Additional order info. Cloth Bound with Access Card. Pearson offers affordable and accessible purchase options to meet the needs of your students. Connect with us to learn more. We're sorry! We don't recognize your username or password. Please try again. Samples of Cash Outflow Estimates First cost of assets. Engineering design costs. Operating costs annual and incremental. Periodic maintenance and rebuild costs.
Loan interest and principal payments. Income taxes. Expenditure of corporate capital funds. Background information for estimates may be available in departments such as accounting, finance, marketing, sales, engineering, design, manufacturing, production, field services, and computer services. The accuracy of estimates is largely dependent upon the experiences of the person making the estimate with similar situations.
Usually point estimates are made; that is, a single-value estimate is developed for each economic element of an alternative.
If a statistical approach to the engineering economy study is undertaken, a range estimate or distribution estimate may be developed. Though more involved computationally, a statistical study provides more complete results when key estimates are expected to vary widely. We will use point estimates throughout most of this book. Final chapters discuss decision making under risk. Once the cash inflow and outflow estimates are developed, the net cash flow can be determined.
The end-oj-period convention means that all cash flows are assumed to occur at the end of an interest period. When several receipts and disbursements occur within a given interest period, the net cash flow is assumed to occur at the end of the interest period. In Example 1.
Thus, end of the period means end of interest period, not end of calendar year. The cash flow diagram is a very important tool in an economic analysis, especially when the cash flow series is complex. It is a graphical representation of cash flows drawn on a time scale. The diagram includes what is known, what is estimated, and what is needed.
That is, once the cash flow diagram is complete, another person should be able to work the problem by looking at the diagram. We assume that the periods are in years for now. The time scale of Figure is set up for 5 years. Since the end-of-year convention places cash flows at the end of years, the" 1" marks the end of year 1. While it is not necessary to use an exact scale on the cash flow diagram, you will probably avoid errors if you make a neat diagram to approximate scale for both time and relative cash flow magnitudes.
The direction of the arrows on the cash flow diagram is important. A vertical arrow pointing up indicates a positive cash flow. Conversely, an arrow pointing down indicates a negative cash flow.
Figure illustrates a receipt cash inflow at the end of year 1 and equal disbursements cash outflows at the end of years 2 and 3. The perspective or vantage point must be determined prior to placing a sign on each cash flow and diagramming it. Possible Figure A typical cash flow lime scale for 5 years. Construct the cash flow diagram. Solution Figure presents the cash tlow diagram from the vantage point of the borrower. The present sum P is a cash inflow of the loan principal at year 0, and the future sum F is the cash outflow of the repayment at the end of year 5.
The interest rate should be indicated on the diagram. Solution Figure 1- 10 indicates the uniform and negative cash flow series expenditures for five periods, and the unknown F value positive cash flow equivalent at exactly the same 33 34 CHAPTER I Foundations of Engineering Economy time as the fifth expenditure. Therefore, the last negative cash flow occurs at the end of the fourth year, when F also occurs.
To make this diagram appear similar to that of Figure] -9 with a full 5 years on the time scale, the addition of the year -1 prior to year 0 completes the diagram for a full 5 years. This addition demonstrates that year 0 is the end-of-period point for the year If the rate of return is estimated to be Solution Figure presents the cash flows from the father's perspective.
Figure Cash flow diagram, Example 1. Additional Examples 1. The rule of 72 for compound interest rates can be used to estimate i or n, given the other value. The estimation is simple; the time required for an initial single amount to double in size with compound interest is approximately equal to 72 divided by the rate of return in percent.
The actual time required is Table compares the times estimated from the rule of 72 to the actual times required for doubling at several compounded rates.
As you can see, very good estimates are obtained. Alternatively, the compound rate i in percent required for money to double in a specified period of time n can be estimated by dividing 72 by the specified n value.
The exact answer is 5. If the interest is simple, a rule of may be used in the same way. In this case the answers obtained will always be exactly correct. A key feature is the use of mathematical relations developed in the cells to perform sensitivity analysis for changing cash flow estimates and the interest rate.
