NED University of Engineering and Technology
NED University of Engineering and Technology
A P P L I E D
A P P L I E D E C OE C ON O MN O M I C S F OI C S F OR E NR E N G I N E E R SG I N E E R S
TOPIC
TOPIC
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5
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BREAK
BREAK
EVEN
EVEN
ANALYSES
ANALYSES
Learning Outcome: Learning Outcome:
Concept of Breakeven Analysis (BEA)Concept of Breakeven Analysis (BEA)
Behavior of Co Behavior of Costs & Revensts & Revenueue
Numerical an Numerical and graphical d graphical presentationspresentations
Practical App Practical Applicationslications
BEA as a Ma BEA as a Management Toolnagement Tool
Thi
This s cchapthapteer r cocovevers rs the bathe basics of sics of brebreaak-ek-eveven n aanalysnalysis is whwhich iich i s s the simplethe simplest st aananalyticalyticall tool in management. It details what break-even analysis is, what it is used for, what tool in management. It details what break-even analysis is, what it is used for, what definitions are used in break-even analysis and
definitions are used in break-even analysis and how break-even analysis can be helpfulhow break-even analysis can be helpful
in decision-making of professionals in construction industry
in decision-making of professionals in construction industry. In construction industry,. In construction industry, break-even analysis can be a handy tool to find answers to questions such as:
break-even analysis can be a handy tool to find answers to questions such as:
How many years should I operate the facility to recover the initial investmentHow many years should I operate the facility to recover the initial investment
and annual operating costs? and annual operating costs?
HHow mucow much does our h does our compacompany neeny need to sell d to sell to reato reach the dech the desirsireed prd profiofi tability?tability?
What should be the better option between alternatives?What should be the better option between alternatives?
An
An eenterprinterprisese, whe, whethether or r or not a profnot a prof it mit maaximizximiz ing orgaing organizniz ation, aation, always walways wants to nts to know:know:
Wha
What prt price or outpuice or output lt leevevel mul must be for st be for total rtotal reevevenue to junue to just equast equal l to total cost?to total cost?
The an
The an sswer wer isis: : a breakeven analysisa breakeven analysis.. S
Stritri ctly speactly speakinkingg, thi, thiss aanalysis inalysis is to s to dedetetermirmine the minimum levene the minimum level l of of output thoutput that aat allllowsows
the firm to break even
the firm to break even, but it could be used, but it could be used to compare and analyze various projectto compare and analyze various project
options and alternatives.
options and alternatives.
Break Even Means
Break Even Means:: ne neither profiither profi t nor lt nor l oss;oss;also also : a financial r: a financial reesult sult reflrefleecting necting neithitheerr profit nor loss
profit nor loss
B
Break-reak-even Poeven Pointint:: The origins The origins of of brebreak-eak-eveven n point point cacan n be be found found in in the the eecoconomicnomic concepts of “the point of indifference.” In simple words, the break-even point can be concepts of “the point of indifference.” In simple words, the break-even point can be defined as a point where total costs (expenses) and total sales (revenue) are equal. In defined as a point where total costs (expenses) and total sales (revenue) are equal. In simple words it can be described as a point where there is no net profit or loss. The simple words it can be described as a point where there is no net profit or loss. The firm just “breaks even.”
firm just “breaks even.” Another way to look at it is that the break-even pointAnother way to look at it is that the break-even point is theis the
point at which your product stops costing you money to produce and sell, and starts
point at which your product stops costing you money to produce and sell, and starts
to ge
Break- Even Analysis: In its simplest form, it facilitates an insight into the fact whether the revenue from a project, service or product incorporates the ability to cover the relevant production cost of that particular project, product or service or not. On the surface, break-even analysis is a tool to calculate a t w h a t p r o d u ct i o n v o l u m e th e variable and fixed costs of producing your product will be recovered . Break-even analysis can also be used to solve other management problems, including setting prices, and evaluating the best strategies to follow.
Break-even analysis is done by using a parameter (or variable) which is an amount of revenue, cost, suppl y, demand, etc. for 1) one project or between 2) tw o alternatives.
BREAKEVEN ANALYSIS FOR A SINGLE PROJECT
Basically, break-even analysis determines the “break-even point”, at which operations neither make money nor lose money (Paek 2000, Blank and Tarquin 2008). At the break-even
point, there is no gain or l oss; hence costs or expenses are equal to revenues/ incomes
.
Costs and Revenue: As far as costs and revenue are concerned we have already discussed them in detail in previous lectures. Here is only a memory refresher.
