L7: Unconventional Equivalence Calculations

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L7 Unconventional Equivalence Calculations

• ECON 320 Engineering Economics
• Mahmut Ali GOKCE
• Industrial Systems Engineering
• Computer Sciences

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200
Composite Cash Flows
150 150 150 150
100
100
100
50
0
1 2 3 4 5 6
7 8 9
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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  withdrawn over 4 subsequent years?

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Unconventional Equivalence Calculations

• Situation 2
• What value of A would make the two cash flow
  transactions equivalent if i 10?

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Multiple Interest Rates
F ?
Find the balance at the end of year 5.
6
4
4
6
5
0
2
4
5
1
3
400
300
500
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Solution
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Cash Flows with Missing Payments
P ?
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15
0
100
i 10
Missing payment
10
Solution
P ?
Add this cash flow to offset the change
100
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15
0
100
Pretend that we have the 10th payment
i 10
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Approach
P ?
100
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15
0
100
i 10
Equivalent Cash Inflow Equivalent Cash Outflow
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Equivalence Relationship
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Unconventional Regularity in Cash Flow Pattern
10,000
i 10
1
2 3 4 5 6 7 8 9 10
11 12 13 14
0
C C C C
C C C
Payment is made every other year
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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
0
A A A A A A A A A
A A A A A
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Relationship Between A and C
10,000
i 10
1
2 3 4 5 6 7 8 9 10
11 12 13 14
0
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
0
A A A A A A A A A
A A A A A
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Solution
i 10
C
A
A
A 1,357.46
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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.
• (10.10)(10.10) 1.21

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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
0
C C C C
C C C