To answer these basic questions using hand solution can be time-consuming; the spreadsheet makes it much easier. This software could be very beneficial as an advance warning of serious tremors in earthquake-prone areas in Japan and the United States. The planning horizon is only 4 years due to the rapid advances made internationally in building-monitoring software.
Develop spreadsheets to answer the questions below. Obtain answers for both simple and compound interest. The financial manager of the U. As mentioned in Section 1. Solution by Computer Refer to Figure a to c for the solutions.
All three spreadsheets contain the same information, but the cell values are altered as required by the question. Actually, all the questions posed here can be answered on one spreadsheet by simply changing the numbers. Three spreadsheets are shown here for explanation purposes only. The Excel functions are constructed with reference to the cells, not the values themselves, so that sensitivity analysis can be perfOlmed without function changes.
This approach treats the value in a cell as a global variable for the spreadsheet. Key Excel relations are detailed in the cell tags. Refer to Figure a, columns C and D, for the answers. Simple interest earned each year column C incorporates Equation [1. I Foundations of Engineering Economy f I:! What is the minimum annual nominal rate that is acceptable for continuous compounding?
By Equation [4. Compute the future worth for both individual s if Marci receives annu al compoundin g and Suzanne receives continuous compounding. For comparison, daily compounding yields an effective rate of Examples of costs are energy and water costs, inventory costs, and labor costs. A realistic model for these activities is to increase the frequency of the cash flows to become continuous.
In these cases, the economic analysis can be performed for continuous cash flow also called continuous fuRds flow and the continuous compounding of interest as discussed above. Different expressions must be derived for the factors for these cases. In fact, the monetary differences for continuous cash flows relative to the discrete cash flow and discrete compounding assumptions are usually not large.
Accordingly, most engineering economy studies do not require the analyst to utilize these mathematical forms to make a sound economic project evaluation and decision. Loan rates may increase from one year to another. Home mortgages financed using ARM adjustable rate mortgage interest is a good example.
The mortgage rate is sljghtly adjusted annually to reflect the age of the loan, the current cost of mortgage money, etc. An example of interest rates that rise over time is inflation-protected bonds that are issued by the U. The dividend rate that the bond pays remains constant over its stated life, but the lump-sum amount due to the owner when the bond reaches maturity is adjusted upward with the inflation index of the Consumer Price Index CPI. This means the annual rate of return will increase annually in accordance with observed inflation.
Bonds and inflation are visited again in Chapters 5 and 14, respectively. When P, F, and A values are calculated using a constant or average interest rate over the life of a project, rises and falls in i are neglected.
If the variation in i is large, the equivalent values will vary considerably from those calculated using the constant rate. Although an engineering economy study can accommodate varying i values mathematically, it is more involved computationally to do so. Since the equivalent P has been determined numerically using the varying rates, this new equation will have only one unknown, namely, A. The following example illustrates this procedure. The net profit from the equipment for each of the last 4 years has been decreasing, as shown below.
Also shown are the annual rates of return on invested capital. The return has been increasing. Determine the present worth P and equivalent uniform series A of the net profit series. Take the annual variation of rates of return into account.
Equation [4. This equation accounts for the varying i values each year. See Figure for the cash flow diagram transformation. When there is a cash flow in year 0 and interest rates vary annually, this cash flow must be included when one is determining P.
This factor value is always 1. It is equally correct to find the A value using a future worth relation for F in year n. When a nomjnal rate r is stated, the effective interest rate per payment period is determjned by using the effective interest rate equation. If interest compounding becomes more and more frequent, the length of a CP approaches zero, continuous compounding results, and the effective i is e r All engineering economy factors require the use of an effective interest rate.
The i and n values placed in a factor depend upon the type of cash flow series. If only single amounts P and F are present, there are several ways to perform equivalence calculations using the factors. However, when series cash flows A, G, and g are present, only one combination of the effective rate i and number of periods n is correct for the factors. This requires that the relative lengths of PP and CP be considered as i and n are determined.
The interest rate and payment periods must have the same time unit for the factors to correctly account for the time value of money. To accurately perform equivalence calculations for P and A when rates vary s ignificantly, the applicable interest rate should be used, not an average or constant rate.
Whether performed by hand or by computer, the procedures and factors are the same as those for constant interest rates ; however, the number of calculations increases. For an interest rate of 0.
