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Why Engineering Economy

Why Engineering Economy. Chapter 1. WHAT IS ECONOMICS ?. The study of how limited resources are used to satisfy unlimited human wants. The study of how individuals and societies choose to use scarce resources that nature and previous generations have provided.

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Why Engineering Economy

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  1. Why Engineering Economy Chapter 1

  2. WHAT IS ECONOMICS ? The study of how limited resources are used to satisfy unlimited human wants. The study of how individuals and societies choose to use scarce resources that nature and previous generations have provided.

  3. Engineers must work within the • realm of economics and justification • of engineering projects • Work with limited funds (capital) • Capital is not unlimited – rationed • Capital does not belong to the firm • Belongs to the Owners of the firm • Capital is not “free”…it has a “cost”

  4. Section 1.1 Definition ENGINEERING ECONOMY IS INVOLVED WITH THE APPLICATION OF DEFINED MATHEMATICAL RELATIONSHIPS THAT AID IN THE COMPARISON OF ECONOMIC ALTERNATIVES

  5. Problem Solving Approach • Understand the Problem • Collect all relevant data/information • Identify the criteria for decision making • Define the feasible alternatives • Evaluate each alternative using a common perspective. • Select the “best” alternative • Implement and monitor

  6. Economic Issues to be Answered before deciding on an alternative • How much does the option cost • How much will the option save • How do we get the money to pay for it • What are the tax effects • What is the criteria to be used to decide on the option • What are the assumptions used in the estimates • How dependent is a decision on the assumptions-sensitivity analysis

  7. Engineering Economy Study Approach • The parameters associated with an alternative include: • First Cost (Initial outlay) • Estimated Useful Life • Estimated Annual Income or Revenue • Estimated Annual Expenses or Costs • Salvage Value • Interest Rate • Tax Effects

  8. Time Value of Money • The time value of money is the change in the amount of money over a given time period. • This is the most important concept in Engineering Economy.

  9. Cash Flows • The parameters listed make up the cash flows associated with an alternative. • Cash flows are said to be positive when they flow into the firm (i.e. revenues) • Cash flows are said to be negative when they flow out of the firm (i.e. expenses)

  10. Alternatives • In addition to list of generated alternatives, there is the do nothing alternative. (status quo) • This is the alternative to choose when none of the generated alternatives achieve the chosen decision criteria. • Alternatives can be either independent or mutually exclusive

  11. Interest • Interest is a rental for the use of money. • It is what establishes equivalent values for different periods of time • It is the difference between a beginning amount and an ending amount

  12. Two Interest Perspectives • Interest Earned – this is the perspective of a person who either saves, invests, or loans a sum of money out, and at a later time receives a larger sum. Interest = total amount now – original amount • Interest paid – this is the perspective of a person who borrows a sum of money, and at a later time repays a larger sum. Interest = Amount owed now – original amount

  13. Interest Rate • The interest rate is the amount of interest accrued for a period of time divided by the original amount The time unit for interest payments is called the interest period. Often the interest period is a year. The above expression is for a single period.

  14. Single Period Interest Paid • Example 1.3 • You borrow $10,000 for one full year • Must pay back $10,700 at the end of one year. Interest Amount? Interest Rate? • Interest Amount (I) = $10,700 - $10,000 • Interest Amount = $700 for the year. The $700 represents the return to the lender for this use of his/her funds for one year • Interest rate (i) = 700/$10,000 = 7%/Yr. 7% is the return earned by the lender

  15. Single Period Interest Paid • Example 1.4 • Borrow $20,000 for 1 year at 9% interest per year • Interest? Total Due? • i = 0.09 per year and N = 1 Year • Interest (I) = (0.09)($20,000) = $1,800 • Pay $20,000 + (0.09)($20,000) at end of 1 year • Total amt. paid one year hence $20,000 + $1,800 = $21,800

  16. Example 1.4 • Note the following • Total Amount Due one year hence is ($20,000) + 0.09($20,000) =$20,000(1+.09) = $21,800 The (1.09) factor accounts for the repayment of the $20,000 and the interest amount This (1+i) factor will be one of the important interest factors to be seen later

