1. Improving Productivity
Breakeven Analysis
Improving Productivity

2. Break-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.

3. BREAKEVEN : 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)

4. Make or Buy Breakeven 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

5. View this example in the Excel file: BreakevenCalc
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 house
Buy: contract with an outside vendor who makes the part
RESULTS
The 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
BREAKEVEN: TWO ALTERNATIVES
Alternative 1
Alternative 2
NAME:
MAKE
BUY
ANNUAL FIXED COSTS:
$ ,000.00
$ ,400.00
VARIABLE COSTS/UNIT: $ $
UNIT OF MEASURE:
Flange
BREAKEVEN VOLUME
19200
ESTIMATED ANNUAL VOLUME
25000
ANNUAL VOLUME
2500
$ ,750.00
$ ,400.00
5000
$ ,500.00
$ ,400.00
7500
$ ,250.00
$ ,400.00
10000
$ ,000.00
$ ,400.00
12500
$ ,750.00
$ ,400.00
15000
$ ,500.00
$ ,400.00
17500
$ ,250.00
$ ,400.00
20000
$ ,000.00
$ ,400.00
22500
$ ,750.00
$ ,400.00
$ ,500.00
$ ,400.00
27500
$ ,250.00
$ ,400.00
30000
$ ,000.00
$ ,400.00
32500
$ ,750.00
$ ,400.00
35000
$ ,500.00
$ ,400.00
37500
$ ,250.00
$ ,400.00
40000
$ ,000.00
$ ,400.00
42500
$ ,750.00
$ ,400.00
45000
$ ,500.00
$ ,400.00
47500
$ ,250.00
$ ,400.00
50000
$ ,000.00
$ ,400.00
View this example in the Excel file: BreakevenCalc

6. Make or Buy Breakeven 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.

7. Example 2 Two 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
Annualize Investment: $165,000
Annual Maintenance: $35,000
Labor: $2.25 / gear
Try to solve this example:
First try the formula;
Then use the BreakevenCalc Excel spreadsheet.

8. CVP 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 + cQ
pQ – cQ = F
Q(p - c) = F
Q* = F / (p – c)

9. 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.

10. Hospital Example Q = F / (p - c) = 100,000 / (200-100)
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.
What is the break-even quantity for this service?
Q = F / (p - c)
= 100,000 / ( )
= 1,000 patients

11. Hospital Example, continued
400 –
300 –
200 –
100 –
0 –
Patients (Q)
Dollars (in thousands)
| | | |
Quantity Total Annual Total Annual
(patients) Cost ($) Revenue ($)
(Q) (100, Q) (200Q)
0 100,000 0
, ,000

12. Total annual revenues Quantity Total Annual Total Annual
(patients) Cost ($) Revenue ($)
(Q) (100, Q) (200Q)
0 100,000 0
, ,000
400 –
300 –
200 –
100 –
0 –
Patients (Q)
Dollars (in thousands)
| | | |
(2000, 400)
Total annual revenues
Quantity Total Annual Total Annual
(patients) Cost ($) Revenue ($)
(Q) (100, Q) (200Q)
0 100,000 0
, ,000

13. Total annual revenues Quantity Total Annual Total Annual
(patients) Cost ($) Revenue ($)
(Q) (100, Q) (200Q)
0 100,000 0
, ,000
Total annual costs
Patients (Q)
Dollars (in thousands)
400 –
300 –
200 –
100 –
0 –
| | | |
Fixed costs
(2000, 400)
(2000, 300)
Total annual revenues

14. Total annual revenues Break-even quantity
Quantity Total Annual Total Annual
(patients) Cost ($) Revenue ($)
(Q) (100, Q) (200Q)
0 100,000 0
, ,000
Total annual revenues
Total annual costs
Patients (Q)
Dollars (in thousands)
400 –
300 –
200 –
100 –
0 –
| | | |
Fixed costs
Break-even quantity
(2000, 400)
(2000, 300)
Profits
Loss

15. Sensitivity Analysis Example A.2
pQ – (F + cQ)
200(1500) – [100, (1500)]
$50,000
Total annual revenues
Total annual costs
Patients (Q)
Dollars (in thousands)
400 –
300 –
200 –
100 –
0 –
| | | |
Fixed costs
Profits
Loss
Forecast = 1,500

16. Example, Denver Zoo
What are: p? F? c?

17. Denver Zoo Setting up the SolutionQ
TR = pQ
TC = F + cQ

18. Denver Zoo Graphical SolutionQ
TR = pQ
TC = F + cQ

19. Denver Zoo Algebraic Solution
pQ = F + cQ Q
TR = pQ
TC = F + pQ