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**Engineering Economics II Choices Between Alternatives**

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Basic Concepts The goal of this topic is to investigate few methods to determine the best alternative out of a set of a small set of alternatives. Maximization of net Profit: Assume that the total benefit (TB), the total cost (TC), and the net benefit (NB) are functions of the scale or size of the project (Q). For Example, the TB, TC or NB of a dam is a function of the storage capacity and they are functions of the number of rooms in a motel. We say: TB(Q), TC(Q) or NB(Q). For a single project, our goal could be to maximize TN Maximize TN (Q) = TB (Q) - TC (Q)

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Examining Figures 14.1 and 14.2, one can see that max or min NB(Q) occurs when a 45° line is tangent to the TB Vs TC curve. In case of comparing multiple projects, one can compare their net benefit values or use a graph such as Figure 14.3 to select the one with highest net benefit. The remainder of this lecture is a discussion of three methods for choosing between alternatives. The idea is to reduce the benefits and the costs to the same time frame (present or annual) and compare them.

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**1- Present Worth Analysis**

First method of choice between alternatives The most commonly used method in Civil and environmental applications. The criterion is still basically to choose the project with max. net benefit but comparing the present worth, we choose the project with max. present worth of net benefit (PWNB). If J is project index, then Maximizej {PWNB = PWBj - PWCj} If PWNB is equal for all the projects, we choose the one with min. present worth of cost (PWC).

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**Examples 14-1 Analysis period must be the same. Four ways:**

use the least common multiplier of the useful lifetime of the alternatives. Figure 14-4. use the market value at the end of the analysis period. Figure 14-5 assume a long analysis period and neglect cost or benefit beyond that. use infinite analysis period Examples 14-1

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Example An engineering company is considering the purchase of one of two computer systems. System 1 is based on small, decentralized personal computers and has an initial cost of $100,000. These will be replaced in five years at the cost, $100,000. Salvage value is $10,000 at the end of years 5 and 10. It is estimated that the benefits for the first five years will be $30,000 per year, and for the second five years, $60,000 per year.

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System 2 is based on larger, more powerful work stations and has an initial cost of $500,000. Replacement will occur at the end of year 10, with a salvage value of $5,000. Benefits are estimated to be $90,000 per year over the ten-year period. The firm uses a 10% interest rate of interest. Which system should the company purchase, if any?

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**Annual Cash Flow Analysis**

Criterion is still choosing the project with max net benefit, but considering the equivalent uniform annual of net benefit (EUANB) instead of (PWNB). the goal is: maximizej = {EUANBj = EUABj - EUACj} In certain cases we may consider the EUAC or the EUAB individually. A very flexible method since we are comparing uniform annual quantities.

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Analysis period: if multiple of any project’s lifetime, simply compute the uniform annual cash flow for all of them. For example, comparing two projects of 12 and 18 years lifetimes over 36 years, the same pattern of cash flow will be repeated three times for project one and two times for project two. We simply compare the annual cash flow computed over one lifetime for project 1 and one lifetime for project 2. if not a multiple of the lifetime of any of the projects’, the value of the project at the end of the analysis period must be computed and considered when computing the annual cash flow.

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Example An engineer must choose between two pumps for use in a water distribution system. Both pump A and pump B will deliver water at an adequate flow rate and pressure head. Data are The interest rate is 7%. Find the best pump. Pump A Pump B Initial cost ($) 200,000 300,000 Operating cost ($/yr) 30,000 23,000 Lifetime (yrs) 12 Salvage value ($) 10,000 60,000

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Example Assume that the lifetime of pump B in the previous xample is 16 years rather than 12. The analysis period is 48 years. Which pump is now the best?

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**3- Incremental Benefit-Cost Ratio Analysis**

The criterion is to compare the B-C ratio: B-C ratio = PWB / PWC or = EUAB / EAUC Simply comparing the B-C ratios does not guarantee max. net benefit. Comparing the B-C ratio can be a second step in the analysis. After neglecting the projects with B-C < 1, one of two cases: if all the projects have either the same benefit or cost choose the one with the largest B-C ratio. Otherwise;

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**conduct incremental B-C analysis:**

1. order the alternatives from the lowest to the highest cost and number the projects 1, 2,..., P. 2. compute the ratio: DB / DC for projects 1 and 2. DB / DC = (PWB2 - PWB1) / (PWC2 - PWC1) or = (EUAB2 - EUAB1) / (EUAC2 - EUAC1) if DB / DC ³ 1 select project 2 as best so far. otherwise select project 1 as best so far. In case of a tie, choose the project with a smaller cost which is still project 1 3. compute DB / DC between the best project so far and the next least costly project not yet tested and select a new best. 4. Repeat step 3 until all projects have been tested. The surviving project is the best. Examples 14-5

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**Example Use the project data from the table below and find the**

best alternative using incremental B-C ratio analysis. Project E C A D F B Benefit ($ million) 3.0 11.0 12.0 17.0 19.0 Cost ($million) 5.0 7.0 10.0 16.0 Net benefit ($ million) -2.0 4.0 2.0 0.0

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Chapter 6 Annual Cash Flow Analysis

Chapter 6 Annual Cash Flow Analysis

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