Q or Q
BE Quantity or Breakeven Quantity
P or A R Price or Average Revenue
TFC Total Fixed Cost (Costs that do not change in short-term) v Variable Cost per Unit of production or sale
TVC Total Variable Cost(v .Q BE)
VC Variable Cost
TC Total Cost (FC + VC) TR Total Revenue (P.Q
BE)
F i x e d c o s t represents the expenses that are not related with the volume of production
(or activity level) over a feasible range of operations. Examples include buildings, insurance expenses, depreciation, overheads, and cost of information systems (Blank and Tarquin 2008). It is the sum of all costs to produce the first unit of a product. Another example could be the cost of excavation equipment regardless of the excavation work perf ormed on diff erent projects.
V a r i a b l e c o st represents the cost items that change with the volume of production or
construction. Input materials and time to produce a unit affect variable costs. Examples include direct labor costs, fuel costs, material types (e.g., a certain type of paint used for painting a facility), and marketing costs (Blank and Tarquin 2008, Paek 2000).
T o t a l c o st is the sum of the fixed and total variable costs for any production or construction.
Cost/ expense and revenue/ income relations are commonly assumed as linear; however non-linear relations are more realistic with more revenue for larger volumes (Blank and Tarquin 2008). Here we will confine our discussion only to linear r elationship.
Below is given the algebraic expression and explanation through which breakeven point is identified as QBEwhich is determined using linear math relations for revenue and cost.
Mathematically, the formula for break-even point can be shown as: TR = TC or Profit = 0
Where TR represents the total revenues and T C represents total costs or expenses for an operation.
T R = TC
Expected unit sales (Q) x Unit pri ce (P) = Fixed cost (FC) + T otal v ariable cost (VC) Q x P = FC + Variable unit cost (v ) x Unit sales(Q)
Q x P = FC + (v x Q)
(Q x P) – (v x Q) = FC
Q (P - v ) = FC
Q = FC / (P - v )
Let QBE denote the break-even output. The difference “P - v ” is often called the average
contribution margin (ACM) because it represents the portion of selling price that "contributes" to paying the fixed costs.
Relationship between FC, TC, TR and QEB
Cost/ Revenue TR Profit TC TVC TFC Q u a n t i t y QBE
The break-even diagram can be employed to see the eff ects of various exogenous changes on the break-even point. Here are a few scenarios
Init ial Change Curv e Af fected Af fect on QBE Increase in Output price The TR curve moves
counterclockwise
Decrease Increase in the price of one the
variable input
TVC and TC curves, Increase both counterclockwise
Higher TFC TFC curve, Increase
parallel-shift up
Effects of TFC, AVC, and P on QBE
Cost/Revenue TR1 TR TC1 TC VC FC Quantity QBE
Ex a m p l e 1 : Assume that as an investor, you are planning to enter the construction
industry as a panel formwork supplier. Given the size of the construction industry and the potential number of forthcoming projects, you forecasted that within two years, your fixed cost for producing formworks is Rs. 3,000,000. The variable unit cost for making one panel is Rs. 1500. The sale price for each panel you charge will be Rs. 2,500. How many panels you need to sell in total, in order to start making money?
Variable Dir ection of Change
Break- even Output Total Fixed Cost
(e.g., cost of equipment) Up Up Down Down Average Variable Cost
(e.g., cost of material)
Up Up
Down Down Product Price Up Down
Down Up
TR TC VC FC
Solution:
Variable unit cost = Rs. 1,500/ panel Total fixed cost = Rs. 3,000,000
Pri ce per unit = Rs. 2,500 TC = TR
VC + FC = TR
1,500 x QBE + 3,000 000 = QBE x 2,500 (Q
BE r efer s to the nu m ber of pan els)
Q
BE = 3,000 000 / (2,500-1,500) = 3,000 panels
Ex a m p l e 2 : Calculate the break-even output f or FC = $20,000, P = $7, and AVC = $5
Solution :
QBE =,
=
,
− = 10,000
Ex a m p l e 3 : A manufacturing company supplies its products to construction job sites. The average monthly fixed cost per site is $ 4500, while each unit costs $ 35 to
produce, and selling price is $ 50.
a) Determine the monthly volume of supplies to j ob sites in order to break-even. b) The company has to modify the selling prices due to severe competition. In this
case, the fixed cost and production costs will be the same, but the sales price per unit will be $ 50 for the first 200 units and $ 40 for all above this threshold level. Determine the monthly breakeven volume.
Solution:
(a) Q = 4500 / (50-35) = 300 units, where Q refers to the number of units per month (b) At 200 units, the profits is negative at -$ 1500, as determined by
Profit = Revenue – cost
Profit at 200 units pr oduction = 200x50 – (4500 + 35x200) = 10 000 – 4500- 7000 = -1500.
