# Contemporary Engineering Economics, 4 th edition, © 2007 Unconventional Equivalence Calculations Lecture No. 9 Chapter 3 Contemporary Engineering Economics.

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Contemporary Engineering Economics, 4 th edition, © 2007 Unconventional Equivalence Calculations Lecture No. 9 Chapter 3 Contemporary Engineering Economics Copyright © 2006

Contemporary Engineering Economics, 4 th edition, © 2007 Equivalent Present Worth Calculation – Brute Force Approach using Only P/F Factors

Contemporary Engineering Economics, 4 th edition, © 2007 \$50 \$100 \$150 \$150 \$200 0 1 2 3 4 5 6 7 8 9 Equivalent Present Worth Calculation – Grouping Approach

Contemporary Engineering Economics, 4 th edition, © 2007 Unconventional Equivalence Calculations – A Personal Savings Problem Situation 1: If you make 4 annual deposits of \$100 in your savings account which earns a 10% annual interest, what equal annual amount (A) can be withdrawn over 4 subsequent years?

Contemporary Engineering Economics, 4 th edition, © 2007 Unconventional Equivalence Calculations – An Economic Equivalence Problem Situation 2: What value of A would make the two cash flow transactions equivalent if i = 10%?

Contemporary Engineering Economics, 4 th edition, © 2007 Method 1: Establish the Economic Equivalence at n = 0

Contemporary Engineering Economics, 4 th edition, © 2007 Method 2: Establish the Economic Equivalence at n = 4

Contemporary Engineering Economics, 4 th edition, © 2007 Multiple Interest Rates \$300 \$500 \$400 5% 6% 4% Find the balance at the end of year 5. 0 1 2 3 4 5 F = ?

Contemporary Engineering Economics, 4 th edition, © 2007 Solution

Contemporary Engineering Economics, 4 th edition, © 2007 Cash Flows with Missing Payments P = ? \$100 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Missing payment i = 10%

Contemporary Engineering Economics, 4 th edition, © 2007 Solution P = ? \$100 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Pretend that we have the 10 th Payment in the amount of \$100 i = 10% \$100 Add \$100 to offset the change

Contemporary Engineering Economics, 4 th edition, © 2007 Approach P = ? \$100 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 i = 10% \$100 Equivalent Cash Inflow = Equivalent Cash Outflow

Contemporary Engineering Economics, 4 th edition, © 2007 Equivalence Relationship

Contemporary Engineering Economics, 4 th edition, © 2007 Unconventional Regularity in Cash Flow Pattern \$10,000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 C C C C C C C i = 10% Payments are made every other year

Contemporary Engineering Economics, 4 th edition, © 2007 Approach 1: Modify the Original Cash Flows \$10,000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 i = 10% A A A A A A A

Contemporary Engineering Economics, 4 th edition, © 2007 Relationship Between A and C \$10,000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 i = 10% A A A A A A A \$10,000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 C C C C C C C i = 10%

Contemporary Engineering Economics, 4 th edition, © 2007 C A =\$1,357.46 AA i = 10% Solution

Contemporary Engineering Economics, 4 th edition, © 2007 Approach 2: Modify the Interest Rate Idea: Since cash flows occur every other year, let's find out the equivalent compound interest rate that covers the two-year period. How: If interest is compounded 10% annually, the equivalent interest rate for two- year period is 21%. (1+0.10)(1+0.10) = 1.21

Contemporary Engineering Economics, 4 th edition, © 2007 Solution \$10,000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 C C C C C C C i = 21% 1 2 3 4 5 6 7

Contemporary Engineering Economics, 4 th edition, © 2007 Example 3.25 – At What Value of C would Make the Two Cash Flows Equivalent?

Contemporary Engineering Economics, 4 th edition, © 2007 Example 3.26 Establishing a College Fund

Contemporary Engineering Economics, 4 th edition, © 2007 Solution: Establish the Economic Equivalence at n = 18

Contemporary Engineering Economics, 4 th edition, © 2007 Example 3.27 Calculating an Unknown Interest Rate with Multiple Factors

Contemporary Engineering Economics, 4 th edition, © 2007 Establish an economic Equivalence at n =7

Contemporary Engineering Economics, 4 th edition, © 2007 Linear Interpolation to Find an Unknown Interest Rate

Contemporary Engineering Economics, 4 th edition, © 2007 Linear Interpolation

Contemporary Engineering Economics, 4 th edition, © 2007 Using the Goal Seek Function to Find the Unknown Interest rate

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