ENGINEERING ECONOMY &
ACCOUNTING
COST CONCEPTS,
BREAK-EVEN ANALYSIS,
And PRESENT ECONOMY
I. COST CONCEPTS
DEMAND – is the quantity of a certain commodity that is bought at a
certain price at a given place and time.
SUPPLY – is the quantity of a certain commodity that is offered for
sale at a certain price at a given place and time.
FIXED COST – are costs that do not vary in proportion to the
quantity of output.
VARIABLE COST – are costs that vary in proportion to quantity of
output.
BREAK EVEN POINT – is the level of production at which revenue
is exactly equal to total costs
LAW OF SUPPLY
The supply of the commodity varies directly as
the price of the commodity, though not
proportionately
p
r
i
c
e
Supply
LAW OF DEMAND
The demand for a commodity varies inversely as
the price of the commodity, though not
proportionately
p
r
i
c
e
Demand
LAW OF DEMAND & SUPPLY
Under conditions of perfect competition, the price at
which any given product will be supplied and purchased
is the price that will result in the supply and the demand
being equal.
p
r
i
c
e
Quantity
The relationship between price and demand
can be expressed as a line
p
r
i
c
e
p = a - bD
Demand (D)
Where a is the intercept on the price
(p)axis and –b is the slope.
TOTAL REVENUE –
VOLUME RELATIONSHIP
T
O
T
A
L
R
e
v
e
n
u
e
Peak point – represents the
Maximum revenue
Demand that maximizes
Total Revenue
D'
Volume
(D)
COST - VOLUME
RELATIONSHIP
Total Cost
C
o
s
t
Variable Cost
Fixed Cost
Volume (D)
COMBINATION OF COST VOLUME & REVENUE VOLUME
RELATIONSHIP
C
o
s
t
R
e
v
or
e
n
u
e
Represents the
Maximum Profit
Total Cost
Demand that maximizes
Total Profit
D*
Volume (D)
COST CONCEPTS
FORMULAS:
A: Price is not constant
price:
p = a – bD
Total Revenue:
TR = pD
Profit:
P = TR – TC
Demand that maximizes total revenue:
Ď = a / 2b
Demand that maximizes total profit: D* = (a – vc) / 2b
Total Cost:
TC = TVC + TFC
Total Variable Cost:
TVC = vcD
Break even points: - (a-vc) ± SQRT {( a-vc )2 – 4(-b)(-TFC)}
2 (-b)
where:
a, the y intercept
b, slope of the line
D, demand
TFC, total fixed cost
Cost / Revenue
Marginal
( Incremental) Cost
Profit is maximum where
Total Revenue exceeds
Total Cost by greatest amount
Maximum
Profit
Cost / Revenue
Quantity ( Output )
Marginal
Demand
Revenue
TC
Profit
Total Revenue
TFC
D’1
D*
D’2
D’1 and D’2 are breakeven points
Quantity ( Output )
Demand
PROFIT MAXIMIZATION D*
 Occurs
where total revenue
exceeds total cost by the greatest
amount;
 Occurs where marginal cost =
marginal revenue;
 Occurs where dTR/dD = d TC /dD;
 D* = [ a - b (uvc) ] / 2
BREAKEVEN POINT
D’1 and D’2
Occurs
where TR = TC
( aD - D2 ) / b = TFC + (uvC ) D
- D2 / b + [ (a / b) - uvC ] D - TFC
Using the quadratic formula:
 D’ = - [ ( a / b ) - uvC ] + { [ (a / b ) - uvC ] 2 - ( 4 / b ) ( - TFC ) }1/2

-----------------------------------------------------------------------2/b
COST CONCEPTS
B: Price is constant
Break even point:
R
C
O or e
v
S
e
T
n
u
e
D’ = TFC / ( p – vc)
IT
F
O
PR
ss
o
L
Volume (D)
Break Even Point
where TR=TC
DESIGN FOR THE ENVIRONMENT
(DFE)
This green-engineering approach has
the following goals:
 Prevention of waste
 Improved materials selection
 Reuse and recycling of resources
Examples:
A company has determined that the price and the monthly
demand of one if its products are related by the equation
D = 400 - p
Where p is the price per unit in dollars and D is the monthly
demand. The associated fixed costs are $1,125/month and
the variable costs are $100/unit. Use this information to
answer the following:
1.1 What is the optimal number of units that should be produced
and sold each month?
