A 85954980 x 20150212

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*Developed By:Dr. Don Smith, P.E.Department of Industrial EngineeringTexas A&M UniversityCollege Station, Texas

Executive Summary Version

Chapter 2Factors: How Time and Interest Affect Money

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*LEARNING OBJECTIVESF/P and P/F factorsP/A and A/P factorsInterpolate for factor valuesP/G and A/G factors5. Geometric gradient6. Calculate i7. Calculate n8. Spreadsheets

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*Sct 2.1 Single-Payment Factors(F/P and P/F) Objective:Derive factors to determine the present or future worth of a cash flow Cash Flow Diagram basic format 0 1 2 3 n-1 nP0Fn i% / periodP0 = Fn1/(1+i)n (P/F,i%,n) factor: Excel: =PV(i%,n,,F)Fn = P0(1+i)n (F/P,i%,n) factor: Excel: =FV(i%,n,,P)

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*Sct 2.2 Uniform-Series: Present Worth Factor (P/A) and Capital Recovery Factor(A/P) Cash flow profile for P/A factorRequired: To find P given A Cash flows are equal, uninterrupted and flow at the end of each interest periodFind P

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*(P/A) Factor Derivation Setup the following:

Multiply by to obtain a second equation

Subtract (1) from (2) to yield

(1)(2)(3)

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*(P/A) and (A/P) Factor Formulas Simplify (3) to yield

Solve (4) for A to get (A/P) factor

(4)(P/A,i%,n) factorExcel: =PV(i%,n,A)(A/P,i%,n) factorExcel: =PMT(i%,n,P)(5)

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*ANSI Standard Notation for Interest Factors Standard notation has been adopted to represent the various interest factors Consists of two cash flow symbols, the interest rate, and the number of time periods General form:(X/Y,i%,n) X represents what is unknown Y represents what is known i and n represent input parameters; can be known or unknown depending upon the problem

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*Notation - continued Example: (F/P,6%,20) is read as:To find F, given P when the interest rate is 6% and the number of time periods equals 20. In problem formulation, the standard notation is often used in place of the closed-form equivalent relations (factor) Tables at the back of the text provide tabulations of common values for i% and n

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*Sct 2.3 Sinking Fund Factor and Uniform Series Compound Amount Factor(A/F and F/A) Cash flow diagram for (A/F) factor

Start with what has already been developed

F = givenFind A, given F

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*(F/A) factor from (A/F) Given:

Solve for F in terms of A to yield(A/F,i%,n) factorExcel: =PMT(i%,n,,F)(F/A,i%,n) factorExcel: =FV(i%,n,A)

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*Sct 2.4 Interpolation in Interest Tables When using tabulated interest tables one might be forced to approximate a factor that is not tabulated Can apply linear interpolation to approximateSee Table 2-4Factors are nonlinear functions, hence linear interpolation will yield errors in the 2-4% rangeUse a spreadsheet model to calculate the factor precisely

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*Sct 2.5 Arithmetic Gradient Factors(P/G) and (A/G) Cash flow profileFind P, given gradient cash flow G CFn = A1 (n-1)GBase amount = A1

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*Gradient ExampleGradients have two components: 1. The base amount and the gradient2. The base amount (above) = $100/time period

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*Gradient ComponentsBase amount = A / period0G1G2G(n-3)G(n-2)G(n-1)G Present worth point is 1 period to the left of the 0G cash flow

For present worth of the base amount, use the P/A factor (already known)

For present worth of the gradient series, use the P/G factor (to be derived)

Find P of gradient series

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*Gradient Decomposition As we know, arithmetic gradients are comprised of two componentsGradient component2. Base amount When working with a cash flow containing a gradient, the (P/G) factor is only for the gradient component Apply the (P/A) factor to work on the base amount component P = PW(gradient) + PW(base amount)

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*Derivation Summary for (P/G) Start with:

Multiply (1) by (1+i)1 to create a second equationSubtract (1) from the second equation and simplifyYields

(1)(P/G,i,n) factorNo Excel relation exists

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*Use of the (A/G) FactorFind A, given gradient cash flow G CFn = (n-1)GEquivalent A of gradient seriesA A A . . . A A A = G(A/G,i,n)

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*Sct 2.6 Geometric Gradient Series Factor Geometric GradientCash flow series that starts with a base amount A1Increases or decreases from period to period by a constant percentage amountThis uniform rate of change defines A GEOMETRIC GRADIENT Notation:g = the constant rate of change, in decimal form, by which future amounts increase or decrease from one time period to the next

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*Typical Geometric GradientA1A1(1+g)A1(1+g)2A1(1+g)n-1Required: Find a factor (P/A,g%,i%,n) that will convert future cash flows to a single present worth value at time t = 0Given A1, i%, and g%

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*Basic Derivation: Geometric Gradient(1)Subtract Eq. (2 ) from Eq. (3 ) to yieldSolve for Pg and simplify to yield.Start with:Factor out A1 out and re-write(2) (3)Multiply by (1+g)/(1+i) to obtain Eq. (3 )

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 2005 by McGraw-Hill, New York, N.Y All Rights Reserved2-*Two Forms to ConsiderCase: g = iCase: g = iA1 is the starting cash flowThere is NO base amount associated with a geometric gradientThe remaining cash flows are generated from the A1 starting valueNo tables available to tabulate this factortoo many combinations of i% and g% to support tablesTo use the (P/A,g%,i%,n) factor

2005 by McGraw-Hill, New York, N.Y All Rights Reserved

*At this point:1. Introduce yourself - your students are likely to want to know something about your qualifications and interests - overall, where you are coming from.2. Have students introduce themselves. Ask why they are taking this class. If you are fortunate enough to have a Polaroid camera, take pictures of each student for later posting on a class board so both they and you get to know each other.3. Discuss both choice of textbook and development of syllabus.4. If you are expecting students to work in teams, at east introduce the choice of team members. If at all possible, have students participate in a team building or team study exercise. It works wonders. Most student have been told to work in teams in prior classes, but have never examined exactly what a team is and how it works. One hour spent in a team building/examination exercise saves many hours and avoids many problems later on.

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