flows. The NPV is a calculation performed on cash flows over time, allowing one to condense that stream of cash flows into a single number. We use the NPV of profits or cash flows as a measure of the value of the new technology project. The NPV calculation makes use of the discount rate, which has several interpretations, but can be thought of as a factor applied to future income to reflect the fact that it is less valuable than income received now. It also reduces the impact of future costs, since costs that can be deferred into the future are preferable to those that must be paid now. In thinking about the value of a scenario, it is helpful to distinguish between direct and indirect values. Direct values are cash flows directly related to a project, for example, the profits resulting from the manufacture and sales of a new product. Indirect values are things that the decision maker values that are not likely to show up in accounting statements. For example, a decision maker may experience “pride” or “goodwill” in producing some products and value such an outcome beyond its direct economic value. These indirect values could include costs associated with, for example, laying off workers, or negative impacts on reputation. While some of these indirect values are intangible, others are tangible but difficult to put a number on. The new technology leads to better NPV although the labor and materials costs is higher. The new technology as shown by the results between Part II and Part II is better than reducing labour cost. We can see that in table 4 comparing it with table 2 and table 5 with table 3. As decision makers ponder the possible outcomes of their decisions they often think about risk, which is the possibility of an undesirable result. In discussing this, it is convenient to consider the notion of a risk-neutral decision maker. Someone who is risk neutral is willing to play the long-run odds when making decisions, and will evaluate alternatives according to their expected values. While an insurance company may evaluate individual policies as if it were risk-neutral, for alternatives with substantial risks, decision makers are often risk averse, which means that they value alternatives at less than their expected values. To make this definition of value precise, we define the certain equivalent, (or certainty equivalent) of an alternative as the amount that the decision maker would be indifferent between (1) having that monetary amount for certain or (2) having the alternative with its uncertain outcome.
Table 4
0,6 0,8 1 1,2 1,4
-210963 -3443 204077 411597 619117
-233266 -46180 140906 327992 515078
-252126 -82549 87029 256606 426184
-268169 -113684 40800 195285 349769
-281891 -140492 907 142305 283704
Chart 3
In the following table we see that when the sales growth factor increases the NPV also increases and when the real equity premium increases the NPV reduces. We prefer high sales growth factor and low real equity premium.
Table 5
0,15 0,17 0,19 0,21 0,23
619117 695553 776468 862095 952678
515078 581471 651682 725909 804357
426184 484155 545398 610080 678375
349769 400638 454323 510967 570718
283704 308550 375832 425671 478194
Recommendations to the Management
Launching a new technology product is a goal. Investing in additional personnel or reducing labour cost, while at the same time stopping the funding of some stalled projects, is a strategy intended to lead to that goal. The outcome of the action of a new technology product is better than that of recucing labour cost. An important special case of a strategy problem is the portfolio problem, in which the various decisions faced in the strategy are of a similar nature, and the decision maker does not have sufficient resources for funding all combinations of alternatives. The profitability of the new product we are developing is sensitive to the market share we achieve. Everyone wants the outcome to be as good as possible, and in that sense might be interested in knowing to what uncertainties the outcome is sensitive. In new technology product we have certain new prices for costs an sales revenues and we can take better decisions. However, if one is interested in achieving clarity of action, as opposed to predicting the future, one need only be concerned about those uncertainties which would change the decision if we could know in advance how they will turn out. The direct value of a new product might be the current value of the future cash flow associated with the manufacture and sale of the product. The indirect value might include effects like increased goodwill or strategic advantage that come from having the product but are not directly associated with the manufacture and sale of the product. Typically, maximizing the NPV associated with a product should be one of the decision maker’s objectives. The decision maker might, however, assign value in excess of a cash flow based NPV, and that increment might be for what is sometimes termed “strategic value.” These indirect sources of value must be included in the NPVs, if one is to think appropriately about values. It is better to put a rough value on these indirect sources (so it can be discussed and evaluated) than to assume they are worth precisely zero. The certain equivalent for a risky new product is the smallest sum of money for which the decision maker would be willing to sell rights to that product. The expected NPV for the product is the hypothetical average NPV from numerous independent launches of identical projects. The new technology project cannot be repeated and we might value gambles at less than their expected values. The attitude towards risk varies from decision maker to decision maker and, even for a specific decision maker, may vary over time. At this time and given the analysis we made we recommend the new technology rather than reducing labour cost.

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