Equivalence Calculations Lecture No 9 Chapter 3 Contemporary Engineering Economics Copyright 2016 Example 323 Uneven Payment Series How much do you need to deposit today P to withdraw 25000 at ID: 586669
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Slide1
Irregular Payment Series and Unconventional Equivalence Calculations
Lecture No. 9
Chapter 3
Contemporary Engineering Economics
Copyright ©
2016Slide2
Example 3.23: Uneven
Payment Series
How much do you need to deposit today (
P
) to withdraw $25,000 at n= 1, $3,000 at n = 2, and $5,000 at n= 4, if your account earns 10% annual interest?
0
1 2 3 4
$25,000
$3,000
$5,000
PSlide3
Check to see if $28,622 is indeed sufficient.
0
1
2
3
4
Beginning Balance
0
28,622
6,484.20
4,132.62
4,545.88
Interest Earned (10%)
0
2,862
648.42
413.26
454.59
Payment
+28,622
−25,000
−3,000
0−5,000Ending Balance$28,6226,484.204,132.624,545.880.47
Rounding error.It should be “0.”Slide4
Example 3.25: Future Value of an Uneven Series with Varying Interest Rates
Given
: Deposit series as given over 5 years
Find
: Balance at the end of year 5Slide5
SolutionSlide6
Composite Cash Flows
Situation 1
: If you make 4 annual deposits of $100 in your savings account, which earns 10% annual interest, what equal annual amount (
A
) can be withdrawn over 4 subsequent years? Situation 2: What value of A would make the two cash flow transactions equivalent if i = 10%?Slide7
Establishing Economic Equivalence
Method 1: At
n
= 0
Method 2: At n = 4Slide8
Example 3.26: Cash Flows with Sub-patterns
Given:
Two cash flow transactions, and
i
= 12% Find: CSlide9
Solution
Strategy
: First select the base period to use in calculating the equivalent value for each cash flow series (say,
n
= 0). You can choose any period as your base period.Slide10
Example 3.27: Establishing a College Fund
Given
: Annual college expenses = $40,000 a year
for 4 years,
i = 7%, and N = 18 yearsFind: Required annual contribution (
X)Slide11
Solution
Strategy
: It would be computationally efficient if you chose
n
= 18 (the year she goes to college) as the base period.Slide12
Cash Flows with Missing Payments
Given
: Cash flow series with a missing payment,
i
= 10% Find: PSlide13
Solution
Strategy
: Pretend that we have the 10
th
missing payment so that we have a standard uniform series. This allows us to use (P/A,10%,15) to find P. Then, we make an adjustment to this
P by subtracting the equivalent amount added in the 10
th period.Slide14
Example 3.28: Calculating an Unknown Interest Rate
Given
: Two payment options
Option 1: Take a lump sum payment in the amount of
$192,373,928.Option 2: Take the 30-installment option ($9,791,667 a year).Find
: i
at which the two options are equivalentSlide15
Solution
Excel Solution:
Contemporary Engineering Economics, 6e, GE, ©2015
15Slide16
Example 3.29: Unconventional Regularity in Cash Flow Pattern
Given
: Payment series given,
i
= 10%, and N = 12 years
Find
:
PSlide17
Solution
Equivalence Calculations for a Skipping Cash Flow Pattern
Strategy
: Since the cash flows occur every other year, find out the equivalent compound interest rate that covers the two-year period.
Solution
Actually, the $10,000 payment occurs every other year for 12 years at 10%.
We can view this same cash flow series as having a $10,000 payment that occurs every period
at an interest rate of 21% over 6 years.