Download Engineering Economy

Engineering Economy
Learning Outcomes
Determine the role of engineering economy in the
decision making process.
Identify what is needed to successfully perform an
engineering economy study.
Perform calculations about interest rate and rate of
return.
Understand what equivalence means in economic terms.
Learning Outcomes
Calculate simple interest and compound interest for one
or more interest periods
Identify and use engineering economy terminology and
symbols.
Understand cash flows, their estimation, and how to
graphically represent them.
To understand and Calculate Break Even Point/Analysis
Foundations of
Engineering Economy
The need for engineering economy is primarily motivated
by the work that engineers do in performing analysis,
synthesizing, and coming to a conclusion as they work on
projects of all sizes.
In other words, engineering economy is at the heart of
making decisions. These decisions involve the
fundamental elements of cash flows of money, time, and
interest rates.
WHAT IS ENGINEERING ECONOMY?
Simplest of terms, engineering economy is a collection of
techniques that simplify comparisons of alternatives on an
economic basis.
Engineering economy is not a method or process for
determining what the alternatives are.
Engineering economic analysis is able to answer
professional and personal financial questions.
PERFORMING AN ENGINEERING ECONOMY
STUDY
In order to apply economic analysis techniques, it is
necessary to understand the basic terminology and
fundamental concepts that form the foundation for
engineering economy studies. Some of these terms and
concepts are described below.
Alternatives
An alternative is a stand-alone solution for a given
situation.
In engineering practice, there are always several ways of
accomplishing a given task, and it is necessary to be able
to compare them in a rational manner so that the most
economical alternative can be selected.
Cash Flows
The estimated inflows (revenues and savings) and
outflows (costs) of money are called cash flows.
These estimates are truly the heart of an engineering
economic analysis.
Alternative Selection
Every situation has at least two alternatives. In addition to
the one or more formulated alternatives, there is always
the alternative of inaction, called the do-nothing (DN)
alternative.
Evaluation Criteria
Whether we are aware of it or not, we use criteria every
day to choose between alternatives.
For example, when you drive to campus, you decide to
take the “best”route.
But how did you define best?
Intangible Factors
In many cases, alternatives have noneconomic or
intangible factors that are difficult to quantify. When the
alternatives under consideration are hard to distinguish
economically, intangible factors may tilt the decision in
the direction of one of the alternatives.
Time Value of Money
It is often said that money makes money.
If a person or company borrows money today, by
tomorrow more than the original loan principal will be
owed. This fact is also explained by the time value of
money.
The change in the amount of money over a given time
period is called the time value of money; it is the most
important concept in engineering economy.
INTEREST RATE, RATE OF RETURN, AND MARR
Interest is the manifestation of the time value of money,
and it essentially represents “rent” paid for use of the
money.
Interest is paid when a person or organization borrows
money (obtains a loan) and repays a larger amount.
Interest is earned when a person or organization saves,
invests, or lends money and obtains a return of a larger
amount.
Interest = end amount - original amount
Eq-1
INTEREST RATE, RATE OF RETURN, AND MARR
 The time unit of the interest rate is called the interest period. By
far the most common interest period used to state an interest
rate is 1 year. Shorter time periods can be used, such as, 1%
per month.
 The term return on investment (ROI) is used equivalently with
ROR in different industries and settings, especially where large
capital funds are committed to engineering-oriented
programs.
 The term interest rate paid is more appropriate from the
borrower’s perspective, while rate of return earned is better
from the investor’s perspective.
EXAMPLE-1
An employee at LaserKinetics.com borrows $10,000 on
May 1 and must repay a total of $10,700 exactly 1 year
later. Determine the interest amount and the interest rate
paid.
The perspective here is that of the borrower since $10,700
repays a loan. Apply Equation 1 to determine the interest
paid.
Interest paid =$10,700 - 10,000 = $700
Equation 2 determines the interest rate paid for 1 year.
EXAMPLE-2
Calculate the amount deposited 1 year ago to have
$1000 now at an interest rate of 5% per year. Then
calculate the amount of interest earned during this time
period.
Minimum Attractive Rate of Return (MARR)
Engineering alternatives are evaluated upon the
prognosis that a reasonable rate of return (ROR) can be
realized. A reasonable rate must be established so that
the accept/reject decision can be made. This reasonable
rate, called the minimum attractive rate of return (MARR),
is the lowest interest rate that will induce companies or
individuals to invest their money.
For example, if a corporation can borrow capital funds at
an average of 5% per year and expects to clear at least
6% per year on a project, the MARR will be at least 11%
per year.
EQUIVALENCE
Equivalent terms are used often in the transfer between
scales and units.
For example, 1000 meters is equal to (or equivalent to) 1
kilometer, 12 inches equals 1 foot, and 1 quart equals 2
pints or 0.946 liter.
