Post on 13-Dec-2015
Breakeven AnalysisBreakeven Analysis
Improving Productivity
Break-Even AnalysisBreak-Even Analysis
• Break-even analysis has TWO forms:– A. CVP (cost-volume-profit): to determine the volume of
sales at which a specific product will generate 0 profit• Total Costs = Revenue, i.e. Revenue – Total Costs = 0
– B. to compare processes by finding the volume at which two different processes have equal total costs.
• Total costs of process X = Total costs of process Y
• Variable costs (c) are costs that vary directly with the volume of output.
• Fixed costs (F) are those costs that remain constant with changes in output level.
BREAKEVEN :BREAKEVEN :Two Processes or Make-or-Buy Decisions Two Processes or Make-or-Buy Decisions
• Choose between two processes or between an internal process and buying those services or materials.
• The solution finds the point at which the total costs of each of the two alternatives are equal.– Total costs of Alt. 1 = Total costs of Alt. 2
– F1 + c1Q = F2 + c2Q
• The forecast volume is then applied to see which alternative has the lowest cost for that volume.
Determining the Breakeven Quantity, Q*F1 + c1Q = F2 + c2Q c1Q – c2Q = F2 – F1
Q(c1 – c2) = F2 – F1
Q* = (F2 – F1) / (c1 – c2)
Make or BuyBreakeven Example
• Analyzing a production process that needs improvement, producing a metal flange.
• Two Alternatives:– Make: buy a new machine and run the process in house– Buy: contract with an outside vendor who makes the part
• Costs of each alternative:– Make:
• Fixed costs: New machine, investment cost = $12,000/yr, Fm
• Variable costs: $1.50 / piece, (material & labor), cm
– Buy:• Fixed costs: annual tooling costs = $2,400, Fb
• Variable costs: $2.00/ piece, cb
BREAKEVEN: TWO ALTERNATIVES
Alternative 1 Alternative 2NAME: MAKE BUY
ANNUAL FIXED COSTS: $ 12,000.00 $ 2,400.00
VARIABLE COSTS/UNIT: $ 1.50 $ 2.00 UNIT OF MEASURE: Flange
BREAKEVEN VOLUME19200
ESTIMATED ANNUAL VOLUME25000
ANNUAL VOLUME MAKE BUY
0 $ 12,000.00 $ 2,400.00
2500 $ 15,750.00 $ 7,400.00
5000 $ 19,500.00 $ 12,400.00
7500 $ 23,250.00 $ 17,400.00
10000 $ 27,000.00 $ 22,400.00
12500 $ 30,750.00 $ 27,400.00
15000 $ 34,500.00 $ 32,400.00
17500 $ 38,250.00 $ 37,400.00
20000 $ 42,000.00 $ 42,400.00
22500 $ 45,750.00 $ 47,400.00
25000 $ 49,500.00 $ 52,400.00
27500 $ 53,250.00 $ 57,400.00
30000 $ 57,000.00 $ 62,400.00
32500 $ 60,750.00 $ 67,400.00
35000 $ 64,500.00 $ 72,400.00
37500 $ 68,250.00 $ 77,400.00
40000 $ 72,000.00 $ 82,400.00
42500 $ 75,750.00 $ 87,400.00
45000 $ 79,500.00 $ 92,400.00
47500 $ 83,250.00 $ 97,400.00
50000 $ 87,000.00 $ 102,400.00
Example: MAKE v. BUY, Analyzing a production process that needs improvement, producing a metal flange. Two Alternatives:Make: buy a new machine and run the process in houseBuy: contract with an outside vendor who makes the part
RESULTSThe Breakeven Volume is 19,200. If the volume is more than 19,200, then MAKE is the better than BUY. But if the Volume is less than the Breakeven, then BUY is better.
Since the estimated annual volume is 25,000, MAKE is the choice.
Costs of each alternative:
Make: Fixed costs: New machine, investment cost = $12,000/yr, Fm
Variable costs: $1.50 / piece, (material & labor), cm
Buy:Fixed costs: annual tooling costs = $2,400, Fb
Variable costs: $2.00/ piece, cb
View this example in the Excel file: BreakevenCalc
Make or BuyBreakeven Example
Algebraic Solution:• Q* = (Fm – Fb) / (cb – cm)
• Q* = (12,000 – 2,400) / (2.00 – 1.50)• Q* = 9600 / 0.50• Q* = 19,200 Breakeven Annual Volume• If the forecast or expected volume is more than
Breakeven (19,200), then the MAKE alternative generates the lowest Total Costs, and vice versa.
