Lecture no05 economic equivalence

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