In engineering economy, when considered together, the
time value of money and the interest rate help develop
the concept of economic equivalence, which means
that different sums of money at different times would be
equal in economic value.
For example, if the interest rate is 6% per year, $100 today
(present time) is equivalent to $106 one year from today.
EQUIVALENCE
EXAMPLE - 3
AC-Delco makes auto batteries available to General
Motors dealers through privately owned distributorships. In
general, batteries are stored throughout the year, and a
5% cost increase is added each year to cover the
inventory carrying charge for the distributorship owner.
Assume you own the City Center Delco facility. Make the
calculations necessary to show which of the following
statements are true and which are false about battery
costs.
EXAMPLE - 3
a. The amount of $98 now is equivalent to a cost of $105.60
one year from now.
b. A truck battery cost of $200 one year ago is equivalent to
$205 now.
c. A $38 cost now is equivalent to $39.90 one year from
now.
d. A $3000 cost now is equivalent to $2887.14 one year ago.
e. The carrying charge accumulated in 1 year on an
investment of $2000 worth
of batteries is $100.
Solution- 3
a. Total amount accrued 98(1.05) $102.90 $105.60;
therefore, it is false. Another way to solve this is as follows:
Required original cost is 105.601.05 $100.57 $98.
b. Required old cost is 205.001.05 $195.24 $200; therefore, it
is false.
c. The cost 1 year from now is $38(1.05) $39.90; true.
d. Cost one year ago is 30001.05 $2857.14 2887.14; false.
e. The charge is 5% per year interest, or $2000(0.05) $100;
true.
SIMPLE AND COMPOUND INTEREST
The terms interest, interest period, and interest rate were
introduced in previous slides for calculating equivalent
sums of money for one interest period in the past and one
period in the future. However, for more than one interest
period, the terms simple interest and compound interest
become important.
SIMPLE AND COMPOUND INTEREST
Simple interest is calculated using the principal only,
ignoring any interest accrued in preceding interest
periods. The total simple interest over several periods is
computed as
where the interest rate is expressed in decimal form.
Therefore, the total (future) amount accumulated after
several periods is the principal plus interest over all n
periods.
SIMPLE AND COMPOUND 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.
Thus, compound interest means interest on top of interest.
Compound interest reflects the effect of the time value of
money on the interest also. Now the interest for one
period is calculated as
EXAMPLE - 4
HP borrowed money to do rapid prototyping for a new
ruggedized computer that targets desert oilfield
conditions. The loan is $1 million for 3 years at 5% per year
simple interest. How much money will HP repay at the end
of 3 years? Tabulate the results in $1000 units.
Solution- 4
 The $50,000 interest accrued in the first year and the $50,000
accrued in the second year do not earn interest. The interest due
each year is calculated only on the $1,000,000 principal.
EXAMPLE - 5
If HP borrows $1,000,000 from a different source at 5% per
year compound interest, compute the total amount due
after 3 years. Compare the results of this and the previous
example.
TERMINOLOGY AND SYMBOLS
P= value or amount of money at a time designated as
the present or time 0. Also, P is referred to as present
worth (PW), present value (PV), net present value (NPV),
discounted cash flow (DCF), and capitalized cost (CC);
dollars
F= value or amount of money at some future time. Also, F
is called future worth (FW) and future value (FV); dollars
TERMINOLOGY AND SYMBOLS
A= series of consecutive, equal, end-of-period amounts of
money. A is also called the annual worth (AW),
equivalent uniform annual worth (EUAW), and equivalent
annual cost (EAC); dollars per year, dollars per month
n= number of interest periods; years, months, days
i= interest rate or rate of return per time period; percent
per year, percent per month, percent per day
t= time, stated in periods; years, months, days
CASH FLOWS: THEIR ESTIMATION AND
DIAGRAMMING
Cash flows are inflows and outflows of money.
These cash flows may be estimates or observed values.
Every person or company has cash receipts—revenue
and income (inflows); and cash disbursements—expenses
and costs (outflows).
Cash flows occur during specified periods of time, such as
1 month or 1 year.
Samples of Cash Inflow Estimates
Revenues (from sales and contracts)
Operating cost reductions (resulting from an alternative)
Salvage value
Construction and facility cost savings
Receipt of loan principal
Income tax savings
Receipts from stock and bond sales
Samples of Cash Outflow Estimates
First cost of assets
Engineering design costs
Operating costs (annual and incremental)
Periodic maintenance and rebuild costs
Loan interest and principal payments
Major expected/unexpected upgrade costs
Income taxes
Once the cash inflow and outflow estimates are
developed, the net cash flow can be determined.
Cash Flow Diagram
The cash flow diagram is a very important tool in an
economic analysis, especially when the cash flow series is
complex.
It is a graphical representation of cash flows drawn on a
time scale.
