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					                                  Lecture No. 1
              Foundations of Engineering Economy

   1. Why Economics Is Important to Engineers
A. Definition
Definition: Engineering Economy involves:
     Formulating
     Estimating
     Evaluating
The economic outcomes when alternatives are available.
        An alternative definition: Engineering Economy is a collection of mathematical
techniques that simplify the comparison of alternatives.

B. Typical Questions
      Engineering Activities
           o Should the highway out go through the mountain or around it
           o Will a stainless steel pump be better than a cast iron pump
           o It is a good idea to upgrade to the latest CAD
      Public Sector
           o How will the taxes increase to fund a project
           o Should Cal Poly teach a particular course or farm it out
      Individuals
           o Should I refinance the mortgage
           o Do my credit cards need to be paid off
           o Is the stock market worth it

2. Decision Making
Procedure for the development and selection of alternative – referred to as the problem-
solving approach or the decision making process.

      Define the objective
      Collect information
      Define alternatives
      Identify the judging criteria
      Evaluate the alternatives
      Select the best alternative
      Implement the solution and monitor the results
      Example 1.2 page 8.
           Lecture No. 1, Foundations of Engineering Economy Page No. 2

       The time value of money is the change in the amount of money over a given time

3. Interest Rate and ROR
From a computational point of view, interest is the difference in money between what
you end with and what you started with. Interest is paid when an entity borrows money
and repays a larger amount; interest is earned when an entity save or invested money and
obtained a return of a larger amount.

Interest = amount owed now – original amount or principal

                     interest accrued per time unit
Interest rate, % =                                  x 100%
                            original amount

      The time unit is called the interest period and is typically one year.
Examples: 1.3 and 1.4 on p. 12.

        Interest paid over a specific period of time is expressed as a percentage of the
original amount and is called the rate of return, ROR.

                        interest accrued per time unit
Rate of Return , % =                                   x 100%
                               original amount

        The equations are the same but interest rate paid is more appropriate from the
borrower’s perspective and the rate of return earned is better for the investor’s
perspective i.e.
Interest rate – borrower
ROR – investor

Inflation – the devaluation of a currency relative to a previous value. From the
borrower’s perspective it is another interest rate; from the investor’s perspective, inflation
reduces the ROR. Engineering economy studies affects all estimated values equally and
an interest rate or ROR of say 8% typically includes inflation.

4. Simple and Compound Interest
       Simple interest is calculated using the principal only, ignoring any interest
accrued in the preceding interest periods.

      Simple interest = principal x number of periods x interest rate (decimal)
           Total (principal + interest) due = Principal + simple interest

        For compound interest, the interest accrued for each interest period is calculated
on the principal plus the total amount of interest accumulated in all previous periods.
            Lecture No. 1, Foundations of Engineering Economy Page No. 3

    Compound interest = (principal + all accrued interest)(interest rate, decimal)
        Total (principal + interest) due = Principal(1 + interest rate) number of years

        Example 1.7, 1.8 p. 17.
        Examples:
Given1.14: A local bank is offering to pay compound interest of 5% per year on new saving accounts. An
e-bank is offering 6% per year but simple interest i.e. not compounded. The time of interest is 3 years.
Find: Which offer is more attractive i.e. yields more money.

Assume any convenient amount of money say $1000
Compound Total = P(1+i)n = 1000(1+.05)3 = 1000(1.157624)
Compound Total= $1157.624

Simple Total= Principal + interest
Simple Total = P + Pni = = 1000 + 1000(.06)(3) = 1000 + 180
Simple Total = $1180

Since Simple (1180) > Compound (1157.624), Simple is the better deal

Given1.16: $100,000
Find: How long will it take to reach $200,000 at a simple interest rate of 10%

Simple Total = Principal + interest
Simple Total = P + Pni
200,000 = 100,000 + 100,000 (n)(10%)
n = 10 years

5. Terminology and Symbols

P = present value or value at time 0.
F = value at some future time
A = series of consecutive, equal, end-of-period amounts of money.
n = number of interest periods
i = interest rate, assumed compound unless otherwise stated.
t = time stated in periods

All problems involve time. Of P, F, A, n and i , every problem will involve at least four
with at least three of them estimated or known.

        Examples 1.10 through 1.14 p.23.

6. Excel
The common economic functions are contained in hand formulas, tables and functions on
hand calculators and/or packages to hand calculators and computer programs such as
Excel. P. 26.
          Lecture No. 1, Foundations of Engineering Economy Page No. 4

BY Hand : Excel, description
P:PV, present value
F:FV, future value
A: PMT, period value
n:NPER, number of periods
i:RATE, compound interest rate
i:IRR, compound interest rate
P:NPV, present value of any series

7. MARR, Minimum Attractive Rate of Return

        For any investment, you want to have more money at the end of the investment
period than what you started with. The reasonable rate that is required is called the
MARR and is higher than safer investments such as bank interest.
        The MARR is also known as the hurdle rate. In order for a project to be
financially viable, the expected ROR must meet or exceed the MARR or hurdle rate.
        Capital is developed in two ways: equity financing and debt financing.
     Equity – The corporation uses it own funds such as savings or stock sales.
     Debt – The corporation borrows from outside sources such as bonds or

ROR  MARR  cost of capital

8. Cash Flows
Cash flows are inflows or outflows of money.
Cash inflows or receipts may include the following:
    Revenues
    Reductions
    Salvage
Cash outflows or disbursements may include the following:
    First cost of assets
    Design costs
    Operating costs

Net cash flows = receipts – disbursements = cash inflows – cash outflows

       The end of period convention means that all cash flows are assumed to occur at
the end of the interest period.

        Cash flow diagram is a graphical representation of cash flows drawn on a time
scale. The diagram includes what is known and what is needed and is a complete
representation of the problem. t=0 is the present and t=1 is the end of the first time
            Lecture No. 1, Foundations of Engineering Economy Page No. 5

period, t = n is the end of the n th time period. An up arrow, , indicates a positive cash
flow and , a down arrow indicates a negative cash flow.

        Examples 1.15, 1.16 and 1.17 p.33

9. Rule of 72

It just so happens that the time required for an initial single amount to double in size with
compound interest is approximately equal to 72 divided by the rate of return in percent:

Estimated n =
Estimated i =

Given: What interest rate must I obtain to double my money in 5 years.
Find: Interest rate
               72 72
Estimated i =      =
                n    5
Estimated i = 14.4%

Given: The interest rate at the local bank is currently 2.5%
Find: How long with it take to double my money
              72 72
Estimated n =     =
               i     2.5
Estimated n = 28.8 years, perhaps the stock market is worth looking into.