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© 2008 by McGraw-Hill All Rights Reserved

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Basics of Engineering EconomyBasics of Engineering Economy

Chapter 1Chapter 1

Foundations of Engineering Foundations of Engineering EconomyEconomy



Chapter 1 - FoundationsChapter 1 - Foundations

PURPOSE

Understand the fundamental concepts of

engineering economy

TOPICS Definition and study

approach Interest rate, ROR, and

MARR Equivalence Interest – simple and

compound Cash flow diagrams Rules of 72 and 100 Spreadsheet

introduction



Sec 1.1 – Definition of Engineering EconomySec 1.1 – Definition of Engineering EconomySec 1.2 – Elements of a StudySec 1.2 – Elements of a Study

DEFINITION: Techniques that simplify comparison of alternatives on an economic basis

Most project decisions consider additional factors – safety, environmental, political, public acceptance, etc.

Fundamental terminology: Alternative -- stand-alone solution Cash flows -- estimated inflows (revenues) and outflows

(costs) for an alternative Evaluation criteria -- Basis used to select ‘best’ alternative;

usually money (currency of the country) Time value of money -- Change in amount of money over time

(Most important concept in Eng. Econ.)



Sec 1.3 - Interest Rate, ROR, MARRSec 1.3 - Interest Rate, ROR, MARR

interest accrued per time unit x 100%

original amount

Interest is a manifestation of time value of money Calculated as difference between an ending amount and a beginning

amount of money Interest = end amount – original amount

Interest rate is interest over specified time period based on original amount

Interest rate (%) =

Interest rate and rate of return (ROR) have same numeric value, but different interpretations



Sec 1.3 - Interest Rate and ROR InterpretationsSec 1.3 - Interest Rate and ROR Interpretations

Borrower’s perspective

Take loan of $5,000 for one year; repay $5,350

Interest paid = $350

Interest rate = 350/5,000 = 7%

INTEREST RATE

Investor’s perspective

Invest (or lend) $5,000 for one year; receive $5,350

Interest earned = $350

Rate of return = 350/5,000 = 7%

RATE OF RETURN



Cost of capital (COC) – interest rate paid for funds to finance projects

MARR – Minimum ROR needed for an alternative to be justified and economically acceptable. MARR ≥ COC. If COC = 5% and 6% must be realized, MARR = 11%

Always, for acceptable projects

ROR ≥ MARR > COC

Sec 1.3 - ROR and MARRSec 1.3 - ROR and MARR

ROR



Sec 1.4 - EquivalenceSec 1.4 - EquivalenceDifferent sums of money at different times may be equal

in economic value

$100 now

$106 one year from

now

Interest rate = 6% per year

Interpretation: $94.34 last year, $100 now, and $106 one year from now are equivalent only at an interest rate of 6% per year

$94.34 last year

-1 0 1



Sec 1.5 – Simple and Compound InterestSec 1.5 – Simple and Compound Interest

Simple interest is always based on the original amount, which is also called the principal

Interest per period = (principal)(interest rate)

Total interest = (principal)(n periods)(interest rate)

Example: Invest $250,000 in a bond at 5% per year simple

Interest each year = 250,000(0.05) = $12,500 Interest over 3 years = 250,000(3)(0.05) = $37,500



Sec 1.5 – Simple and Compound InterestSec 1.5 – Simple and Compound Interest

Compound interest is based on the principal plus all accrued interest

Interest per period = (principal + accrued interest)(interest rate)

Total interest = (principal)(1+interest rate)n periods - principal

Example: Invest $250,000 at 5% per year compounded

Interest, year 1 = 250,000(0.05) = $12,500

Interest, year 2 = 262,500(0.05) = $13,125

Interest, year 3 = 275,625(0.05) = $13,781

Interest over 3 years = 250,000(1.05)3 – 250,000 = $39,406



Sct 1.6 - Terminology and SymbolsSct 1.6 - Terminology and Symbols t = time index in periods; years, months, etc. P = present sum of money at time t = 0; $

F = sum of money at a future time t; $ A = series of equal, end-of-period cash flows;

currency per period, $ per year n = total number of periods; years, months i = compound interest rate or rate of return;

% per year



Sct 1.6 - Terminology and SymbolsSct 1.6 - Terminology and Symbols

Example: Borrow $5,000 today and repay annually for 10 years starting next year at 5% per year compounded. Identify all symbols.

Given: P = $5,000 Find: A = ? per year

i = 5% per year

n = 10 years

t = year 1, 2, …, 10 (F not used here)



Sec 1.7 – Cash Flow EstimatesSec 1.7 – Cash Flow Estimates

Cash inflow – receipt, revenue, income, saving

Cash outflows – cost, expense, disbursement, loss

Net cash flow (NCF) = inflow – outflow

End-of-period convention: all cash flows and NCF occur at the end of an interest period



Sec 1.7 – Cash Flow DiagramsSec 1.7 – Cash Flow Diagrams

0 1 2 3 4 5

Year 1 Year 5

Time, t

0 1 2 3 4 5

+ Cash flow

- Cash flow

Find P in year 0, given 3

cash flows

P = ?

Typical time scale or 5 years



Sec 1.7 – Cash Flow DiagramsSec 1.7 – Cash Flow Diagrams

Example: Find an amount to deposit 2 years from now so that $4,000 per year can be available for 5 years starting 3 years from now. Assume i = 15.5% per year



Sec 1.8 – Rule of 72 ( and 100)Sec 1.8 – Rule of 72 ( and 100)

Approximate n = 72 / i

Estimates # of years (n) for an amount to double (2X) at a stated compound interest ratee.g., at i = 10%, $1,000 doubles to $2,000 in ~7.2 yearsSolution for i estimates compound

rate to double in n years

Approximate i = 72 / n

For simple interest, doubling time is exact, using rule of 100

n = 100/i

or

i = 100/n

$1,000 doubles in 10 years at 10% simple interest



Sec 1.9 – Introduction to Spreadsheet Sec 1.9 – Introduction to Spreadsheet Functions Functions

To display Excel FunctionPresent value, P = PV(i%,n,A,F)Future value, F = FV(i%,n,A,P)Annual amount, A = PMT(i%,n,P,F)# of periods, n = NPER(i%,A,P,F)Compound rate, i = RATE(n,A,P,F)i for input series = IRR(first_cell:last_cell)P for input series = NPV(i%,second_cell:

last_cell)+first_cell

slide to accompany blank and tarquin basics of engineering economy, 2008 © 2008 by mcgraw-hill all...

Documents

rate of return slide

marr ror slide

rate of return ror

spreadsheet introduction

rate investors perspective

projects marr minimum

marr equivalence

year interpretation