1.2 Determine the values of D that represents the breakeven
point?
Examples
2. A manufacturing company leases a building for
$100,000 per year for its manufacturing facilities
in addition; the machinery in this building is being
paid for in installments of $20,000 per year. Each
unit of the product produced costs $15 in labor and
$10 in materials. The product can be sold for $40.
Use this information to answer the following
problems.
2.1. How many units per year must be sold for the
company to breakeven?
2.2. If 10,000 units per year are sold, what is the
annual profit?
Examples:
3.
A bicycle component manufacturer
produces hubs for bike wheels. Two
processes are possible for manufacturing,
and the parameters of each process are as
follows:
Assume that the daily demand for hubs allows
all defect-free hubs to be sold. Additionally,
tested or rejected hubs cannot be sold.
Find the process that maximizes profit per
day if each part is made from Php 200
worth of material and can be sold for Php
1500. Both processes are fully automated,
and variable overhead cost is charged at
the rate of Php 2000 per hour.
4. In determining the cost involved in sub-assembly B
within a company, the following data have been
generated:
Direct Material
Direct Labor
Testing Set-up
-
Php 0.30 per unit
Php 0.50 per unit
Php 300 per set-up
It is decided to subcontract the manufacturing of
assembly B to an outside company. For an order of
100 units, what is the cost per unit that is
acceptable to the company?
BREAK – EVEN ANALYSIS,
TWO ALTERNATIVES
Industry is faced with certain situations where two or more
alternatives can be considered. When the cost for two alternatives is
affected by a common decision variable, there may exist a value of the
variable for which the two alternatives will incur equal cost. This value
is known as the break-even cost. Below this cost, one method will be
more economical, and above this cost, the other will prove to be better
economically.
TCA
TCB
Total Cost
D’
Volume (D)
TCA = TCB
Examples:
1.
A machine part requires the making of several
holes in each piece. Two methods are available. The
first consists of laying out the position of the holes
with dividers and a center punch and the drilling.
In this method, a workman, who is paid P28.00 per
hour, can complete 2 pieces per minute. The other
method is to make a drill jig costing P3,000 for use
in drilling the holes. By this method, a workman,
who is paid P24.00 per hour, can complete 6 pieces
per minute. All other costs are the same for both
methods.
a.
Determine the comparative costs for
making 24,000 pieces. Assume that the cost of the
drill jig is charged to this operation.
b.
Determine the number of pieces that will
have to be made so that the costs will be the same
for both methods
Examples
Machine A has a fixed cost of $40,000
per year and a variable cost of $60 per
unit. Machine B has an unknown fixed
cost, but with this process 200 units can
be produced each month at a total
variable cost of $2,000. If the total
costs of the two machines break even at
a production rate of 2000 units per year,
what is the fixed cost of machine B?
2.
SELECTIONS IN PRESENT
ECONOMY
Present Economy involves the analysis
of problems for manufacturing a
product or rendering a service upon
the basis of present or immediate
costs. The period of time involved in
this study is relatively short and the
influence of time of money is not a
significant consideration
PRESENT ECONOMY STUDIES
When alternatives for accomplishing a task are
compared for one year or less (I.e., influence of
time on money is irrelevant)
Rules for Selecting Preferred Alternative
Rule 1 – When revenues and other economic
benefits are present and vary among
alternatives, choose alternative that maximizes
overall profitability based on the number of
defect-free units of output
Rule 2 – When revenues and economic benefits are
not present or are constant among alternatives,
consider only costs and select alternative that
minimizes total cost per defect-free output
PRESENT ECONOMY STUDIES
Total Cost in Material Selection
In many cases, selection of among materials
cannot be based solely on costs of materials.