• Since the forecast volume is 25,000, the choice is to MAKE, so you should buy the machine and get started.
Example 2Two Processes
• A new machine is needed for a process that produces a gear:• Alt. 1: Machine A
– Fixed Costs: • Annualize Investment: $120,000• Annual Maintenance: $20,000
– Variable costs:• Material: $2.25 / gear• Labor: $6.25 / gear
• Alt. 2: Machine B (faster and more efficient in terms of labor– Fixed Costs:
• Annualize Investment: $165,000• Annual Maintenance: $35,000
– Variable costs:• Material: $2.25 / gear• Labor: $2.25 / gear
Try to solve this example:First try the formula;Then use the BreakevenCalc Excel spreadsheet.
CVP Break-Even AnalysisCVP Break-Even Analysis• Notation:
– Q is the volume of customers or units, – c is the unit variable cost, – F is fixed costs and – p is the revenue per unit
• cQ = the total variable cost.• Total cost = F + cQ• Total revenue = pQ• Profit = Revenue – Total Costs
• Breakeven Profit = 0• pQ = F + cQ (Total revenue = Total cost)
Determining the Breakeven Quantity, Q*
pQ = F + cQpQ – cQ = FQ(p - c) = FQ* = F / (p – c)
Break-Even Analysis can tell you…
• If a forecast sales volume is sufficient to break even (no profit or no loss)
• How low variable cost per unit must be to break even given current prices and sales forecast.
• How low the fixed cost need to be to break even.
• How price levels affect the break-even volume.
Hospital ExampleHospital Example
A hospital is considering a new procedure to be offered at $200 per patient. The fixed cost per year would be$100,000, with total variable costs of $100 per patient.
Q = F / (p - c) Q = F / (p - c) = 100,000 / (200-100) = 100,000 / (200-100) = 1,000 patients= 1,000 patients
What is the break-even quantity for this service?
400 –400 –
300 –300 –
200 –200 –
100 –100 –
0 –0 –
Patients (Q)Patients (Q)
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|| || || ||
500500 10001000 15001500 20002000
Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
Hospital Example, Hospital Example, continuedcontinued
Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
400 –400 –
300 –300 –
200 –200 –
100 –100 –
0 –0 –
Patients (Q)Patients (Q)
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|| || || ||
500500 10001000 15001500 20002000
(2000, 400)(2000, 400)
Total annual revenuesTotal annual revenues
Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
Total annual costsTotal annual costs
Patients (Q)Patients (Q)
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400 –400 –
300 –300 –
200 –200 –
100 –100 –
0 –0 –|| || || ||
500500 10001000 15001500 20002000
Fixed costsFixed costs
(2000, 400)(2000, 400)
(2000, 300)(2000, 300)
Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
Total annual revenuesTotal annual revenues
Total annual revenuesTotal annual revenues
Total annual costsTotal annual costs
Patients (Q)Patients (Q)
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400 –400 –
300 –300 –
200 –200 –
100 –100 –
0 –0 –|| || || ||
500500 10001000 15001500 20002000
Fixed costsFixed costs
Break-even quantityBreak-even quantity
(2000, 400)(2000, 400)
(2000, 300(2000, 300))
ProfitsProfits
LossLoss
Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
Total annual revenuesTotal annual revenues
Total annual costsTotal annual costs
Patients (Q)Patients (Q)
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400 –400 –
300 –300 –
200 –200 –
100 –100 –
0 –0 –|| || || ||
500500 10001000 15001500 20002000
Fixed costsFixed costs
ProfitsProfits
LossLoss
Sensitivity AnalysisSensitivity AnalysisExample A.2Example A.2
Forecast = 1,500Forecast = 1,500
pQ – (F + cQ)
200(1500) – [100,000 + 100(1500)]
$50,000
Example, Denver Zoo
What are:p?F?c?
Denver ZooSetting up the Solution
TR = pQTR = pQ TC = F + cQTC = F + cQQQ
Denver ZooGraphical Solution
TC = F + cQTC = F + cQTR = pQTR = pQQQ
Denver ZooAlgebraic Solution
TR = pQTR = pQQQ TC = F + pQTC = F + pQ
pQ = F + cQpQ = F + cQ