MER 439 Design of Thermal Fluid Systems

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• MER 439 - Design of Thermal Fluid Systems
• Econ Lecture 2
• Professor Bruno
• Fall Term 2006

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Gradient Factors

• Engineering Economic problems frequently involve
  disbursements or receipts that increase or
  decrease each year (i.e. equipment maintenance)
• If the increase is the same every year this is
  called a uniform arithmetic gradient.

The Uniform amount of increase each period is
the gradient amount
The amount in the initial year is called a
base amount, and it doesnt need to equal the
gradient amount
Present Value _at_ time zero
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Gradient Factors
To get the Gradient Factors we subtract off the
base amount, and start things in year (period) 2
PG Present worth of the gradient starting in
year 2 This is what is calculated by P/G factor.
PT (total) PGPA
PA comes from using the P/A factor on an annuity
equal to the base amount.

• P/G factor to convert a gradient series to a
  present worth.
• A/G factor to convert a gradient series to an
  equivalent uniform annual series.

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PG/G and AG/G
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Gradients

• Example
• Find the PW of an income series with a cash flow
  in Year 1 of 1200 which increases by 300 per
  year through year 11. Use i 15

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Review of Factors

• Using the tables..
• Single Payment factors (P/F), (F/P)
• Uniform Series factors (P/A), (F/A)
• Gradients (A/G), (P/G)

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Unknown Interest Rates and Years

• -Use tables
• Unknown Interest rate
• i.e. F 20K, P 10K, n 9 ? i ?
• Or A 1770, n 10, P 10K ? i ?
• Unknown Years sometimes want to determine the
  number of years it will take for an investment to
  pay off ( n is unknown)
• A 100, P 2000, i 2 ? n ?

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Unknown interest example

• If you would like to retire with 1million 30
  years from now, and you plan to save 6000 per
  year every year until then, what interest rate
  must your savings earn in order to get you that
  million?

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Use of Multiple Factors

• Many cash flow situations do not fit the single
  factor equations.
• It is often necessary to combine equations
• Example? What is P for a series of 100
  payments starting 4 years from now?

years
1 2 3 4 5 6 7 8 9 10 11 12 13
100
P ?
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Use of Multiple Factors

• Several Methods
• 1. Use P/F of each payment
• 2. F/P of each and then multiply by P/F
• 3. Get F A (F/A, i,10), then P F (F/P,i,13)
• 4. Get P3 A(P/A,I,10) and P0 P3(P/F,i,3)

years
1 2 3 4 5 6 7 8 9 10 11 12 13
100
P ?
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Use of Multiple Factors

• Step for solving problems like this
• 1. Draw Cash Flow Diagram.
• 2. Locate P or F on the diagram.
• 3. Determine n by renumbering if necessary.
• 4. use factors to convert all cash flows to
  equivalent values at P or F.

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Use of Multiple Factors

• Example
• A woman deposited 700 per year for 8 years.
  Starting in the ninth year she increased her
  deposits to 1200 per year for 5 more years. How
  much money did she have in her account
  immediately after she made her last deposit?

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Eng Econ Practice Problems

• Check Website for Practice ProblemsRemember you
  ALL have a quiz on Engineering Econ Next Friday,
  not just the economists.
• You can see me (as Prof. Bruno) for free help on
  engineering econ!