Is the weekly rate a nominal or effective rate? Assume 26 weeks per 6 months. Identify the payment and compounding periods. What payment and compounding periods are associated with deposits of daily receipts? Equivalence for Single Amounts and Series 4. A new cell phone company estimates that by advertising its favorable 1.
Army, is designed to shoot down aircraft and other missiles. If the total project development time was 10 years and costs increased at a rate of 0. A day strike at Boeing resulted in 50 fewer deliveries of commercial jetliners at the end of the first quarter of Assume 4 weeks per month. The delayed payment essentially represents a subsidy by the irrigation district to the water utility. At an interest rate of 0. Yes Is the given rate's period shorter, same as, or longer than the period of the effecti ve rate you seek?
Negative cash fiow s payments are treated as occuring at the end of the CP Shoner Same Multi ply the given rate to find a new nominal rate. No Determine the number of compounding peri ods, m, per effecti ve interest peri od you are seeking Contributed by Dr.
The chapters in this level develop the four different methods by which one or more alternatives can be evaluated economically using the factors and formulas learned in the previous Level One. In professional practice, it is typical that the evaluation method and parameter estimates necessary for the economic study are not specified. The last chapter in this level begins with a focus on selecting the best evaluation method for the study.
It continues by treating the fundamental question of what MARR to use and the historic dilemma of how to consider noneconomic factors when selecting an alternative. Similarly, the interest rate is referred to as the discount rate. Up to this point, present worth computations have been made for one project or alternative.
In this chapter, techniques for comparing two or more mutually exclusive alternatives by the present worth method are treated. Several extensions to PW analysis are covered here-future worth, capitalized cost, payback period, life-cycle costing, and bond analysis-these all use present worth relations to analyze alternatives.
In order to understand how to organize an economic analysis, this chapter begins with a description of independent and mutually exclusive projects, as well as revenue and service alternatives. The case study examines the payback period and sensitivity for a public sector project. This chapter will help you: 1. Identify mutually exclusive and independent projects, and define a service and a revenue alternative.
Select the best of equa l-life alternatives using present worth analysis. Select the best of different-life alternatives using present worth ana lysis. FWanalysis 4. Select the best alternative using future worth analysis. Capitalized cost Ce 5. Select the best alternative using capitalized cost calculations.
Payback period 6. Life-cycle cost LCC 7. Perform a life-cycle cost analysis for the acquisition and operations phases of a system alternative. PW of bonds 8.
Calculate the present worth of a bond investment. Spreadsheets 9. Develop spreadsheets that use PW analysis and its extensions, including payback period. The alternatives are developed from project proposals to accomplish a stated purpose. This progression is depicted in Figure Some projects are economjcally and technologically viable, and others are not. Once the viable projects are defined, it is possible to formulate the alternatives.
For example, assume Med-supply. Three projects have been proposed: closer networking with UPS and FedEx for shortened delivery time; partnering with local medical supply houses in major cities to provide same-day delivery; and developing a 3-d fax -like machine to ship items not physically larger than the machine. Economically and technologically only the first two project proposals can be pursued at this time; they are the two alternatives to evaluate.
The description above correctly treats project proposals as precursors to economic alternatives. Only one of the viable projects can be selected by the economic analysis. Each viable project is an alternative. More than one viable project may be selected by the economic analysis. There may be dependent projects requiring a particular project to be selected before another, and contingent projects where one project may be substituted for another.
The do-nothing DN option is usually understood to be an alternative when the evaluation is performed. If it is absolutely required that one of the defined alternatives be selected, do nothing is not considered an option.
This may occur when a mandated function must be installed for safety, legal, or other purposes. Selection of the DN alternative means that the current approach is maintained; nothing new is initiated. No new costs, revenues, or savings are generated by the DN alternative. A mutually exclusive alternative selection takes place, for example, when an engineer must select the one best diesel-powered engine from several competing models.
Mutually exclusive alternatives are, therefore, the same as the viable projects; each one is evaluated, and the one best alternative is chosen. Mutually exclusive alternatives compete with one another in the evaluation. All the analysis techniques through Chapter 9 are developed to compare mutually exclusive alternatives. Present worth is discussed in the remainder of this chapter. If no mutually exclusive alternative is considered economically acceptable, it is possible to reject all alternatives and by default accept the DN alternative.
