11 INVESTMENT ANALYSIS TO MITIGATE COSTS OF PQ
RomanTargoszandJonathanManson
11.1 Investment Analysis
Companies have several choices about how to spend capital in order to produce a return on their investment ranging from two possible extremes, on the one hand, of investing in a project, or, on the other, just depositing the money into an investment account.
Whatever the option, including PQ investments, it must compete for scarce capital with other investment opportunities. Therefore, the economic analysis of PQ investment should be conducted in the same way as the analysis of other capital investments to ensure that all options are compared on an equal basis. This decision process is called capital budgeting.
A particular problem arises for PQ investment, which is typical of any investment proposed in a cost reduction environment. In the capital budgeting process, some investments are earmarked as ‘strategic’, i.e. they are needed for the survival and growth of the firm, and hence receive priority. Another group of investments is required by law. They have little or no return on investment, but regulation requires them and the firm would never do them under purely economic criteria. Some typical examples of this are those investments made to reduce the environmental impact of a given operation.
Once the strategic investments and investments required by law are fulfilled, usually little capital budget remains for investment in cost reduction measures, such as PQ investments.
These rely on specific business units, using operating not capital income, to see the light of day. Such investment planning is usually made within the confines of very short acceptable payback or time perspectives, which for PQ investments can be expected to be anything up to 1–2 years. Put another way, this represents the equivalent of a 50–100% return rate, which is much higher than the average return on assets. Therefore, the scarcity of capital for PQ investments, and the requirement to finance from operating income, suboptimizes the firm’s performance, and opens up opportunities for thirdparty financing.
A brief definition of capital budgeting principles and a summary of some useful definitions follow.
11.2 Capital Budgeting
The decision on whether to accept a project depends on the analysis of the cash flows resulting from the project. A capital budgeting decision rule should satisfy the following criteria:
• It must consider all of the project’s cash flows (including working capital).
• It must consider the time value of money.
• It must always lead to the correct decision when choosing among mutually exclusive projects over different investment horizons.
The entire capital budgeting process relies on precise cash flow estimates. In general it is very important for the decision makers to obtain the most accurate forecasts possible. In order to do so they must do basically two things:
• identify all the variables that affect cash flows and determine which of those variables are critical to the success of the project;
• define the degree of forecasting accuracy required.
In the following subsections the most relevant capital budgeting decision rules will be presented. A distinction will be made between deterministic and stochastic methods. An evaluation method is considered to be deterministic if each cash flow can be precisely estimated, and it will be defined as stochastic when cash flows vary over a range and thus introduce a degree of uncertainty.
The focus will be on deterministic methods.
11.3 Project Classifications
When dealing with capital budgeting, projects can be classified as either independent or mutually exclusive.
An independent project is a project whose cash flows are not affected by the accept– reject decision of other projects. Thus, all independent projects which meet the company’s capital budgeting criterion should be accepted.
Mutually exclusive projects are a set of projects among which only one will be accepted, e.g. a set of projects which accomplish the same task. Thus, when choosing among mutually exclusive projects, more than one project may satisfy the company’s capital budgeting criterion, whilst only one, i.e. the best project, can be accepted.
11.4 Cost of Capital
As described below, discounted cash flow methods measure cash flows in terms of a required rate of return (hurdle rate) to determine their acceptability. This hurdle rate can be referred to as the firm’s cost of capital.
The company’s cost of capital is the discount rate which should be used in capital budgeting. The weighted average cost of capital (WACC) reflects the company’s cost of
obtaining capital to invest in longterm assets. Thus it reflects a weighted average of the company’s cost of debt (longterm and shortterm) and cost of equity (preferred stock, common stock).
Another way to define it is that the cost of capital represents the cost of funds used to acquire the total assets of the firm. Generally it refers to the rates of return expected by those parties contributing to the financial structure – preferred and common shareholders as well as creditors. Thus, it is generally calculated as a weighted average of the cost associated with each type of liability included in the financial structure of the enterprise.
With reference to capital budgeting, the concept underlying the definition of the cost of capital is that a firm must manage its assets and select capital projects with the goal of obtaining a yield at least sufficient to cover its cost of capital. Financial management separates the investment decision from the financing decision. A firm’s financial structure is considered as fixed, and yields a WACC figure. Sometimes, the required rate of return for investment opportunities can be risk adjusted, i.e. lowrisk projects have a lower hurdle rate, whereas highrisk projects must produce a return well above the WACC.
