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8/21/2019 Class 25- Breakeven Analysis
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Breakeven Analysis
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Introduction
Breakeven analysis examines the short run
relationship between changes in volume and
changes in total sales revenue, expenses and
net profit
Also known as C-V-P analysis (Cost Volume
Profit Analysis)
C-V-P analysis is an important tool in terms of
short-termplanning and decision making
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Key Terminologies
Break even point-the point at which acompany makes neither a profit or a loss.
Contribution per unit-the sales price minus
the variable cost per unit. It measures thecontribution made by each item of output to
the fixed costs and profit of the organisation.
Margin of safety-a measure in which thebudgeted volume of sales is compared with
the volume of sales required to break even
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Break Even Formula
Contribution per unit
Is the selling price of a product less variable costs
per unit.
Break-even level of output=
Fixed Cost
Contribution per unit
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Algebraic Solution
Equate total revenue and total cost functions and solve for
Q
TR = P x Q
TC = FC + (VC x Q)
TR = TC
P x QB= FC + VC x QB
(P x QB)(VC x QB) = FC
QB(P
VC) = FCQB= FC/(PVC)
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Break-even Formula Example
Fixed costs = $200,000
Contribution per unit = $50
What is the Break-even level of output?
Fixed Cost
Contribution per unitBreak-even level of output=
200,000 / 50 = 4000 units
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Graphical Method
The break-even graph shows 3 pieces of
information:
Fixed costs
Total costs (fixed costs + variable costs)
Sales revenue (selling price * units sold)
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Graphical Method Example
The maximum profit is made when the maximum output is produced.
0
Fixed Costs
Variable Costs
Total Costs
Sales Revenue
Break-even point
BE
Profit at full capacity
Full
Capacity
Costsand
revenu
e
Output
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Profit vs Loss
Profits are to the right of the break-even point.
Losses are to the left of the break-even point.
0
Fixed Costs
Variable Costs
Total Costs
Sales Revenue
Break-even point
BE
Profit at full capacity
Profit
Loss
Full
Capacity
Costsand
revenu
e
Output
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Margin of Safety
The difference between budgeted or actual
sales and the breakeven point
The margin of safety may be expressed in
units or revenue terms
Shows the amount by which sales can drop
before a loss will be incurred
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Margin of Safety
Margin of safetyis the amount by which the sales level exceeds
the break-even level. If sales drop below this level, a loss will occur.
0
Fixed Costs
Variable Costs
Total Costs
Sales Revenue
Break-even
point
BE
Profit at full capacity
Full
Capacity
Current
Output
Safetymargin
If margin of safety is
positive, production
is above break even.
If margin of safety is
negative, production
is below break even.
Costsand
revenu
e
Output
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Additional Uses of Break-even Analysis
Marketing decision: The impact of price increases
This raises sales revenue line at all quantitiesassumingthat sales do not decline which may be unlikely.
Operations Management decision: Purchase of newequipment with lower variable costs
This lowers the variable cost line at each quantity level.
Choosing between two locations for a new factorywith different fixed and variable costs.
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Target Revenues & Profits
A modified break-even formula can be used to
determine a target profit level.
Target profit level of output=
Target profit is $25,000
Fixed Costs are $200,000
Contribution per unit $50
Fixed Costs + Target Profit
Contribution per Unit
200,000 + 25,000
504500 =
Units
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Break-even Revenue
Break-even Revenue is the amount of revenue
needed to cover bothfixed and variable costs so that
the business breaks even.
Fixed Costs
1(Variable cost / Price)Break-even Revenue =
This is helpful in a service business.
Story: If the monthly fixed costs of a law practice are $60,000, lawyers are paid$15 per hour, and clients are charged a price of $30 per hours, what is the
break-even revenue?
60,000
1(15 / 30)= $120,000
How many hours must they bill?
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Breakeven Between Two Alternatives
To determine value of common variable between 2 alternatives, do thefollowing:
1. Define the common variable2. Develop equivalence PW, AW or FW relations as function of common
variable for each alternative
3. Equate the relations; solve for variable. This is breakeven value
Selection of alternative is based on
anticipated value of common variable:
Value BELOW breakeven;
select higher variable cost
Value ABOVE breakeven;
select lower variable cost
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Example
Alternative A (Make): First cost= 18000,
Salvage Value= 2000 and Per Unit cost of 0.4
Alternative B (Buy): 1.5 per unit.
MARR= 15% and Life= 6 Years
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Example: Two Alternative Breakeven Analysis
Perform a make/buy analysis where the
common variable is X, the number of units
produced each year. AW relations are:
AWmake= -18,000(A/P,15%,6)
+2,000(A/F,15%,6)0.4X
AWbuy = -1.5X
Solution: Equate AW relations, solve for X
-1.5X = -4528 - 0.4X
X = 4116 per year
X, 1000 units per year
Breakeven
value of X
1 2 3 4 5
AWbuy
AWmake
If anticipated production > 4116,
select make alternative (lower variable cost)
AW, 1000
$/year
8
7
6
5
4
3
2
1
0
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Payback Period Analysis
Caution: Payback period analysis is a good initial screeningtool, rather than the primary method to justify a project or
select an alternative (Discussed later)
Payback period: Estimated amount of time (np) for cash inflows to recover aninitial investment (P) plus a stated return of return (i%)
Types of payback analysis: No-returnand discountedpayback
1. No-return payback means rate of return is ZERO (i = 0%)2. Discounted payback considers time value of money (i > 0%)
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Payback Period Computation
Formula to determine payback period (np)
varies with type of analysis.NCF = Net Cash Flow per period t
Eqn. 1
Eqn. 2
Eqn. 3
Eqn. 4
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Points to Remember About Payback Analysis
No-return payback neglects time value of money, so no
return is expected for the investment made No cash flows after the payback period are considered in the
analysis. Return may be higher if these cash flows areexpected to be positive.
Approach of payback analysis is different from PW, AW, RORand B/C analysis. A different alternative may be selected usingpayback.
Rely on payback as a supplemental tool; use PW or AW at the
MARR for a reliable decision Discounted payback (i > 0%) gives a good sense of the risk
involved
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Example: Payback Analysis
System 1 System 2First cost, $ 12,000 8,000NCF, $ per year 3,000 1,000 (year 1-5)
3,000 (year 6-14)Maximum life, years 7 14
Problem: Use (a) no-return payback, (b) discounted payback at
15%, and (c) PW analysis at 15% to select a system. Commenton the results.
Solution: (a) Use Eqns. 1 and 2np1 = 12,000 / 3,000 = 4 years
np2 = -8,000 + 5(1,000) + 1(3,000) = 6 years
Select system 1
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Example: Payback Analysis (continued)System 1 System 2
First cost, $ 12,000 8,000NCF, $ per year 3,000 1,000 (year 1-5)
3,000 (year 6-14)Maximum life, years 7 14
Solution: (b) Use Eqns. 3 and 4System 1: 0 = -12,000 + 3,000(P/A,15%,np1)
np1= 6.6 years
System 2: 0 = -8,000 + 1,000(P/A,15%,5)+ 3,000(P/A,15%,np2- 5)(P/F,15%,5)
np1= 9.5 years
Select system 1
(c) Find PW over LCM of 14 years
PW1= $663PW2= $2470
Select system 2Comment: PW method considers cash flows after payback period.
Selection changes from system 1 to 2