The diagram includes what is known, what is estimated,
and what is needed.
Example of positive and negative cash
flows.
The direction of the arrows on the cash flow diagram is
important. A vertical arrow pointing up indicates a
positive cash flow. Conversely, an arrow pointing down
indicates a negative cash flow. Figure 1.4 illustrates a
receipt (cash inflow) at the end of year 1 and equal
disbursements (cash outflows) at the end of years 2 and 3.
EXAMPLE - 6
A new college graduate has a job with Boeing
Aerospace. She plans to borrow $10,000 now to help in
buying a car. She has arranged to repay the entire
principal plus 8% per year interest after 5 years. Identify
the engineering economy symbols involved and their
values for the total owed after 5 years. Construct the cash
flow diagram.
EXAMPLE - 7
A father wants to deposit an unknown lump-sum amount
into an investment opportunity 2 years from now that is
large enough to withdraw $4000 per year for state
university tuition for 5 years starting 3 years from now. If
the rate of return is estimated to be 15.5% per year,
construct the cash flow diagram.
Solution - 7
Each year Exxon-Mobil expends large amounts of funds
for mechanical safety features throughout its worldwide
operations. Carla Ramos, a lead engineer for Mexico and
Central American operations, plans expenditures of $1
million now and each of the next 4 years just for the
improvement of field-based pressure release valves.
Construct the cash flow diagram to find the equivalent
value of these expenditures at the end of year 4, using a
cost of capital estimate for safety-related funds of 12%
per year.
Your boss asks…
How many of these things do
we have to sell before
we start making money?
Use your arrow keys to navigate the slides
Then your boss asks…
If we sell 100,000 units,
what will our profit be?
Finally, your boss asks…
How much do we make
on one of these?
Are you
going to have
the answers?
Surprisingly, it is pretty
easy to answer these questions...
If you know how.
In fact, those who become good at this
can answer these questions in their heads.
Here is how it is done…
Break Even Analysis
Break-Even Analysis is used to
predict future profits/losses
predict results eg produce Product A or Product B
Break-Even Point is when Sales Revenue
equals Total Costs
at this point no profit or loss is incurred
the firm merely covers its total costs
Break-Even Point can be shown in graph
form or by use of formulae
Break Even Analysis
In order to calculate how profitable a product will be, we must
firstly look at the Costs involved There are two basic types of costs a company incurs.
• Variable Costs
• Fixed Costs
Variable costs are costs that change with changes in production
levels or sales. Examples include: Costs of materials used in the
production of the goods.
Fixed costs remain roughly the same regardless of sales/output
levels. Examples include: Rent, Insurance and Wages
Break Even Analysis
TOTAL COSTS
Total Costs is simply Fixed Costs and Variable Costs
added together.
TC = FC + VC
As Total Costs include some of the Variable Costs then
Total Costs will also change with any changes in
output/sales.
If output/sales rise then so will Total Costs.
If output/sales fall then so will Total Costs.
Break Even Analysis
The Break-even point occurs when Total Costs equals
Revenue (Sales Income)
Revenues (Sales Income) = Total Costs
At this point the business is not making a Profit nor incurring a Loss
– it is merely covering its Total Costs
Let us have a look at a simple example.
Bannerman Trading Company
opens a flower shop.
Break Even Chart
Costs/Revenue
TR
BEP
TC
VC
The Break-even
point occurs
where total
revenue equals
total costs – the
firm, in this
example would
have to sell Q1 to
generate
sufficient revenue
(income) to cover
its total costs.
FC
Q1
Output/Sales
Assumptions of Break Even Analysis
All Fixed and Variable costs can be identified
Variable costs are assumed to vary directly with
output
Fixed costs will remain constant
Selling prices are assumed to remain constant
for all levels of output
Assumptions of Break Even Analysis
The sales mix of products will remain constant –
break even charts cannot handle multi-product
situations
It is assumed that all production will be sold
The volume of activity is the only relevant factor
which will affect costs
Limitations of Break Even Analysis
Some costs cannot be identified as precisely
Fixed or Variable
Semi-variable costs cannot be easily
accommodated in break-even analysis
Costs and revenues tend not to be constant
With Fixed costs the assumption that they are
constant over the whole range of output from
zero to maximum capacity is unrealistic
Limitations of Break Even Analysis
Price reduction may be necessary to protect sales
in the face of increased competition
The sales mix may change with changes in tastes
and fashions
Productivity may be affected by strikes and
absenteeism
The balance between Fixed and Variable costs
may be altered by new technology
Break Even Analysis Example
Fixed Costs:
• Rent: $400
• Helper (Wages): $ 200
Variable Costs:
• Flowers: $ 0.50 per bunch
Selling Price:
• Flowers: $ 2 per bunch
So we know that:
Total Fixed Costs = $ 600
Variable Cost per Unit = $ 0.50
Selling Price per Unit = $ 2.00
Break Even Analysis
SP = $2.00
VC = $0.50
FC = $600
We must firstly calculate how much income from each
bunch of flowers can go towards covering the Fixed
Costs.