Another consideration is the debttoequity ratio. Firms may not wish to carry too much debt compared to equity, as this increases risk exposure of the firm. So projects may not be pursued, even if they provide an attractive return, because the firm wants to limit or reduce debt. Again, such a situation presents an opportunity for thirdparty financing.
11.5 The Time Value of Money
A given amount of money on hand today is worth more than the same amount to be received in the future because money available today can be invested to earn interest to yield more than the same amount in the future. The time value of money mathematics quantifies the value of a given amount of money through time. This, of course, depends upon the rate of return or interest rate which can be earned on the investment.
The time value of money concepts can be divided into two categories:
• Future value
• Present value
Future value describes the process of finding to which extent an investment today will grow to in the future. Present Value describes the process of determining what a given amount of money to be received in the future is worth in today’s money.
11.6 Future Value of a Single Cash Flow
The future value of a single cash flow represents the amount, at some time in the future, that an investment made today will grow to if it is invested to earn a specific interest rate.
For example, if you were to deposit € 100 today in a bank account to earn an interest rate of 10% compounded annually, this investment will grow to €110 in one year.
This can be shown as follows:
100x（1+0.10） = 110€
The interest rate in the example is 10% compounded annually. This implies that interest is paid annually. Thus the balance in the account was €110 at the end of the first year.
Thus, in the second year the account pays 10% on the initial principal of €100 and the €10 of interest earned in the first year. Thus, the € 121 balance in the account after two years can be computed as follows:
110x（1+0.10） = 121€
or
100x（1+0.10）x（1+0.10） = 121€
At the end of two years, the initial investment will have grown up to € 121. Notice that the investment earned € 11 in interest during the second year, whereas it only earned €10 in interest during the first year. Thus, in the second year, interest was earned not only on the initial investment of € 100 but also on the € 10 in interest that was paid at the end of the first year. This occurs because the interest rate in the example is a compound interest rate.
If the money were left in the account for one more year, interest would be earned on € 121 and the balance in the account at the end of year 3 would be €133.10. This can be computed as follows:
121x（1+0.10） = 133.10€
or
100x（1+0.10）x（1+0.10）x （1+0.10）= 133.10€
快乐十分app下载
A pattern should be becoming apparent. The future value of an initial investment at a given interest rate compounded annually at any point in the future can be found using the following equation:
11.7 Present Value of a Single Cash Flow and of a Cash Flow Stream
Present value describes the process of determining what a cash flow to be received in the future is worth in today’s money. Therefore, the present value of a future cash flow represents the amount of money today which, if invested at a particular interest rate, will grow to the amount of the future cash flow at that time in the future. The process of finding present values is called discounting and the interest rate used to calculate present values is called the discount rate. For example, the present value of E100 to be received one year from now is € 90.91 if the discount rate is 10% compounded annually.
This can be demonstrated as follows:
90.91x（1+0.10） = 100€ or 90.91€= 100/（1+0.10）
Notice that the future value equation was used to describe the relationship between the present value and the future value. Thus, the present value of E100 to be received in two years can be shown to be E82.64 if the discount rate is 10 %.
This can be demonstrated as follows:
82.64 x（1+0.10）x（1+0.10） = 100€
A pattern should be becoming apparent. The following equation can be used to calculate the present value of a future cash flow given the discount rate and number of years in the future that the cash flow occurs:
where PV is the present value; CFt is the future cash flow which occurs t years from now; r is the interest or discount rate; and t is the number of years.
The present value of a cash flow stream is equal to the sum of the present values of the individual cash flows:
11.8 Deterministic Approach to PQ Investment Analysis
The economic analysis of investments is one of the fundamental steps in any decision process because cost reduction is the main target for PQ investments.
The main elements of an investment to be investigated are:
• the capital cost or initial investment;
• the cost of capital;
• cost reduction;
• operating and maintenance expenses for the investment;
• the economic life of the investment.
Several evaluation methods can be used for investment, depending on the company’s internal evaluation criteria. More or less sophisticated methods can be used as appropriate for the importance of the investment.
A distinction can be made between evaluation methods that use life cycle costing and those that do not. Evaluation methods that use life cycle costing are based on the conversion of investment and annual cash flows at various times to their equivalent present values.
