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Engineering Economy Learning Outcomes Determine the role of engineering economy in the decision making process. Identify what is needed to successfully perform an engineering economy study. Perform calculations about interest rate and rate of return. Understand what equivalence means in economic terms. Learning Outcomes Calculate simple interest and compound interest for one or more interest periods Identify and use engineering economy terminology and symbols. Understand cash flows, their estimation, and how to graphically represent them. To understand and Calculate Break Even Point/Analysis Foundations of Engineering Economy The need for engineering economy is primarily motivated by the work that engineers do in performing analysis, synthesizing, and coming to a conclusion as they work on projects of all sizes. In other words, engineering economy is at the heart of making decisions. These decisions involve the fundamental elements of cash flows of money, time, and interest rates. WHAT IS ENGINEERING ECONOMY? Simplest of terms, engineering economy is a collection of techniques that simplify comparisons of alternatives on an economic basis. Engineering economy is not a method or process for determining what the alternatives are. Engineering economic analysis is able to answer professional and personal financial questions. PERFORMING AN ENGINEERING ECONOMY STUDY In order to apply economic analysis techniques, it is necessary to understand the basic terminology and fundamental concepts that form the foundation for engineering economy studies. Some of these terms and concepts are described below. Alternatives An alternative is a stand-alone solution for a given situation. In engineering practice, there are always several ways of accomplishing a given task, and it is necessary to be able to compare them in a rational manner so that the most economical alternative can be selected. Cash Flows The estimated inflows (revenues and savings) and outflows (costs) of money are called cash flows. These estimates are truly the heart of an engineering economic analysis. Alternative Selection Every situation has at least two alternatives. In addition to the one or more formulated alternatives, there is always the alternative of inaction, called the do-nothing (DN) alternative. Evaluation Criteria Whether we are aware of it or not, we use criteria every day to choose between alternatives. For example, when you drive to campus, you decide to take the “best”route. But how did you define best? Intangible Factors In many cases, alternatives have noneconomic or intangible factors that are difficult to quantify. When the alternatives under consideration are hard to distinguish economically, intangible factors may tilt the decision in the direction of one of the alternatives. Time Value of Money It is often said that money makes money. If a person or company borrows money today, by tomorrow more than the original loan principal will be owed. This fact is also explained by the time value of money. The change in the amount of money over a given time period is called the time value of money; it is the most important concept in engineering economy. INTEREST RATE, RATE OF RETURN, AND MARR Interest is the manifestation of the time value of money, and it essentially represents “rent” paid for use of the money. Interest is paid when a person or organization borrows money (obtains a loan) and repays a larger amount. Interest is earned when a person or organization saves, invests, or lends money and obtains a return of a larger amount. Interest = end amount - original amount Eq-1 INTEREST RATE, RATE OF RETURN, AND MARR The time unit of the interest rate is called the interest period. By far the most common interest period used to state an interest rate is 1 year. Shorter time periods can be used, such as, 1% per month. The term return on investment (ROI) is used equivalently with ROR in different industries and settings, especially where large capital funds are committed to engineering-oriented programs. The term interest rate paid is more appropriate from the borrower’s perspective, while rate of return earned is better from the investor’s perspective. EXAMPLE-1 An employee at LaserKinetics.com borrows $10,000 on May 1 and must repay a total of $10,700 exactly 1 year later. Determine the interest amount and the interest rate paid. The perspective here is that of the borrower since $10,700 repays a loan. Apply Equation 1 to determine the interest paid. Interest paid =$10,700 - 10,000 = $700 Equation 2 determines the interest rate paid for 1 year. EXAMPLE-2 Calculate the amount deposited 1 year ago to have $1000 now at an interest rate of 5% per year. Then calculate the amount of interest earned during this time period. Minimum Attractive Rate of Return (MARR) Engineering alternatives are evaluated upon the prognosis that a reasonable rate of return (ROR) can be