1. L7: Unconventional Equivalence Calculations
ECON 320 Engineering Economics
Mahmut Ali GOKCE
Industrial Systems Engineering
Computer Sciences

2. Composite Cash Flows $200 $150 $150 $150 $150 $100 $100 $100 $50
$150 $150 $150 $150
$100
$100
$100
$50

3. Unconventional Equivalence Calculations
Situation 1: If you make 4 annual deposits of $100 in your savings account which earns 10% annual interest, what equal annual amount can be withdrawn over 4 subsequent years?

4. Unconventional Equivalence Calculations
Situation 2:
What value of A would make the two cash flow transactions equivalent if i = 10%?

7. Multiple Interest Rates
F = ?
Find the balance at the end of year 5. 6% 4% 4% 6% 5% 2 4 5 1 3
$400
$300
$500

8. Solution

9. Cash Flows with Missing Payments
$100
i = 10%
Missing payment

10. Solution P = ? i = 10% Add this cash flow to offset the change $100
$100
Pretend that we have the 10th
payment
i = 10%

11. Approach
P = ?
$100
$100
i = 10%
Equivalent Cash Inflow = Equivalent Cash Outflow

12. Equivalence Relationship

13. Unconventional Regularity in Cash Flow Pattern
$10,000
i = 10% 1
C C C C C C C
Payment is made every other year

14. Approach 1: Modify the Original Cash Flows
$10,000
i = 10% 1
A A A A A A A A A A A A A A

15. Relationship Between A and C
$10,000
i = 10% 1
C C C C C C C
$10,000
i = 10% 1
A A A A A A A A A A A A A A

16. Solution
i = 10% C A A
A =$1,357.46

17. 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

18. Solution
$10,000
i = 21% 1
C C C C C C C