In other words, the wholelife span of the investment is taken into consideration. Typical examples of life cycle costing methods are: net present value (NPV) and internal rate of return (IIR).
Evaluation methods that do not use life cycle costing are for instance payback time (PBT) and breakeven analysis. They do not take into consideration the life of the investment; they only define how long it will take to earn back the money spent on the project.
11.9 Discounted Cash Flow Methods
11.9.1 Net Present Value
The NPV of a project indicates the expected impact of the project on the value of the company.
Projects with a positive NPV are expected to increase the value of the company. Thus, the NPV decision rule specifies that all independent projects with a positive NPV should be accepted. If the NPV is greater than 0, the project is valid since the revenues are enough to pay the interest and to recover the initial capital cost before the end of the life of investment. When the NPV equals 0, the investment balances out at the end of the period and is consequently an unattractive proposition.
When choosing among mutually exclusive projects, the project with the largest (positive) NPV should be selected.
The NPV is calculated as the present value of the project’s cash inflows minus the present value of the project’s cash outflows. This relationship is expressed by the following formula:
where CFt is the net cash flow at time t; r is the cost of capital; and T is life of the project.
The example in Table 18.12 illustrates the calculation of the NPV. Consider projects A and B which yield the following cash flows over their fiveyear lives. The cost of capital for the project is 10 %.
Table 18.12 Example that illustrates the calculation of NPV Thus, if projects A and B are independent projects then both projects should be accepted. On the other hand, if they are mutually exclusive projects then project A should be chosen since it has the larger NPV.
Year 
Project A 
Project A 
Year 
Project A 
Project A 
0 
1000 
1000 
4 
200 
400 
1 
500 
100 
5 
100 
700 
2 
400 
200 
NPV 
143.08 
114.31 
3 
200 
200 



The NPV method takes all of the project’s cash flows and the time value of money into consideration.
Projects can also be compared on the basis of the ratio between the present worth of the project and the related investment (NPV/I) being taken as a comparative parameter.
11.9.2 Internal Rate of Return
The IRR of a project is the discount rate at which the NPV of a project equals zero.
The IRR decision rule specifies that all independent projects with an IRR greater than the cost of capital should be accepted. When choosing among mutually exclusive projects, the project with the highest IRR should be selected as long as the IRR is greater than the cost of capital:
The example in Table 18.13 illustrates the determination of IRR. Consider projects A and B which yield the following cash flows over their fiveyear lives. The cost of capital for both projects is 10 %.
Thus, if projects A and B are independent projects then both projects should be accepted since their IRRs are greater than the cost of capital. On the other hand, if they are mutually exclusive projects then project A should be chosen since it has the higher IRR.
11.9.3 Annual Equivalent
If we assume the same cash flow every year,i.e. CF0= CF1= ... = CFT , we can simplify Equation (18.3) toTable 18.13 Example that illustrates the calculation of IIR
Year 
Project A 
Project A 
Year 
Project A 
Project A 
0 
1000 
1000 
4 
200 
400 
1 
500 
100 
5 
100 
700 
2 
400 
200 
IRR(%) 
17 
13 
3 
200 
200 



This equation can be used to calculate annualized cash flows (ACFs) equivalent to an investment (I) made. For example, if an investment I is made in PQ mitigation, it is effective if the annual cost savings (ACS) are higher than this ACF+operating & maintenance expenses (OME):
Year 
Project A 
Project A 
Year 
Project A 
Project A 
0 
1000 
1000 
4 
200 
400 
1 
500 
100 
5 
100 
700 
2 
400 
200 
IRR(%) 
17 
13 
3 
200 
200 



This equation can be used to calculate annualized cash flows (ACFs) equivalent to an investment (I) made. For example, if an investment I is made in PQ mitigation, it is effective if the annual cost savings (ACS) are higher than this ACF+operating & maintenance expenses (OME):
The annual cost of ownership (ACO) for this investment is ACS − OME − ACF. The investment decision should be positive when ACO is greater than 0. A variant of this method is used in PQ Leonardo application note 5.5.1 [4] where the annual cost of poor power quality is added to annual investment (ACF) and operating and maintenance costs for various mitigation approaches. The minimum cost solution is proposed.
快乐十分app下载
The ACO can be converted to total cost of ownership (TCO) through reuse of Equation (18.3):
The decision process and the rules applied to both the NPV and IIR take all of the project’s cash flows and the time value of money into consideration. The NPV and IRR differ with respect to their reinvestment rate assumptions.
