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Irregular Payment Series and Unconventional Irregular Payment Series and Unconventional

Irregular Payment Series and Unconventional - PowerPoint Presentation

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Irregular Payment Series and Unconventional - PPT Presentation

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

000 cash series payment cash 000 payment series solution period year flow annual find interest years equivalent strategy flows

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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) can be withdrawn over 4 subsequent years?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.