Transcript CHAPTER IV - mixed disinfectants

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ENGINEERING ECONOMY Fifth Edition
Blank and Tarquin
Mc
Graw
Hill
CHAPTER III
COMBINING FACTORS
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.1 Uniform Series that are SHIFTED
A shifted series is one whose present
worth point in time is NOT t = 0.
Shifted either to the left of “0” or to the
right of t = “0”.
Dealing with a uniform series:


The PW point is always one period to the
left of the first series value
No matter where the series falls on the time
line.
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.1 Shifted Series
Consider:
0
1
2
3
4
5
6
7
8
A = -$500/year
P0
P2
P of this series is at t = 2 (P2 or F2)
P2 = $500(P/A,i%,4) or, could refer to as F2
P0 = P2(P/F,i%,2) or, F2 (P/F,i%,2)
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.1 Shifted Series: P and F
Require F6
0
1
2
3
4
5
6
7
8
P0
A = -$500/year
P3
F6 = ??
•F for this series is at t = 6
•F6 = A(F/A,i%,4) where n = 4 time periods
forward.
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.1 Suggested Steps
Draw and correctly label the cash flow
diagram that defines the problem
Locate the present and future worth
points for each series
Write the time value of money
equivalence relationships
Substitute the correct factor values and
solve
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.2 Series with other single cash flows
It is common to find cash flows that are
combinations of series and other single
cash flows.
Solve for the series present worth
values then move to t = 0.
Solve for the PW at t = 0 for the single
cash flows.
Add the equivalent PW’s at t = 0.
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.2 Series with Other cash flows
F4 = $300
Consider:
A = $500
0
1
2
3
4
5
6
7
8
i = 10%
F5 = -$400
•Find the PW at t = 0 and FW at t = 8 for this
cash flow –watch the signs!
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.2 The PW Points are:
F4 = $300
A = $500
1
0
1
2
2
3
3
4
5
6
7
8
i = 10%
F5 = -$400
t = 1 is the PW point for the $500 annuity;
“n” = 3
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.2 The PW Points are:
Back 4 periods
F4 = $300
A = $500
1
0
1
2
2
3
3
4
5
6
7
8
i = 10%
Back 5 Periods
F5 = -$400
t = 1 is the PW point for the two other
single cash flows
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.2 Write the Equivalence Statement
P = $500(P/A,10%,3)(P/F,10%,1)
+
$300(P/F,10%,4)
400(P/F,10%,5)
Substituting the factor values into the
equivalence expression and solving….
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.2 Substitute the Factors and Solve
P = $500( 2.4869 )( 0.9090 )
+
$300( 0.6830 )
400( 0.6209 )
=
$1,130.30
$204.90
$248.36
$1086.84
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.3 The Linear Gradient – Revisited
The Present Worth of an arithmetic
gradient (linear gradient) is always
located:
 One period to the left of the first cash
flow in the series ( “0” gradient cash
flow) or,
 Two periods to the left of the “1G”
cash flow
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.3 Shifted Gradient
A Shifted Gradient is one whose
present value point is removed from
time t = 0.
A Conventional Gradient is one whose
present worth point is t = 0.
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.3 Example of a Conventional Gradient
Consider:
Gradient Series
……..Base Annuity ……..
0
1
2
…
n-1
n
•This Represents a Conventional Gradient.
•The present worth point is t = 0.
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.3 Example of a Shifted Gradient
Consider:
Gradient Series
……..Base Annuity ……..
0
1
2
3
4
n-1
n
The Present Worth Point for the
Base Annuity and the Gradient
would be here!
This Represents a Shifted Gradient.
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.3 Shifted Gradient: Example
Given:
G = +$100
Base Annuity = $100
0
1
2
3
4 ………..
………..
9
10
•Let Cash Flow (CF) start at t = 3:
•$100/ yr increasing by $100/year
through year 10; i = 10%; Find the
PW at t = 0.
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.3 Shifted Gradient: Example
PW of the Base Annuity
P2 = $100(P/A,10%,8)
Base Annuity = $100
0
1
2
3
4 ………..
………..
9
10
nannuity = 8 time periods
P2 = $100( P/A,10%,8 ) = $100( 5.3349 ) = $533.49
P0 = $533.49( P/F,10%,2 ) = $533.49( 0.8264 )
= $440.88
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.3 Gradient Present Worth
For the gradient component
P2 = $100(P/G,10%,8)
G = +$100
0
1
2
3
4 ………..
………..
9
10
• PW of gradient is at t = 2:
•P2 = $100( P/G,10%,8 ) = $100( 16.0287 ) = $1,602.87
•P0 = $1,602.87( P/F,10%,2 ) = $1,602.87( 0.8264 )
• = $1,324.61
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.3 Example: Final Solution
For the Base Annuity
 P0 = $440.88
For the Linear Gradient
 P0 = $1,324.61
Total Present Worth:

