Economic Equivalence Lecture No Chapter Contemporary Engineering Economics Copyright © 2016 th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Economic Equivalence What we mean by “economic equivalence?” Why we need to establish an economic equivalence? How we measure and compare various cash payments received at different points in time? th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved What is “Economic Equivalence?” th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Equivalence Example: Compounding Concept • If you deposit P dollars today for N periods at interest rate i, you will have F dollars at the end of period N th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Equivalence – Discounting Concept • F dollars at the end of period N is equal to a single sum P dollars now, if your earning power is measured in terms of interest rate i th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Equivalence Example 3.3 Given: If you deposit $2,042 today in a savings account that pays an 8% interest annually, how much would you have at the end of years? Find: At an 8% interest, what is the equivalent worth of $2,042 now in years? th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Solution Various dollar amounts that will be economically equivalent to $3,000 in five years, at an interest rate of 8% th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Equivalent Example 3.4: Cash Flows Given: $2,042 today was equivalent to receiving $3,000 in five years, at an interest rate of 8% Find: Are these two cash flows are also equivalent at the end of year 3? th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Solution Equivalent cash flows are equivalent at any common point in time, as long as we use the same interest rate (8%, in our example) th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Finding an Equivalent Value for Multiple Payments Solution Compute the equivalent value of the cash flow series at n = 3, using i = 10% V3 $200 $150 $120 $100 $100 $80 th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Comparing Two Different Cash Flows Find C, making the two cash flow transactions equivalent at i = 10% Approach Step 1: Select a base period to use, say n = Step 2: Find the equivalent lump sum value at n = for both A and B Step 3: Equate both equivalent values and solve for the unknown, C th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Finding an Interest Rate that Establishes an Economic Equivalence At what interest rate would you be indifferent choosing between the two cash Approach flows? Step 1: Select a base period to compute the equivalent value (say, n = 3) Step 2: Find the equivalent worth of each cash flow series at n = $1,000 $500 $1,000 A $500 A i = 8% $502 $502 $502 B th Contemporary Engineering Economics, edition Park Option A : F33 = $500(1.08)33 + $1,000 = $1,630 Option B : F33 = $502(1.08)2 + $502(1.08) + $502 = $1,630 $502 $502 B Copyright © 2016 by Pearson Education, Inc All Rights Reserved $502 .. .Economic Equivalence What we mean by economic equivalence? ” Why we need to establish an economic equivalence? How we measure and compare various... Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved What is Economic Equivalence? ” th Contemporary Engineering Economics, edition Park... Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Finding an Interest Rate that Establishes an Economic Equivalence At what interest