realized. A reasonable rate must be established so that the accept/reject decision can be made. This reasonable rate, called the minimum attractive rate of return (MARR), is the lowest interest rate that will induce companies or individuals to invest their money. For example, if a corporation can borrow capital funds at an average of 5% per year and expects to clear at least 6% per year on a project, the MARR will be at least 11% per year. EQUIVALENCE Equivalent terms are used often in the transfer between scales and units. For example, 1000 meters is equal to (or equivalent to) 1 kilometer, 12 inches equals 1 foot, and 1 quart equals 2 pints or 0.946 liter. In engineering economy, when considered together, the time value of money and the interest rate help develop the concept of economic equivalence, which means that different sums of money at different times would be equal in economic value. For example, if the interest rate is 6% per year, $100 today (present time) is equivalent to $106 one year from today. EQUIVALENCE EXAMPLE - 3 AC-Delco makes auto batteries available to General Motors dealers through privately owned distributorships. In general, batteries are stored throughout the year, and a 5% cost increase is added each year to cover the inventory carrying charge for the distributorship owner. Assume you own the City Center Delco facility. Make the calculations necessary to show which of the following statements are true and which are false about battery costs. EXAMPLE - 3 a. The amount of $98 now is equivalent to a cost of $105.60 one year from now. b. A truck battery cost of $200 one year ago is equivalent to $205 now. c. A $38 cost now is equivalent to $39.90 one year from now. d. A $3000 cost now is equivalent to $2887.14 one year ago. e. The carrying charge accumulated in 1 year on an investment of $2000 worth of batteries is $100. Solution- 3 a. Total amount accrued 98(1.05) $102.90 $105.60; therefore, it is false. Another way to solve this is as follows: Required original cost is 105.601.05 $100.57 $98. b. Required old cost is 205.001.05 $195.24 $200; therefore, it is false. c. The cost 1 year from now is $38(1.05) $39.90; true. d. Cost one year ago is 30001.05 $2857.14 2887.14; false. e. The charge is 5% per year interest, or $2000(0.05) $100; true. SIMPLE AND COMPOUND INTEREST The terms interest, interest period, and interest rate were introduced in previous slides for calculating equivalent sums of money for one interest period in the past and one period in the future. However, for more than one interest period, the terms simple interest and compound interest become important. SIMPLE AND COMPOUND INTEREST Simple interest is calculated using the principal only, ignoring any interest accrued in preceding interest periods. The total simple interest over several periods is computed as where the interest rate is expressed in decimal form. Therefore, the total (future) amount accumulated after several periods is the principal plus interest over all n periods. SIMPLE AND COMPOUND INTEREST For compound interest, the interest accrued for each interest period is calculated on the principal plus the total amount of interest accumulated in all previous periods. Thus, compound interest means interest on top of interest. Compound interest reflects the effect of the time value of money on the interest also. Now the interest for one period is calculated as EXAMPLE - 4 HP borrowed money to do rapid prototyping for a new ruggedized computer that targets desert oilfield conditions. The loan is $1 million for 3 years at 5% per year simple interest. How much money will HP repay at the end of 3 years? Tabulate the results in $1000 units. Solution- 4 The $50,000 interest accrued in the first year and the $50,000 accrued in the second year do not earn interest. The interest due each year is calculated only on the $1,000,000 principal. EXAMPLE - 5 If HP borrows $1,000,000 from a different source at 5% per year compound interest, compute the total amount due after 3 years. Compare the results of this and the previous example. TERMINOLOGY AND SYMBOLS P= value or amount of money at a time designated as the present or time 0. Also, P is referred to as present worth (PW), present value (PV), net present value (NPV), discounted cash flow (DCF), and capitalized cost (CC); dollars F= value or amount of money at some future time. Also, F is called future worth (FW) and future value (FV); dollars TERMINOLOGY AND SYMBOLS A= series of consecutive, equal, end-of-period amounts of money. A is also called the annual worth (AW), equivalent uniform annual worth (EUAW), and equivalent annual cost (EAC); dollars per year, dollars per month n= number of interest periods; years, months, days i= interest rate or rate of return per time period; percent per year, percent per month, percent per day t= time, stated in periods; years, months, days CASH FLOWS: THEIR ESTIMATION AND DIAGRAMMING Cash flows are inflows