l7: unconventional equivalence calculations
DESCRIPTION
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 9TRANSCRIPT
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L7: Unconventional Equivalence Calculations
ECON 320 Engineering EconomicsMahmut Ali GOKCEIndustrial Systems EngineeringComputer Sciences
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$50
$100 $100 $100
$150 $150 $150 $150$200
Group 1 $50( / ,15%,1)
$43.48
P P F
Group 2 $100( / ,15%,3)( / ,15%,1)
$198.54
P P A P F
Group 3 $150( / ,15%, 4)( / ,15%, 4)
$244.85
P P A P F
Group 4 $200( / ,15%,9)
$56.85
P P F
$43.48 $198.54 $244.85 $56.85$543.72
P
01 2 3 4 5 6 7 8 9
Composite Cash Flows
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Unconventional Equivalence CalculationsSituation 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4 annual deposits of $100 in your savings account which earns 10% annual interest, what equal annual amount can be withdrawn over 4 subsequent years?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
$300$500
$400
5% 6% 6% 4% 4%
Find the balance at the end of year 5.
0
12
34 5
F = ?
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Solution1:
$300( / ,5%,1) $3152 :
$315( / ,6%,1) $500 $833.903:
$833.90( / ,6%,1) $883.934 :
$883.93( / , 4%,1) $400 $1,319.295 :
$1,319.29( / , 4%,1) $1,372.06
nF P
nF P
nF P
nF P
nF P
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Cash Flows with Missing Payments
P = ?
$100
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Missing paymenti = 10%
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Solution
P = ?
$100
01 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Pretend that we have the 10th
paymenti = 10%
$100Add this cash flow tooffset the change
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Approach
P = ?
$100
01 2 3 4 5 6 7 8 9 10 11 12 13 14 15
i = 10%
$100
Equivalent Cash Inflow = Equivalent Cash Outflow
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$100( / ,10%,10) $100( / ,10%,15)$38.55 $760.61
$722.05
P P F P AP
P
Equivalence Relationship
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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%
Payment is made every other year
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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 A A A A A A A
$10,000( / ,10%,14)$1,357.46
A A P
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Relationship Between A and C
$10,000
01 2 3 4 5 6 7 8 9 10 11 12 13 14
i = 10%
A A A A A A A A A A A A A A
$10,000
01 2 3 4 5 6 7 8 9 10 11 12 13 14
C C C C C C C
i = 10%
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C
A =$1,357.46
A A
i = 10%
$10,000( / ,10%,14)$1,357.46
( / ,10%,1)1.12.12.1($1,357.46)$2,850.67
A A P
C A F P AA AA
Solution
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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%.
(1+0.10)(1+0.10) = 1.21
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Solution$10,000
01 2 3 4 5 6 7 8 9 10 11 12 13 14
C C C C C C C
i = 21%
$10,000( / , 21%,7)$2,850.67
C A P
1 2 3 4 5 6 7