This option is indicated in Figure by colored shading on the DN mutually exclusive alternative. Each project is evaluated separately, and thus the comparison is between one project at a time and the do-nothing alternative. If there are m independent projects, zero, one, two, or more may be selected. Since each project may be in or out of the selected group of projects, there are a total of 2m mutually exclusive alternatives. This number includes the DN alternative, as shown in Figure Commonly, in real-world applications, there are restrictions, such as an upper budgetary limit, that eliminate many of the alternatives.
Independent project analysis without budget limits is discussed in this chapter and through Chapter 9. Chapter 12 treats independent projects with a budget limitation; this is called the capital budgeting problem. Finally, it is important to recognize the nature or type of alternatives before starting an evaluation. The cash flows determine whether the alternatives are revenue-based or service-based. All the alternatives evaluated in one particular engineering economy study must be of the same type.
Each alternative generates cost or disbursement and revenue or receipt cash flow estimates, and possibly savings. Revenues are dependent upon which alternative is selected.
Purchasing new equipment to increase productivity and sales is a revenue alternative. Each alternative has only cost cash flow estimates. Revenues or savings are not dependent upon the alternative selected, so these cash flows are assumed to be equal. These may be public sector government initiatives as discussed in Chapter 9. Also, they may be legally mandated or safety improvements.
Often an improvement is justified; however, the anticipated revenues or savings are not estimable. In these cases the evaluation is based only on cost estimates. The alternative selection guidelines developed in the next section are tailored for both types of alternatives.
The present worth method is popular because future cost and revenue estimates are transformed into equivalent dollars now; that is, all future cash flow s are converted into present dollars. This makes it easy to determine the economic advantage of one alternative over another. The PW comparison of alternatives with equal lives is straightforward. If both alternatives are used in identical capacities for the same time period, they are termed equal-service alternatives.
One alternative. Two or more alternatives. Select the alternative with the PW value that is numerically largest, that is, less negative or more positive, indicating a lower PW of cost cash flows or larger PW of net cash flows of receipts minus disbursements.
Note that the guideline to select one alternative with the lowest cost or the highest income uses the criterion of numerically largest. This is not the absolute value of the PW amount, because the sign matters. The selections below co[rectly apply the guideline for the listed PW values. This compares each project with the do-nothing alternative. The projects must have positive and negative cash flows to obtain a PW value that exceeds zero; that is, they must be revenue projects.
Revenues for all three alternatives are expected to be the same. If it costs money to dispose of an asset, the estimated disposal cost has a - sign. Use subscripts E, G, and S. This is necessary, since a present worth comparison involves calculating the equivalent present value of all future cash flow s for each alternative. A fair co mpari son can be made only when the PW values represent costs and receipts associated with equal service.
Failure to compare equal service will always favor a shorter-lived alternati ve for costs , even if it is not the most economical one, because fewer periods of costs are in volved. Compare the alternatives using a study period of length n years, which does not necessarily take into consideration the useful lives of the alternatives.
This is also called the planning horizon approach. In either case, the PW of each alternative is calculated at the MARR, and the selecti on guideline is the same as that for equal-life alternatives. The LCM approach automatically makes the cash flow s for all alternati ves extend to the same time period. For example, alternatives with expected lives of 2 and 3 years are compared over a 6-year time period.
Such a procedure requires that some assumpti ons be made about subsequent life cycles of the alternatives. The service provided by the alternatives will be needed for the LCM of years or more. The selected alternative will be repeated over each life cycle of the LCM in exactly the same manner. The cash flow estimates will be the same in every life cycle. As will be shown in Chapter 14, the third assumption is valid only when the cash flows are expected to change by exactly the inflation or deflation rate that is applicable through the LCM time period.
If the cash flows are expected to change by any other rate, then the PW analysis must be conducted using constant-value dollars, which considers inflation Chapter A study period analysis is necessary if the first assumption about the length of time the alternatives are needed cannot be made. A present worth analysis over the LCM requires that the estimated salvage values be included in each life cycle. For the study period approach, a time horizon is chosen over which the economic analysis is conducted, and only those cash flows which occur during that time period are considered relevant to the analysis.