This is called the Unit Contribution.
Selling Price – Variable Costs = Unit Contribution
$2.00 - $0.50 = $1.50
For every bunch of flowers sold $1.50 can go towards
covering Fixed Costs
Break Even Analysis
Now to calculate how many units must
be sold to cover Total Costs (FC + VC)
SP = $2.00
VC = $0.50
This is called the Break Even Point
Break Even Point =
Fixed Costs  Unit Contribution
$600  $1.50 = 400 Units
Unit cont =
$1.50
FC = $600
Therefore 400 bunches of flowers must be sold to Break Even – at
this the point the business is not making a Profit nor incurring a
Loss – it is merely covering its Total Costs
Break Even Analysis
Lets try another example:
Selling Price per unit = $5
Variable Cost per unit = $2
Fixed Costs = $300
How many units must be sold in order to Break Even?
Break Even Analysis
SP = $5.00
VC = $2.00
First calculate the Unit Contribution
FC = $300
SP – VC = Unit Contribution
$5.00 - $2.00 = $3.00
Now calculate Break Even point by using the formula
–
Fixed Costs  Unit Contribution
$300  $3.00 = 100 units
Therefore 100 units must be sold in order to Break
Even
Break Even Analysis
Break Even can also be used to calculate Profit (or Loss) at a given level of
output
For example:
J Bannerman sells Golf Clubs. How much profit/loss is made when 5000
golf clubs are sold?
Each Golf Club is sold for $20
Variable Costs per golf club are $10
Fixed Costs total $24,000
Break Even Analysis
SP = $20.00
VC = $10.00
FC = $24,000
Sales = 5,000 units
Firstly, calculate Unit Contribution
SP – VC = Unit Contribution
$20.00 - $10.00 = $10.00
Now calculate Total Contribution when 5,000 golf clubs are sold
Unit Contribution x no of units = Total Contribution
$10.00 x 5,000 = $50,000
Now calculate Net Profit at 5,000 units
Total Contribution – Fixed Costs = Net Profit
$50,000 - $24,000 = $26,000
Break Even Analysis
SP = $2.50
Lets try another example.
Fixed Costs =
Caroline Wilson owns a florist shop.
Rent
$1,050
Insurance
$200
Total FC $1,250
She buys each bunch of flowers for $1.49 Variable Costs =
$1.49
and special wrapping paper for $3 per Flowers
$0.01
roll. Each roll of wrapping paper will Paper
wrap 300 bunches of flowers. Rent of ($3/300)
her premises is $1,050 per month and Total VC $1.50
she pays monthly insurance of $200. So:
Caroline sells each bunch of flowers
SP = $2.50
for $2.50. What do we know?
VC = $1.50
FC = $1,250
Break Even Analysis
SP = $2.50
VC = $1.50
Calculate Caroline’s Break Even
FC = $1,250
Point and also how much Profit
would she make if she sold 2,000 bunches of flowers?
Firstly, calculate Unit Contribution
SP – VC = Unit Contribution
$2.50 - $1.50 = $1.00
Now calculate Break Even
Fixed Costs  Unit Contribution
$1,250  $1.00 = 1,250 units
Break Even Analysis
SP = $2.50
How much Profit would she make
FC = $1,250
if she sold 2,000 bunches of flowers?
Unit Cont = $1.00
VC = $1.50
Now, calculate the profit at 2,000 bunches of
flowers
Unit Contribution x No of Units = Total contribution
$1.00 – 2,000 units = $2,000
Total Contribution – Fixed Costs = Net Profit
$2,000 - $1,250 = $750
Break Even Analysis
The formulae used so far assumes that Unit Costs are
known ie Unit Selling Price and Unit Variable Cost
When no unit costs are known, the Profit/Volume
Ratio should be used instead
Profit Volume Ratio
P/V Ratio (Profit/Volume Ratio) =
Total Contribution / Sales
x 100
If asked to calculate the volume of sales needed to BreakEven (when no unit costs are given) the following formula
should be used:
Sales at BEP = Fixed Costs / Profit/Volume Ratio
Profit Volume Ratio Example
Sales $60,000
Variable Costs $24,000
Fixed Costs $14,000
Calculate the P/V Ratio and the BEP
Answer
Sales – Variable Costs = Total Contribution
$60,000 - $24,000 = $36,000
Total Contribution / Sales = P/V Ratio
($36,000 / $60,000) x 100 = 60%
Fixed Costs / P/V Ratio = Sales at BEP
$14,000 / 60% = $23,333
Therefore $23,333 of Sales are necessary in order to
Break-Even