Frequently, change in materials affect design,
processing, and shipping costs.
Alternative Machine Speeds
Machines can frequently be operated at
different speeds, resulting in different rates of
product output. However, this usually results in
different frequencies of machine downtime.
Such situations lead to present economy studies
to determine preferred operating speed.
PRESENT ECONOMY STUDIES
Make Versus Purchase (Outsourcing) Studies
A company may choose to produce an item in
house, rather than purchase from a supplier at
a price lower than production costs if:
1.
direct, indirect or overhead costs are incurred
regardless of whether the item is purchased
from an outside supplier, and
2. The incremental cost of producing the item in
the short run is less than the supplier’s price
PRESENT ECONOMY STUDIES
Make Versus Purchase (Outsourcing) Studies
 The relevant short-run costs of the make versus
purchase decisions are the incremental costs
incurred and the opportunity costs of resources
 Opportunity costs may become significant when
in-house manufacture of an item causes other
production opportunities to be foregone (E.G.,
insufficient capacity)
 In the long run, capital investments in additional
manufacturing plant and capacity are often
feasible alternatives to outsourcing.
Examples: (C.E. Board,
August 1975)
1. An engineer bidding on the asphalting of a 7-km stretch of
road is confronted with the problem of choosing between two
possible sites on which to set up the asphalt-mixing
machine. At site A, the average hauling distance is 2.5 km;
the monthly rental would be Php 3,500 and the cost of
installing and dismantling the equipment would be Php
17,000. At site B, the average hauling distance is 3.25km; the
monthly rental would be Php650 and the cost of installing
and dismantling the equipment would be Php7,200. The
asphalt mix is to be hauled by a sub-contractor at Php0.42
per cu.m. per km of haul. At site A, it would be necessary to
hire 2 flagmen at Php15 each per workday. The job can be
completed in 30 weeks or 7 months working 6 days a week.
The project requires 16,670 cu.m. of asphalt mix per km of
road. Which site should be choose and how much lower
would his bid price be if he made the better choice?
Examples:
2. The “We Win Them All’ Formula-Car manufacturing
company needs spindles for their rolling chassis.
They can buy them from an outside manufacturer for
$200 per spindle plus shipping costs. Each spindle
weighs 18 lbs. and shipping costs are $1.50 per
pound.
The outside manufacturer will give a
discount for bulk orders (does not include shipping
costs). The first 50 spindles are at full price, the next
50 have 10% discount per spindle, and the next 50
have a 15% discount per spindle. Or they can make
spindles themselves. It costs $0.75/lb for aluminum,
takes 72 minutes per unit to machine, and the cost of
machine operator is $14 per hour. Assume there is
no scrap. Should the company produce or buy the
spindles if 125 are needed?
Examples: (M.E. Board,
August 1952)
3. In manufacturing a kerosene stove, it is
necessary to make two half-inch holes in
No.22 gage metal. If these are drilled with
the help of the jig, each hole will require one
minute. The jig will cost Php40. The drill
press operator receives Php1.10 per hour.
The holes could be made also on a punch press
at the rate of 2 holes each 10 seconds. A die
would be required at a cost of Php80. The
punch operator will receive Php0.90 per
hour.
If 1,000 stoves are to be produced and the jig
or die will have no scrap value, which
method will you recommend?
Examples:
4.
Women’s Hospital operates a cafeteria
for its employees. Fixed operating costs
are Php8,000 per month, and variable costs
are Php0.40 per peso of sales. Sales for an
average month are Php16,000.
Burns
Vending Company has offered to replace
the cafeteria with a set of vending
machines for which revenue is estimated to
be Php14,000 monthly. Women’s would
receive 14% of total revenue as rental
income and would avoid all cafeteria fixed
and variable costs. Should Women’s accept
Burns’ offer to replace the cafeteria with
vending machines?