and outflows of money. These cash flows may be estimates or observed values. Every person or company has cash receipts—revenue and income (inflows); and cash disbursements—expenses and costs (outflows). Cash flows occur during specified periods of time, such as 1 month or 1 year. Samples of Cash Inflow Estimates Revenues (from sales and contracts) Operating cost reductions (resulting from an alternative) Salvage value Construction and facility cost savings Receipt of loan principal Income tax savings Receipts from stock and bond sales 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 Major expected/unexpected upgrade costs Income taxes Once the cash inflow and outflow estimates are developed, the net cash flow can be determined. Cash Flow Diagram 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. Example of positive and negative cash flows. 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 1.4 illustrates a receipt (cash inflow) at the end of year 1 and equal disbursements (cash outflows) at the end of years 2 and 3. EXAMPLE - 6 A new college graduate has a job with Boeing Aerospace. She plans to borrow $10,000 now to help in buying a car. She has arranged to repay the entire principal plus 8% per year interest after 5 years. Identify the engineering economy symbols involved and their values for the total owed after 5 years. Construct the cash flow diagram. EXAMPLE - 7 A father wants to deposit an unknown lump-sum amount into an investment opportunity 2 years from now that is large enough to withdraw $4000 per year for state university tuition for 5 years starting 3 years from now. If the rate of return is estimated to be 15.5% per year, construct the cash flow diagram. Solution - 7 Each year Exxon-Mobil expends large amounts of funds for mechanical safety features throughout its worldwide operations. Carla Ramos, a lead engineer for Mexico and Central American operations, plans expenditures of $1 million now and each of the next 4 years just for the improvement of field-based pressure release valves. Construct the cash flow diagram to find the equivalent value of these expenditures at the end of year 4, using a cost of capital estimate for safety-related funds of 12% per year. Your boss asks… How many of these things do we have to sell before we start making money? Use your arrow keys to navigate the slides Then your boss asks… If we sell 100,000 units, what will our profit be? Finally, your boss asks… How much do we make on one of these? Are you going to have the answers? Surprisingly, it is pretty easy to answer these questions... If you know how. In fact, those who become good at this can answer these questions in their heads. Here is how it is done… Break Even Analysis Break-Even Analysis is used to predict future profits/losses predict results eg produce Product A or Product B Break-Even Point is when Sales Revenue equals Total Costs at this point no profit or loss is incurred the firm merely covers its total costs Break-Even Point can be shown in graph form or by use of formulae Break Even Analysis In order to calculate how profitable a product will be, we must firstly look at the Costs involved There are two basic types of costs a company incurs. • Variable Costs • Fixed Costs Variable costs are costs that change with changes in production levels or sales. Examples include: Costs of materials used in the production of the goods. Fixed costs remain roughly the same regardless of sales/output levels. Examples include: Rent, Insurance and Wages Break Even Analysis TOTAL COSTS Total Costs is simply Fixed Costs and Variable Costs added together. TC = FC + VC As Total Costs include some of the Variable Costs then Total Costs will also change with any changes in output/sales. If output/sales rise then so will Total Costs. If output/sales fall then so will Total Costs. Break Even Analysis The Break-even point occurs when Total Costs equals Revenue (Sales Income) Revenues (Sales Income) = Total Costs At this point the business is not making a Profit nor incurring a Loss – it is merely covering its Total Costs Let us have a look at a simple example. Bannerman Trading Company opens a flower shop. Break Even Chart Costs/Revenue TR BEP TC VC The Break-even point occurs where total revenue equals total costs – the firm, in this example would have to sell Q1 to generate sufficient revenue (income) to cover its total costs. FC Q1 Output/Sales Assumptions of Break Even Analysis All Fixed and Variable costs can be identified Variable costs are assumed to vary directly with output Fixed costs will remain constant Selling prices are assumed to remain constant for all levels of output Assumptions of Break Even Analysis The sales mix of products will remain constant – break even charts cannot handle multi-product situations It is assumed that all production will be sold The volume of activity is the only relevant factor which will affect costs Limitations of Break Even Analysis