The NPV decision rule implicitly assumes that the project’s cash flows can be reinvested at the company’s cost of capital, whereas the IRR decision rule implicitly assumes that the cash flows can be reinvested at the project’s IRR. Since each project is likely to have a different IRR, the assumption underlying the NPV decision rule is more reasonable.
In general, engineering economic analysis presents the NPV as the most appropriate method on which to base investment decisions. The IRR has particular problems – for example, Equation (18.5) above does not always give a unique solution for the IRR. In addition, for a project where the IRR is high, e.g. 40 %, the assumption that the firm will be able to earn a 40% return on the proceeds from the project is flawed. In today’s information age, with the amount of desktop computing power available, there is no reason not to use the NPV systematically for making investment decisions.
11.10 Non Discounted Cash Flow Methods
11.10.1 Payback Time
The payback time (PBT) represents the amount of time that it takes for a project to recover its initial cost.
The use of the PBT as a capital budgeting decision rule specifies that all independent projects with a PBT less than a specified number of years should be accepted.
When choosing among mutually exclusive projects, the project with the shortest payback is to be preferred.
The calculation of the PBT is best illustrated with an example (Table 18.14). Consider project A which yields the cash flows over its fiveyear life.
To begin the calculation of the PBT for project A an additional column to the above table is added (Table 18.15) and this represents the net cash flow (NCF) for the project in each year.
Notice that after two years the NCF is negative (−1000+500+400=−100) while after three years the NCF is positive (−1000+500+400+200 = 100).
Table 18.14 PBT project A
Year 
Cash flow（€） 
Year 
Cash flow（€） 
0 
1000 
3 
200 
l 
500 
4 
200 
2 
400 
5 
100 
Table 18.15 PBT project A (NCF)
Year 
Cash flow（€） 
NCF（€） 
Year 
Cash flow（€） 
NCF（€） 
0 
1000 
1000 
3 
200 
100 
l 
500 
500 
4 
200 
300 
2 
400 
 100 
5 
100 
400 
Thus the PBT, or breakeven point, occurs sometime during the third year. If we assume that the cash flows occur regularly over the course of the year, the PBT can be
computed using the following equation:
where YLN is the last year with a negative NCF; NCF(YLN ) is the NCF in that year; and CF(YLN+1) is the total cash flow in the following year.
Thus in the example above, the last year with a negative NCF is year 2; the absolute value of the NCF in that year is equal to E100; the total cash flow in the following
year (year 3) is equal to E200; therefore the project will recoup its initial investment in 2−(100/200) = 2.5 years.
Although widely used, the PBT suffers from several drawbacks. Firstly, it assumes that E200 received one year from today is equivalent to E200 received five years from today; in other words, it does not consider the time value of money. This issue can be resolved by calculating the discounted payback (DPBT), where cash flows are discounted to their present value based on the discount rate, making the DPBT consistent with life cycle costing methods such as the NPV and IIR.
Secondly, the PBT does not consider the effects of different lives of alternatives, penalizing projects that have long potential life. For example, if alternative investments A
and B each cost E1000 and save E200 per year, then both would have a PBT of five years, making them seem equally acceptable. However, if investment A has an estimated useful life of five years and investment B has an estimated useful life of ten years, investment B would obviously be a better choice.
The third drawback is that the accept–reject criterion is often arbitrarily short. For example, many organizations require a one to threeyear payback period to consider a costsaving project and place a higher priority on shorter payback projects. Therefore, the PBT will reject many interesting investment opportunities, though it may even accept projects that reduce a company’s value. While it was used in the 1960s and 1970s before the computer era, today it should be avoided as much as possible. A fairly recent survey [3] shows that the NPV is by far the preferred tool among Fortune 1000 companies, with 85% of respondents
using it always or often.
11.11 Breakeven Analysis
Breakeven analysis can be used for projects where there is a gradual buildup of costs and benefits over time. For example, a production plant will need several years of investment in facilities, labor, training or services. After a certain time, the output of the plant will start to rise gradually as experience grows and output/sales develop. The point where accumulated costs equal accumulated benefits is called the breakeven point. It typically applies for complex projects, and rarely applies for PQ investments.
 Pre：None
 Next：10 PQ SOLUTIONS 2015/8/23