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

Composite Cash Flows $200 $150 $150 $150 $150 $100 $100 $100 $50 $150 $150 $150 $150 $100 $100 $100 $50 1 2 3 4 5 6 7 8 9

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make 4 annual deposits of $100 in your savings account which earns 10% annual interest, what equal annual amount can be withdrawn over 4 subsequent years?

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

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

Solution

Cash Flows with Missing Payments 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 $100 i = 10% Missing payment

Solution P = ? i = 10% Add this cash flow to offset the change $100 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 $100 Pretend that we have the 10th payment i = 10%

Approach P = ? $100 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 $100 i = 10% Equivalent Cash Inflow = Equivalent Cash Outflow

Equivalence Relationship

Unconventional Regularity in Cash Flow Pattern $10,000 i = 10% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 C C C C C C C Payment is made every other year

Approach 1: Modify the Original Cash Flows $10,000 i = 10% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 A A A A A A A A A A A A A A

Relationship Between A and C $10,000 i = 10% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 C C C C C C C $10,000 i = 10% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 A A A A A A A A A A A A A A

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

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

Solution $10,000 i = 21% 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 C C C C C C C