Some costs cannot be identified as precisely Fixed or Variable Semi-variable costs cannot be easily accommodated in break-even analysis Costs and revenues tend not to be constant With Fixed costs the assumption that they are constant over the whole range of output from zero to maximum capacity is unrealistic Limitations of Break Even Analysis Price reduction may be necessary to protect sales in the face of increased competition The sales mix may change with changes in tastes and fashions Productivity may be affected by strikes and absenteeism The balance between Fixed and Variable costs may be altered by new technology Break Even Analysis Example Fixed Costs: • Rent: $400 • Helper (Wages): $ 200 Variable Costs: • Flowers: $ 0.50 per bunch Selling Price: • Flowers: $ 2 per bunch So we know that: Total Fixed Costs = $ 600 Variable Cost per Unit = $ 0.50 Selling Price per Unit = $ 2.00 Break Even Analysis SP = $2.00 VC = $0.50 FC = $600 We must firstly calculate how much income from each bunch of flowers can go towards covering the Fixed Costs. This is called the Unit Contribution. Selling Price – Variable Costs = Unit Contribution $2.00 - $0.50 = $1.50 For every bunch of flowers sold $1.50 can go towards covering Fixed Costs Break Even Analysis Now to calculate how many units must be sold to cover Total Costs (FC + VC) SP = $2.00 VC = $0.50 This is called the Break Even Point Break Even Point = Fixed Costs Unit Contribution $600 $1.50 = 400 Units Unit cont = $1.50 FC = $600 Therefore 400 bunches of flowers must be sold to Break Even – at this the point the business is not making a Profit nor incurring a Loss – it is merely covering its Total Costs Break Even Analysis Lets try another example: Selling Price per unit = $5 Variable Cost per unit = $2 Fixed Costs = $300 How many units must be sold in order to Break Even? Break Even Analysis SP = $5.00 VC = $2.00 First calculate the Unit Contribution FC = $300 SP – VC = Unit Contribution $5.00 - $2.00 = $3.00 Now calculate Break Even point by using the formula – Fixed Costs Unit Contribution $300 $3.00 = 100 units Therefore 100 units must be sold in order to Break Even Break Even Analysis Break Even can also be used to calculate Profit (or Loss) at a given level of output For example: J Bannerman sells Golf Clubs. How much profit/loss is made when 5000 golf clubs are sold? Each Golf Club is sold for $20 Variable Costs per golf club are $10 Fixed Costs total $24,000 Break Even Analysis SP = $20.00 VC = $10.00 FC = $24,000 Sales = 5,000 units Firstly, calculate Unit Contribution SP – VC = Unit Contribution $20.00 - $10.00 = $10.00 Now calculate Total Contribution when 5,000 golf clubs are sold Unit Contribution x no of units = Total Contribution $10.00 x 5,000 = $50,000 Now calculate Net Profit at 5,000 units Total Contribution – Fixed Costs = Net Profit $50,000 - $24,000 = $26,000 Break Even Analysis SP = $2.50 Lets try another example. Fixed Costs = Caroline Wilson owns a florist shop. Rent $1,050 Insurance $200 Total FC $1,250 She buys each bunch of flowers for $1.49 Variable Costs = $1.49 and special wrapping paper for $3 per Flowers $0.01 roll. Each roll of wrapping paper will Paper wrap 300 bunches of flowers. Rent of ($3/300) her premises is $1,050 per month and Total VC $1.50 she pays monthly insurance of $200. So: Caroline sells each bunch of flowers SP = $2.50 for $2.50. What do we know? VC = $1.50 FC = $1,250 Break Even Analysis SP = $2.50 VC = $1.50 Calculate Caroline’s Break Even FC = $1,250 Point and also how much Profit would she make if she sold 2,000 bunches of flowers? Firstly, calculate Unit Contribution SP – VC = Unit Contribution $2.50 - $1.50 = $1.00 Now calculate Break Even Fixed Costs Unit Contribution $1,250 $1.00 = 1,250 units Break Even Analysis SP = $2.50 How much Profit would she make FC = $1,250 if she sold 2,000 bunches of flowers? Unit Cont = $1.00 VC = $1.50 Now, calculate the profit at 2,000 bunches of flowers Unit Contribution x No of Units = Total contribution $1.00 – 2,000 units = $2,000 Total Contribution – Fixed Costs = Net Profit $2,000 - $1,250 = $750 Break Even Analysis The formulae used so far assumes that Unit Costs are known ie Unit Selling Price and Unit Variable Cost When no unit costs are known, the Profit/Volume Ratio should be used instead Profit Volume Ratio P/V Ratio (Profit/Volume Ratio) = Total Contribution / Sales x 100 If asked to calculate the volume of sales needed to BreakEven (when no unit costs are given) the following formula should be used: Sales at BEP = Fixed Costs / Profit/Volume Ratio Profit Volume Ratio Example Sales $60,000 Variable Costs $24,000 Fixed Costs $14,000 Calculate the P/V Ratio and the BEP Answer Sales – Variable Costs = Total Contribution $60,000 - $24,000 = $36,000 Total Contribution / Sales = P/V Ratio ($36,000 / $60,000) x 100 = 60% Fixed Costs / P/V Ratio = Sales at BEP $14,000 / 60% = $23,333 Therefore $23,333 of Sales are necessary in order to Break-Even