$440.88 + $1,324.61 = $1,765.49
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.3 Shifted Geometric Gradient
Conventional Geometric Gradient
P of G. Grad. Is at t = “0”
A1
0
1
2
3
…
…
…
n
Present worth point is at t = 0 for a conventional
geometric gradient!
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.3 Shifted Geometric Gradient
Shifted Geometric Gradient
A1
0
1
2
3
…
…
…
n
Present worth point is at t = 2 for this example
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.3 Geometric Gradient Example
i = 10%/year
0
1
2
3
4
5
6
7
8
A = $700/yr
A1 = $400 @ t = 5
12% Increase/yr
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
3.3 Geometric Gradient Example
i = 10%/year
0
1
2
3
4
5
6
7
8
A = $700/yr
PW point for the
annuity
12% Increase/yr
PW point for the
gradient
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.3 The Gradient Amounts
t
Base Amt
$400.00
51
62
73
84
$448.00
$501.76
$561.97
Present Worth of the Gradient at t = 4
3.73674
P4 = $400{ P/A1,12%,10%,4 } = $
1,494.70
P0 = $1,494.70( P/F,10%,4) = $1,494.70( 0. 6830 )
P0 = $1,020,88
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.3 The Annuity Present Worth
PW of the Annuity
i = 10%/year
0
1
2
3
4
5
6
7
8
A = $700/yr
P0 = $700(P/A,10%,4)
= $700( 3.1699 ) = $2,218.94
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.3 Total Present Worth
Geometric Gradient @ t =

P0 = $1,020,88
Annuity

P0 = $2,218.94
Total Present Worth”

$1,020.88 + $2,218.94

= $3,239.82
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.4 Shifted Decreasing Linear Gradients
Given the following shifted, decreasing
gradient:
F = $1,000; G=-$100
3
i = 10%/year
0
1
2
3
4
5
6
7
8
Find the Present Worth @ t = 0
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
3.4 Shifted Decreasing Linear Gradients
Given the following shifted, decreasing
gradient:
F = $1,000; G=-$100
3
i = 10%/year
0
1
2
3
4
5
6
7
8
PW point @ t = 2
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.4 Shifted Decreasing Linear Gradients
F3 = $1,000; G=-$100
i = 10%/year
0
1
2
3
4
5
6
7
8
Use
(P/F,10%,2)
P0 here
P2 or, F2: Then take back to t = 0
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
3.4 Shifted Decreasing Linear Gradients
F3 = $1,000; G=-$100
Base Annuity = $1,000
i = 10%/year
(P/F,10%,2)
0
1
2
3
4
5
6
7
8
P2 or, F2: Then take back to t = 0
P0 here
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.4 Time Periods Involved
F3 = $1,000; G=-$100
i = 10%/year
1
0
1
2
2
3
3
4
4
5
5
6
7
8
P2 or, F2: Take back to t = 0
P0 here
Dealing with n = 5 periods.
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.4 Time Periods Involved
F3 = $1,000; G=-$100
G = -$100/yr
$1,000
i = 10%/year
1
0
1
2
2
3
3
4
4
5
5
6
7
8
P2 = $1,000( P/A,10%,5 ) – 100( P/G,10%.5 )
P2= $1,000( 3.7908 ) - $100( 6.8618 ) = $3,104.62
P0 = $3,104.62( P/F,10%,2 ) = $3104.62( 0 .8264 ) = $2,565.65
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.5 Spreadsheet Applications
Assume Excel is the spreadsheet of
choice
Instructors may vary on the degree of
emphasis placed on spreadsheet use
Student’s Goal:


Learn the Excel Financial Functions
Create your own spreadsheets to solve a
variety of problems
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.5 NPV Function in Excel
NPV function is basic
Requires that all cell in the range so
defined have an entry.
The entry can be $0…but not blank!
Incorrect results can be generated if
one or more cells in the defined range is
left blank .
A “0” value must be entered.
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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3.5 Spreadsheets
It is assumed if an instructor desires to
apply spreadsheets, he or she will
provide examples and go over each
example and the associated cell
formulas.
See Appendix A for further details on
Excel applications
Blank & Tarquin: 5th Edition. Ch.3 Authored by Dr. Don Smith, Texas A&M University
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