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EGR 403 Capital Allocation Theory Dr. Phillip R. Rosenkrantz PowerPoint PPT Presentation


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Chapter 4 More Interest Formulas Click here for Streaming Audio To Accompany Presentation (optional). EGR 403 Capital Allocation Theory Dr. Phillip R. Rosenkrantz Industrial & Manufacturing Engineering Department Cal Poly Pomona. EGR 403 - The Big Picture.

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EGR 403 Capital Allocation Theory Dr. Phillip R. Rosenkrantz

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Chapter 4 more interest formulas click here for streaming audio to accompany presentation optional

Chapter 4More Interest FormulasClick here for Streaming Audio To Accompany Presentation (optional)

EGR 403 Capital Allocation Theory

Dr. Phillip R. Rosenkrantz

Industrial & Manufacturing Engineering Department

Cal Poly Pomona


Egr 403 the big picture

EGR 403 - The Big Picture

  • Framework:Accounting& Breakeven Analysis

  • “Time-value of money” concepts - Ch. 3, 4

  • Analysis methods

    • Ch. 5 - Present Worth

    • Ch. 6 - Annual Worth

    • Ch. 7, 8 - Rate of Return (incremental analysis)

    • Ch. 9 - Benefit Cost Ratio & other techniques

  • Refining the analysis

    • Ch. 10, 11 - Depreciation & Taxes

    • Ch. 12 - Replacement Analysis

EGR 403 - Cal Poly Pomona - SA6


Components of engineering economic analysis

Components of Engineering Economic Analysis

  • Calculation of P and F are fundamental.

  • Some problems are more complex and require an understanding of added components:

    • Uniform series.

    • Arithmetic or geometric gradients.

    • Nominal and effective interest rates (covered in presentation #5 on Chapter 3).

    • Continuous compounding.

EGR 403 - Cal Poly Pomona - SA6


Uniform payment series capital recovery factor

Uniform Payment SeriesCapital Recovery Factor

  • The series of uniform payments that will recover an initial investment.

    A = P(A/P, i, n)

EGR 403 - Cal Poly Pomona - SA6


Uniform payment series compound amount factor f

Uniform Payment SeriesCompound Amount Factor F

  • The future value of an investment based on periodic, constant payments and a constant interest rate.

    F = A(F/A, i, n)

EGR 403 - Cal Poly Pomona - SA6


Egr 403 capital allocation theory dr phillip r rosenkrantz

Year

Cash in

Cash out

0

0

1

$500

2

$500

3

$500

4

$500

5

$500

-$2763

Example 4-1

At 5%/year

F = $500(F/A, 5%, 5) = $500(5.526) = $2763

EGR 403 - Cal Poly Pomona - SA6


Uniform payment series sinking fund factor

Uniform Payment SeriesSinking Fund Factor

  • The constant periodic amount, at a constant interest rate that must be deposited to accumulate a future value.

    A = F(A/F, i, n)

EGR 403 - Cal Poly Pomona - SA6


Uniform payment series present worth factor

Uniform Payment SeriesPresent Worth Factor

The present value of a series of uniform future payments.

P = A(P/A, i, n)

EGR 403 - Cal Poly Pomona - SA6


Example 4 6

Year

Cash flow

1

$100

2

$100

3

$100

4

$0

5

F

Example 4-6

F’ = $100(F/A, 15%, 3) = $347.25

F’’ = $347.25(F/P, 15%, 2) = $459.24

EGR 403 - Cal Poly Pomona - SA6


Egr 403 capital allocation theory dr phillip r rosenkrantz

Year

Cash flow

0

P

1

0

2

$ 20

3

$ 30

4

$ 20

Example 4-7Finding the Present Value (P) for each cash flow is sometimes the easiest way to find the equivalent P.

P = $20(P/F, 15%, 2) + $30(P/F, 15%, 3) + $20(P/F, 15%, 4) = $46.28

EGR 403 - Cal Poly Pomona - SA6


Arithmetic gradient

Arithmetic Gradient

  • A uniform increasing amount.

  • The first cash flow is always equal to zero.

  • G = the difference between each cash amount.

G = $10

EGR 403 - Cal Poly Pomona - SA6


Arithmetic gradient combined with a uniform series

Arithmetic Gradient combined with a Uniform Series

  • Decompose the cash flows into a uniform series and a pure gradient. Then add or subtract the Present Value of the gradient to the Present Value of the Uniform series

  • Example 4-8: Use P/G factor to find present value of the pure gradient portion of the cash flow

EGR 403 - Cal Poly Pomona - SA6


Arithmetic gradient uniform series factor

Arithmetic Gradient Uniform Series Factor

A pure gradient (uniformly increasing amount) can also be converted into the equivalent present value of uniform series:

AG = G(A/G, i, n)

See Example 4-9: Notice that the uniform series portion of the cash flow was subtracted to separate the pure gradient.

EGR 403 - Cal Poly Pomona - SA6


Geometric series present worth factor

Geometric Series Present Worth Factor

Sometimes cash flows increase at a constant rate rather than a constant amount. Inflation, for example, could be reflected in a cash flow diagram that way. The equivalent present value of a geometrically increasing amount. g = the rate of increase (e.g., .05)

P = A(P/A, g, i, n) where (P/A, g, i, n) must be computed from equation 4-30 or 4-31

  • Example 4-12 uses g = .10 and i = .08

EGR 403 - Cal Poly Pomona - SA6


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