All cash flows occurring beyond the study period are ignored. An estimated market value at the end of the study period must be made. The time horizon chosen might be relatively short, especially when short-term business goals are very important.
The study period approach is often used in replacement analysis. It is also useful when the LCM of alternatives yields an unrealistic evaluation period, for example, 5 and 9 years.
Example 5. Also, Example 5. Two lease options are available, each with a first cost, annual lease cost, and deposit-return estimates shown below. EnvironCare has a standard practice of evaluating all projects over as-year period.
If a study period of 5 years is used and the deposit returns are not expected to change, which location should be selected? For life cycles after the first, the first cost is repeated in year 0 of each new cycle, which is the last year of the previous cycle. These are years 6 and 12 for location A and year 9 for B.
The cash flow diagram is in Figure 5- 2. Noneconom ic factors are likely to enter into the final decision. Comments In part a and Figure 5- 2, the deposit return for each lease is recovered after each life cycle, that is, in years 6, 12, and 18 for A and in years 9 and 18 for B. The project engineer should reexamine these estimates before making a final deci sion. Therefore, it is an extension of present worth analysis.
Analysis of one alternative, or the comparison of two or more alternatives, using FW values is especially applicable to large capital investment decisions when a prime goal is to maximize the future wealth of a corporation's stockholders.
Future worth analysis is often utilized if the asset equipment, a corporation, a building, etc. An FW value at an intermediate year estimates the alternative 's worth at the time of sale or disposal. Suppose an entrepreneur is planning to buy a company and expects to trade it within 3 years. FW analysi s is the best method to help with the decision to sell or keep it 3 years hence. Another excellent application of FW analysis is for projects that will not come online until the end of the investment period.
Alternatives such as electric generation facilities , toll roads, hotels, and the like can be analyzed using the FW value of investment commitments made during construction. For two or more mutually exclusive alternatives, select the one with the numerically larger largest FW value.
This means that breakeven net cash flow was achieved this year. If the British conglomerate continues to own the chain, what selling price must be obtained at the end of 5 years of ownership to make the MARR? Figure S-3b presents the cash flow diagram. This i. Comment If the 'rule of 72' in Equation [l. This does not consider any annual net positive or negative cash flows during the years of ownership. In addition, permanent and charitable orgartization endowments are evaluated using the capitalized cost methods.
For a public sector alternative with an infinite or very long life, the A value determined by Equation [5. This method is covered in Chapter 9. The cash flows costs or receipts in a capitalized cost calculation are usually of two types: recurring, also called periodic, and nonrecurring.
The following procedure assists in calculating the CC for an infinite sequence of cash flows. Draw a cash flow diagram showing all nonrecurring one-time cash flows and at least two cycles of all recurring periodic cash flows.
Find the present worth of all nonrecurring amounts. This is their CC value. Find the equivalent uniform annual worth A value through one life cycle of all recurring amounts.
This is the same value in all succeeding life cycles, as explained in Chapter 6. Add this to all other uniform amounts occurring in years 1 through infinity and the result is the total equivalent uniform annual worth AW. Divide the AW obtained in step 3 by the interest rate i to obtain a CC value.
This is an application of Equation [5. Add the CC values obtained in steps 2 and 4. Drawing the cash flow diagram step 1 is more important in CC calculations than elsewhere, because it helps separate nonrecurring and recurring amounts.
In step 5 the present worths of all component cash flows have been obtained; the total capitalized cost is simply their sum. The property appraisal district for Marin County has just installed new software to track residential market values for property tax computations. The manager wants to know the total equivalent cost of all future costs incurred when the three county judges agreed to purchase the software system.
If the new system will be used for d1e indefinite future, find the equ ivalent va lue a now and b for each year hereafter. Solution a The five-step procedure is applied. Draw a cash flow diagram for two cycles Figure Label this CCI' 1. Comment The CC 2 value is calculated using n. Rework the problem using the second method suggested for calculating CC 2. For the comparison of two or more alternatives on the basis of capitalized cost, use the procedure above to find CC T for each alternative.