50 x 200 + 40 x Q = 4500 + 35x (200 + Q) Q
BE = (4500 + 7000 -10 000) / (40 – 35) = 1500 / 5 = 300 units per month
Hence the required volume is 500 units per month, the point at which revenue and total cost break even at $ 22 000
Ex a m p l e 4 : Suppose TFC = $10,000, P = $5, AVC = $2. What is the output necessary to earn $5000 total profit? What is the “average contribution margin”?
Answer :
QBE =,,
=
,
− = 5,000
Ex a m p l e 5 : Suppose that product price decreases from P1 to P2. Show on the diagram how much output would change to m a i n t a i n t h e sa m e lev e l of p r o f i t t a r g et
Cost/Revenue TR TR1 TC A Profit FC Quantity QBE QBE
A n s w e r : Draw a line parallel to TC through A. This line cuts the TR1 line at B, drop a vertical line from B to determine the new output level. [Note: The solution may not be feasible if we are told that the market size cannot accommodate this quantity.]
Ex a m p l e 6 : Given TR and TC, a firm is currently operating at 50% of i ts capacity at some profit target. How much of a price drop would cause the firm to operate at 75% capacity at the same level of profit?
A n s w e r : Cost/Revenue TR1 TR TC1 B TC A FC Quantity QBE
Answer: The vertical dotted line on the right marks the firm’s capacity. Current output is half of that. Draw the line through A and parallel to TC. From 75%capacity output point, draw the vertical line. B is the intersection. Draw the line TR2 through B. The slope of TR2 gives the required output price.
BREAKEVEN ANALYSIS BETWEEN TWO ALTERNATIVES OR PROJECT
Break-even analysis can also be used to select among alternatives (e.g., projects or construction processes). In order to perform break-even analysis between alternatives, there needs to be a parameter (e.g., cost or revenue variables) that is common in both alternatives. When two alternatives are compared, the break-even point represents the point of indif fer ence between the alternatives (i.e., the point at which two alternatives are equally desirable) (Badiru 1996).
The steps to find the point of indiff erence between alternatives:
Find th e com m on var iable betw een th e altern atives
Expr ess the total cost of each alter nat ive as a f un ction of the com m on va r iable Equ ate expr essions and solve for th e poin t of in dif fer ence
Select the alter na tiv e w ith hi gh er va r iable cost (lar ger slope) if t he expected level
is below t he point of in diff er ence, and select th e altern ative with lower v ar iable cost if th e level is above th e point of in dif fer ence.
For the example provided below, profit functions are graphed. This graph shows that Project B is favorable over the other alternatives if the production is between 0 and 100 units, Project A is favorable if the production is between 100 and 200 units, and Project C is favorable if the production is larger than 200 units.
Profit ($) Project C Project A Project B Units (X) -200 - 300 100 150 200
Selection of alternative is based on anticipated value of common variable:
Value BELOW breakeven; select the alternate with higher variable cost (Alt 1) Value ABOVE breakeven; select the alternate with lower variable cost (Alt 2)
Example 5: There exist two alternative locations for an asphalt mixing plant to transport materials from. Characteristics of these two locations and associated costs are tabulated below. Which location is best for the asphalt mixing plant, the cheaper Location A or closer Location B? (Thi s example ha s been ad opted fr om M IT Engin eeri ng Econom ics lectur e n o t es , c o p y r i g h t © M I T , En v i r o n m e n t & C i v i l E n g i n e er i n g D e p a r t m e n t ).
Location A Location B Transportation distance 6 km 4.3 km
Transportation expense $ 1.15/ m3-km $ 1.15/ m3-km Monthly rental expense $ 1000/ month $ 5000/ month Set-up cost $ 15 000 $ 25 000
Workmanship costs 0 $ 96/ day Total volume available 50000 m3 50000 m3
Time to use the location 4 months (85 days) 4 months (85 days)
Solution:
First obtain the total cost functions for all alternatives
Location A Location B
Fixed Costs
Rental expense 4 month x $1000/ month =$ 4000 4 month x $5000/ month =$ 20 000 Set-up cost $ 15 000 $ 25 000
Workmanship costs 0 85 days x $96/ day =$ 8160 Tr ansportation/ Variable costs
Transportation 6 km x $1.15 x Q 4.3 km x $1.15 x Q Total Cost $ 19 000 +6.9 Q $ 53 160 +4.945 Q
Equate the total cost functions to solve for volume to be transported for break-even point
$ 19 000 + 6.9 QBE = $ 53 160 + 4.945 QBE QBE = 17473 m3.
