Economic Analysis Methods Engineering Economics Day 3: Rate of Return Analysis Three commonly used economic analysis methods are 1. Present Worth Analysis 2. Annual Worth Analysis 3. www.engr.sjsu.edu/bjfurman/courses/me195/presentations/engeconpatel3nov4.ppt Meaning of Rate of Return Solution: $13,312, In 197, when Wal-Mart Stores, Inc. went public, an investment of 1 shares cost $1,65. That investment would have been worth $13,312, on January 31, 2. What is the rate of return on that investment? 3 $1,65 n F = P ( 1 + i )
Opportunity Cost Suppose that you invested that same amount ($1,65) in a savings account at 6% per year. You would have on January, 2. What is the meaning of this 6% interest here? This is your if putting money in savings account was the best you can do at that time. ROR & MARR In 197, as long as you could earn more than 6% interest in another investment, you should take that investment. Therefore, that 6% is viewed as a or required rate of return. Apply the following decision rule to see if a proposed investment is a good one. Minimum Attractive Rate of Return (MARR) Sometimes referred to as the hurdle rate. This is the rate of return ( ) required by a particular organization or company It is based on the the associated with the proposal the likely Example #1 An initial investment of $5K is being considered. The revenues from this investment are $25K at the end of the first year, $2K at the end of the second, and $15K at the end of the third. If the desired return on investment is 18%, is the project acceptable? Is present value of benefits greater than present value of costs? www.latrobe.edu.au/eemanage/ele2emt-7/economics-7/2emt-7-4e.ppt.
Example #1 - CFD Rate of Return (ROR) Analysis Steps to determine rate of return for a single stand-alone investment Step 1: Take the dollar amounts to the same using the compound interest formulas Step 2: Equate the sum of the revenues to the sum of the costs at that point in time and www.engr.sjsu.edu/bjfurman/courses/me195/presentations/engeconpatel3nov4.ppt Example #2 At what minimum attractive rate of return (MARR) would the project of Example #1 be acceptable? At what interest rate is the present value of benefits equal present value of costs? Present Value Calculation in Excel PV(rate, nper, pmt, fv, type) is the interest rate per period. is the total number of payment periods in an annuity. is the payment made each period; it cannot change over the life of the annuity. Note that Excel will return a negative PV for a positive payment and vice-versa is future value = for payments at end of period
Present Value Calculation in Excel PV(rate, nper, pmt, fv, type) (P/F, 8%, 7) (P/A, 6%, 1) Future Value Calculation in Excel FV(rate, nper, pmt, pv, type) is the interest rate per period. is the total number of payment periods in an annuity. is the payment made each period; it cannot change over the life of the annuity. Note that Excel will return a negative PV for a positive payment and vice-versa is present value = for payments at end of period Future Value Calculation in Excel FV(rate, nper, pmt, pv, type) (F/P,1%, 6) (F/A, 5%, 2) Annual Payment Calculations in Excel PMT(rate, nper, pv, fv, type) is the interest rate for the loan is the total number of payment periods for the loan is present value (or principal) is future value (assumed if omitted) = for payments at end of period
Future Value Calculation in Excel PMT(rate, nper, pv, fv, type) (A/F, 4%,1) (A/P, 7%, 15) Example #2 - Spreadsheet i = 18.% Benefit / Present Present Year Cost ($K) Worth Factor Worth ($K) -5 1-5. 1 25.8475 21.188 2 2.7182 14.364 3 15.686 9.129 Total: -5.319 Example #3 Find the ROR of an investment of $1K with a revenue of $16K a year for 1 years. Example #4 Find the ROR an investment of $16K a year for 1 years with a return of $25K at year 1 25 16 1 2 3 4 5 6 7 8 9 1-1 -16 1 2 3 4 5 6 7 8 9 1 http://www.me.utexas.edu/~jensen/ormm/instruction/powerpoint/economics/5.1ror.ppt. http://www.me.utexas.edu/~jensen/ormm/instruction/powerpoint/economics/5.1ror.ppt.