  17. Interest Earned and Rate of Return (Ex 1.4 data) • Assume you invest $20,000 for one year in a venture that will return to you, 9% per year. • Original $20,000 back • Plus…….. • The 9% return on $20,000 = $1,800 We say that you earned 9%/year on the investment! This is your RATE of RETURN (ROR) on the investmen

  18. Interest rate • ROI or Return on Investment is another term for rate of return used in settings where the original amount invested is provided by capital funds • The calculation for determining interest rate, rate of return, and return on investment are identical. • The time unit for which the amount of interest accrues is the interest period.

  19. Economic Equivalence • Economic Equivalence • Two sums of money at two different points in time can be economically equivalent if: • We consider an interest rate and, • No. of time periods between the two sums • This illustrates the time value of money concept

  20. T=0 t = 1 Yr Equivalence Example • Return to Example 1.4 i = 9% • Diagram the loan (Cash Flow Diagram) • The company’s perspective is shown + $20,000 is received here $21,800 paid back here _

  21. T=0 t = 1 Yr Equivalence Example $20,000 now is economically equivalent to $21,800 one year from now IF the interest rate is set to equal 9%/year $20,000 is received here $21,800 paid back here

  22. The Cash Flow Diagram: • Extremely valuable analysis tool • First step in the solution process • Graphical Representation on a time scale • Does not have to be drawn “to exact scale” • But, should be neat and properly labeled • Will be helpful on most in-class exams

  23. Important TERMS • CASH INFLOWS • Money flowing INTO the firm from outside • Revenues, Savings, Salvage Values, etc. • CASH OUTFLOWS • Disbursements • First costs of assets, labor, salaries, taxes paid, utilities, rents, interest, etc.

  24. Net Cash Flows • A NET CASH FLOW is • Cash Inflows – Cash Outflows • (for a given time period) • We normally assume that all cash flows occur: • At the END of a given time period. This is the end-of-period convention

  25. Cash Flow diagrams - timeline • Assume a 5-year problem • The basic time line is shown below The present is time 0, generally.

  26. Displaying Cash Flows • A sign convention is applied • Positive cash flows (Inflows) are normally drawn upward from the time line • Negative cash flows (Outflows) are normally drawn downward from the time line

  27. Negative CF’s at t = 2 & 3 Sample CF Diagram Positive CF at t = 1

  28. Example 1.17 • A father wants to deposit an unknown lump‑sum amount into an investment opportunity 2 years from now that is large enough to withdraw $4,000 per year for state university tuition for 5 years starting 3 years from now. • Construct the cash flow diagram, assume the rate of return is estimated to be 15.5% per year.

  29. Example 1.17 CF Diagram Using PV(.155,5,4000), P = $13,251.40

  30. Multi-Period Simple and Compound Interest • Prior discussion on interest and interest rate were for one interest period • For more than one interest period there are two “types” of interest calculations • Simple Interest • Compound Interest • Compound Interest is more common worldwide and applies to most analysis situations

  31. Simple Interest Over Time • Simple Interest • Calculated on the principal amount only • Easy (simple) to calculate • Simple Interest is: • (principal)*(interest rate)*(number of periods) • $I = (P)*(i)*(n) i = interest rate I = interest

  32. Simple Interest Over Time • Ex 1.7 • An engineer borrows $1,000 for 3 years at 5% per year, simple interest • Let “P” = the principal sum ($1,000) • i = the interest rate (5%/year) • Let n = number of years (3)

  33. Simple Interest Over Time • Simple Interest Definition • I = P(i)(N) • For Ex. 1.7: • I = $1,000(0.05)(3) = $150.00 • Total Interest over 3 Years

  34. P=$1,000 1 2 3 I1=$50.00 Simple Interest Over Time • Year-by-Year Analysis: Simple Interest • Year 1 • I1 = $1,000(0.05) = $50.00 accrues 0 $50 interest accrues but is not paid