At 17473 m3 of material usage, both sites are equally desirable. If less m ater ial i s t r a n sp o r t e d t h a n 1 7 4 7 3 m 3 , th en selecting location A is fa vor able , and if m ore volum e is expected to be tr ansported th an 1 7473 m 3, then selecting location B is m or e favor able
Example: Perform a make/ buy analysis where the common variable is Q, the number of units produced each year. AW relations are:
(N o t e : In examples like the one given below, deter m ine one of the par am eters P, A, F, i, or n ,wi th others constan t, that m akes tw o elements equal )
AWmake. =- 18,000(A/ P, 15%,6) +2,000(A/ F, 15%,6) – 0.4Q 10 AWbuy =- 18,000 x 0.2642 + 2,000 x 0.1142 – 0.4Q
8
AW
buy =- 1.5Q 6 AWmake
Solution: Equate AW relations, solve for Q
4
1.5Q = - 4528 - 0.4Q ,
2
Q = 4116 per year 0
1 2 3 4 5
If anticipated production > 4116, select AWmake alternative (lower variable cost)
TH E EXCEL SHEET HAS AN IN BUILT FUNCTION NA MED “GOAL SEEK” WHICH CAN BE USED FOR BREAK EVEN ANALYSIS: Data
What- If A nalysis
Goal Seek
If you want to learn it then arrange extra class other than regular classes, I will explain how to use it. INTRODUCTION TO COMPOUND INTEREST FACTOR
Notations Used in Compound Interest i = Interest rate per interest period*. n = Number of interest periods. P = A present sum of money. F = A future sum of money.
A = An end-of-period cash receipt or disbursement in a uniform series continuing for n periods. G = Uniform period-by-period increase or decrease in cash receipts or disbursements.
g = Uniform rate of cash flow increase or decrease from period to period; the geometric gradient. r = Nominal interest rate per interest period*.
m = Number of compounding sub periods per periods*. Concept of Compound Interest
Interest (i) applies to total amount (P + sum of all I) during each period. Consider the following Cash flow:
A $1000 deposit for 5 years at 10% / year would result in: Amount accrued
Year Begin Year Int. End year
1 P = 1000 100 F1 = 1100 F1 = P + Pi
2 1100 110 F2 = 1210 F2 = P + Pi+ (P + Pi) i
3 1210 121 F3 = 1331 F3 = P + Pi+ (P + Pi) i + (P + Pi+ (P + Pi) i) i
4 1331 133 1464 = P + Pi+ Pi+Pi2 + Pi+Pi2 + Pi2 + Pi3
5 1464 146 1610 = P + 3Pi + 3Pi2 + Pi3
= P(1+3i +3i2 + i3) = P(1 + i)3
Solving Problems
It is now easy to solve problems regarding the Equivalence of Present (P) and Future (F) values over time (N) with interest (i). These steps will help: 1) Identify cash flows. 2) Identify P, F, i & N.
3) Determine the missing value. 4) Solve for missing value using equation.
E x a m p l e : What annual interest rate must you get if you need $7000 in 4 years and have $5000 to invest now? P = $5000, F = $7000, N = 4 years, i =? 7000 = 5000(1 + i)4 7000 / 5000 = (1 + i)4 (1.4)1/4= 1 + i 1.0878 = 1 + i 0.0878 = i = 8.78% / year Functional Notation
Standardized notation has been established to avoid writing the equation each time, and to give a logical method by which to find the correct factor to use.
Read the factor as saying "Find F given P at i% for N periods".
E x a m p l e : What is F for $1000 deposit for 5 years @ 10% / year?
F = 1000( F/P,10,5)
(F/P,10,5) = 1.611 --- See table at the end of any book on Engineering Economy F = 1000(1.611) = $1611
E x a m p l e : Find i for P = $5000, F = $7000, N = 4 years
Using F = P(F/P, i, N) 7000 = 5000(F/P, i, 4) 1.4 = (F/P, i, 4)
Search the Compound Interest Factor tables (Pages 180 - 208) to find the Interest rate that matches the factor.
i = 9% (F/P, 9, 4) = 1.412, i = 8% (F/P, 8, 4) =1.360
Since an even i value can't be found to match (F/P,i,4) = 1.4, you must interpolate to find the solution.
Interest Factor Formulas
Compound Amount:To find F, given P (F/P, i, n) Present Worth: To find P, given F (P/F, i, n) Series Compound Amount:
To find F, given A (F/A, i, n) Sinking Fund: To find A, given F (A/F, i, n)
Capital Recovery: To find A, given P (A/P, i, n)
Series Present Worth: To find P, given A (P/A, i, n)
Arithmetic Gradient Uniform Series: To find A, given G (A/G, i, n)
Arithmetic Gradient Present Worth: To find P, given G (P/G, i, n)
Geometric Gradient: To find P, given A1, g (P/G, g, i, n)