Since the capitalized cost represents the total present worth of financing and maintaining a given alternative forever, the alternatives will automatically be compared for the same number of years i. The alternative with the smaller capitalized cost will represent the more economical one. This evaluation is illustrated in Example 5. As in present worth analysis , it is only the differences in cash flow between the alternatives that must be considered for comparative purposes.
Therefore, whenever possible, the calculations should be simplified by eliminating the elements of cash flow which are common to both alternatives. On the other hand, if true capitalized cost values are needed to reflect actual financial obligations, actual cash flows should be used. The north site, which connects a major state highway with an interstate loop around the city, would alleviate much of the local through traffic. The disadvantages of this site are that the bridge would do little to ease local traffic congestion during rush hours, and the bridge would have to stretch from one hill to another to span the widest part of the river, railroad tracks, and local highways below.
This bridge would therefore be a suspension bridge. Solution Construct the cash flow diagrams over two cycles 20 years. If a finite-life alternative e. To determine capitalized cost for the alternative with a finite life, calculate the equivalent A value for one life cycle and divide by the interest rate Equation [5. This procedure is illustrated in the next example. The lead production engineer has outl ined below two simplified, but viable, alternatives. Alternative LT long-te rm.
There is no time limit placed on the contract, and the costs do not escalate. Alternative ST short-term. The usefu l life of a soldering system is 5 years. Perform a capitalized cost evaluation by hand and by computer. Once the evaluation is complete, use the spreadsheet for sensitivity anaJysis to determine the maximum number of soldering machines that can be purchased now and still have a capitalized cost less than that of the long-term alternative.
Add this aJTIount to the initial contract fee, which is already a capitalized cost present worth amount. Then determine the total CC using Equation [5. Cell B8 uses the same relation as in the solution by hand.
Cell B 16 uses Eq uation [5. As expected, alternative ST is selected. Compare CCST for the hand and computer solutions to note that the roundoff eITor using the tabulated interest factors gets larger for large P values. The type of sensitivity analysis requested here is easy to perform once a spreadsheet is developed.
Columns C and D replicate the evaluation for 13 and 14 machines. Thirteen is the maximum number of machines that can be purchased and have a CC for the ST alternative d1at is less than that of the LT contract. This conclusion is easily reached by comparing total CC values in rows 8 and Note: It is not necessary to duplicate column B into C and D to perform this sensitivity analysis.
Changing the entry in cell B 12 upward from 10 will provide tile same information. Duplication is shown here in order to view all the results on one spreadsheet. There is a logical linkage between payback and breakeven analysis, which is used in several chapters and discussed in detail in Chapter The payback period n" is the estimated time, usually in years, it will take for the estimated revenues and other economic benefits to recover the initial investment Chap] 13 CHAPTER 5 Present Worth Analysis and a stated rate of return.
The np value is generally not an integer. It is important to remember the following: The payback period np should never be used as the primary measure of worth to select an alternative.
Rather, it should be determined in order to provide initial screening or supplemental information in conjunction with an analysis performed using present worth or another method.
It is very important to realize that in payback analysis all net cashjlows occurring after np years are neglected. Since thi s is significantly different from the approach of PW or annual worth, or rate of return, as discussed later , where all cash flows for the entire useful life are included in the economic analysis, payback analysis can unfairly bias alternative selection.
So use payback analysis only as a screening or supplemental technique. For example, if a company plans to produce a product under contract for only 3 years and the payback period for the equipment is estimated to be 6 years, the company should not undertake the contract.
Even in this situation, the 3-year payback period is only supplemental information, not a good substitute for a complete economic analysis. This n" value serves merely as an initial indicator that a proposal is a viable alternative worthy of a full economic evaluation.
It is incorrect to use the no-return payback period to make final alterna- tive selections because it: 1. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them better absorb course material and understand difficult concepts.
Instructors, contact your Pearson representative for more information. I picked the book bought the printed edition for supplementary text for my corporate finance course I was taking for my MBA. But, I was hoping that the supplementary excel files for students are available without paying extras for MyEngineeringLab, but it was just a wish not come true till now.
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