  35. P=$1,000 1 2 3 I1=$50.00 I2=$50.00 Simple Interest Over Time • Year 2 • I2 = $1,000(0.05) = $50.00 accrues 0 Another $50.00 interest accrues but is not paid

  36. P=$1,000 1 2 3 Pay back $1,000 + $150 of interest I2=$50.00 I1=$50.00 I3=$50.00 Simple Interest Over Time • Year 3 • I3 = $1,000(0.05) = $50.00 accrues 0 The unpaid interest did not earn interest over the 3-year period

  37. Simple Interest Summary • In a multi-period situation with simple interest: • The accrued interest does not earn interest during the succeeding time period. • Normally, the total sum borrowed (lent) is paid back at the end of the agreed time period PLUS the accrued (owed but not paid) interest.

  38. Compound Interest Over Time • Compound Interest is different • For compound interest the interest accrued for each interest period is calculated on the principal plus the total amount of interest accumulated in all prior periods. This accrued interest is then added to the prior balance to form a new principal balance. • Interest then “earns interest” • Compound interest is the interest type used to calculate the time value of money for Engineering Economy Analysis

  39. Compound Interest Over Time • Unlike simple interest, compound interest does not have a formula for calculating the total amount of interest over several interest periods. • Compound interest has to be calculated each period to determine the principal plus accumulated interest that the interest rate is applied to in the next period. Interest = (interest rate) X [principal + accrued interest]

  40. Compound Interest Example 1.8 • Here an engineer borrows $1000 @ 5% per year compound interest. How much is due after 3 years. • P = $1,000 • i = 5% per year compounded annually (C.A.) • N = 3 years

  41. P=$1,000 1 2 3 I1=$50.00 I2=$52.50 I3=$55.13 Example 1.8 Cash Flow For 3 yrs of compound interest, accrued not paid: i = 5% Owe at t = 3 years: $1,000 + 50.00 + 52.50 + 55.13 = $1,157.63 + 0 - $1157.63

  42. Compound interest • For the example: • P0 = +$1,000 • I1 = $1,000(0.05) = $50.00 • Owe P1 = $1,000 + 50 = $1,050 (but we don’t pay yet!) • New Principal sum at end of t = 1: = $1,050.00

  43. Compound Interest: t = 2 • Principal at end of year 1: $1,050.00 • I2 = $1,050(0.05) = $52.50 (owed but not paid) • Add to the current unpaid balance yields: • $1,050 + 52.50 = $1,102.50 • New unpaid balance or New Principal Amount • Now, go to year 3…….

  44. Compound Interest: t = 3 • New Principal sum: $1,102.50 • I3 = $1102.50(0.05) = $55.125 = $55.13 • Add to the beginning of year principal yields: • $1102.50 + 55.13 = $1157.63 • This is the loan payoff at the end of 3 years • Note how the interest amounts were added to form a new principal sum with interest calculated on that new amount

  45. Comparison of simple and compound interest, Ex 1.7 and 1.8

  46. Example 1.9 • Five plans are shown that will pay off a loan of $5,000 over 5 years with interest at 8% per year. We illustrate differences in equivalence depending upon interest type, interest timing, and method for repaying principal. • Plan 1. Simple Interest, pay all at the end • Plan 2. Compound Interest, pay all at the end • Plan 3. Simple interest, pay interest at end of each year. Pay the principal at the end of N = 5 • Plan 4. Compound Interest, pay interest and part of the principal each year (pay 20% of the Prin. Amt.)

  47. Example 1.9 • Plan 5. Compound Interest, make equal payments of the compound interest and principal reduction over 5 years with end-of-year payments. Note: The following tables will show the five approaches. For now, do not try to understand how all of the numbers are determined (that will come later!). Focus on the plans and how these tables illustrate economic equivalence.

  48. Plan 1: @ 8% Simple Interest • Simple Interest: Pay all at end on $5,000 Loan

  49. Plan 2: Compound Interest @ 8%/yr • Compound interest: Pay all at the End of 5 Years

  50. Plan 3: Simple Interest Pd. Annually • Principal Paid at the End (balloon Note)

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