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Title

fbep: Financial Break-Even Point Analysis (BEP)

Table of Contents

Syntax

Options

Description

(1) (BEPs) Break-Even Point (Single Product)

(2) (BEPm) Break-Even Point (Multiple Products)

(3) Contribution Margin

(4) Safety Margin

(5) (WACC) Weighted Average Cost of Capital

References

*** Examples

Authors

Syntax

fbep Pd Pw [if] [in] , tfc(var) [pf(var) tax(var) qh(var) id(var) ratio(var) save(file_name) pcm list mp txt ]

Options

varlist Two Variables only uP & uVC respectively:
1- (uP) Unit Price (uP)
2- (uVC) Unit Variable Cost (uVC)

tfc(var) Total Fixed Cost (TFC)

id(var) ID Variable for Multiple Products (BEP)

ratio(var) Unit Price Ratio for Multiple Products (BEP)

pf(var) Target Profit

tax(var) Tax Rate (integer number (10, 20,...etc)

qh(var) Expected Quantity

mp Estimate Multiple Products (BEP)

list Add (BEP) Variables to Data List

pcm Print Contribution Margin output

txt Save Results in text File (*.txt) instead of (*.csv)

save(file_name) Save (BEP) Results in File (*.txt).

*** Important Notes:
fbep generates some variables names starting with prefix "_":
So, you must avoid to include variables names with these prefixes

Description

fbep estimates Financial Break-Even Point Analysis (BEP) with both Single and Multiple Products,
at Units and Value, Target Profit, Target Profit before Tax, Safety Margin, Marginal Cost Ratio, Contribution Margin, Contribution Margin Ratio.

(1) (BEPs) Break-Even Point (Single Product)

* Definition:

* Break-Even Point (BEP) is the point of zero loss or profit.

* Break-Even Point (BEP), is the point which let total revenue equal total cost

* Break-Even Point (BEP) is the minimum quantity of output sold at which total revenue equal total cost, and ensure at this point the project will not neither make profit nor make loses

* before (BEP) the project will make loses, and after (BEP) the project will make profit

* (BEP) Advantages:

1. Quick and simple

2. Easy to understand

3. Helps spot potential problems

4. Can assist when applying for a loan

* (BEP) Disadvantages:

1. It is only a forecast!

2. Assumes all products are made AND sold

3. Costs may change

4. Not very good for services because prices vary enormously

* Formula:
At Break-Even Point, TR = TC.

TR - TC = 0

where:
TR = Total Revenue
TC = Total Cost

TR = TFC + TVC
TC = TFC + TVC
TVC = uVC x Q

TFC = Total Fixed Cost
TVC = Total Variable Cost

uVC = Unit Variable Cost
uP = Unit Price
Q = Quantity of Production

Marginal Cost Ratio = (Unit Variable Cost ÷ Unit Price)
MCR = (uVC ÷ uP) × 100

Contribution Margin = (Unit Price - Unit Variable Cost)
CM = (uP - uVC)

Marginal Profit = Unit Price - Unit Variable Cost
Contribution Margin = Marginal Profit

Contribution Margin Ratio = (Unit Price - Unit Variable Cost) ÷ Unit Price
CMR = (uP - uVC) ÷ uP × 100

Profit = TR - TC
set Profit = 0
TR - TC = 0
TR - TVC - TFC = 0
(uP x Q) - (uVC x Q) - TFC = 0

TFC = (uP x Q) - (uVC x Q)
TFC = Q x (uP - uVC)
Q = TFC ÷ (uP - uVC)

------------------------------------------------
* (1) Break-Even Point:

BEP(Q) = TFC ÷ (uP - uVC)
BEP(Q) = TFC ÷ CM

BEP(V) = BEP(Q) x uP
BEP(V) = BEP(Q) ÷ [CM/uP]
BEP(V) = BEP(Q) ÷ CMR
BEP(V) = TFC ÷ [1 - (uVC/uP)]
BEP(V) = TFC ÷ [1 - MCR]

where:
BEP(Q) = Break-Even Point in Quantity (Units)
BEP(V) = Break-Even Point in Value (Sales)

------------------------------------------------
* (2) Break-Even Point Target Profit:

BEP(Qf) = (TFC + Target Profit) ÷ (uP - uVC)

BEP(Vf) = BEP(Q) x Pu

where:
BEP(Qf) = Break-Even Point Target Profit in Quantity (Units)
BEP(Vf) = Break-Even Point Target Profit in Value (Sales)

------------------------------------------------
* (3) Break-Even Point Target Profit before Tax:

Target Profit before Tax = Target Profit after Tax ÷ (1 - Tax Rate)

BEP(Qft) = (TFC + Target Profit before Tax) ÷ (uP - uVC)

BEP(Vft) = BEP(Qt) x Pu

where:
BEP(Qft) = Break-Even Point Target Profit before Tax in Quantity (Units)
BEP(Vft) = Break-Even Point Target Profit before Tax in Value (Sales)

* Decision Rule:
1- if Quantity > BEP(Q): Accept Project (Investment Make Profit)
2- if Quantity < BEP(Q): Regect Project (Investment Make Loss)

3- if Sales > BEP(V): Accept Project (Investment Make Profit)
4- if Sales < BEP(V): Regect Project (Investment Make Loss)

------------------------------------------------
* Example:
Q = 100
TFC = 1800
uVC = 2

Break-Even Point:
Q x P = TFC + uVC x Q
100 P = 1800 + (2 x 100)
100 P = 1800 + (200)
100 P = 2000
P = 2000 ÷ 100 = 20

------------------------------------------------
* Example:

TFC = Total Fixed Cost = 250
uVC = Unit Variable Cost = 10
uP = Unit Price = 15

------------------------------------------------
* (1) Break-Even Point:

TR = TVC + TFC = 0
TR - TVC - TFC = 0
(uP x Q) - (uVC x Q) - TFC = 0

uP x Q = uVC x Q + TFC
15 x Q = (10 x Q) + 250

250 = (15 x Q) - (10 x Q)
250 = Q x (15 - 10)

BEP(Q) = TFC ÷ (uP - uVC)
= 250 / (15-10)
= 50
BEP(Q) = 50

BEP(V) = BEP(Q) x uP
= 50 x 15
BEP(V) = 750

------------------------------------------------
* (2) Break-Even Point Target Profit:
* if Target Profit = 100

BEP(Qf) = (TFC + Target Profit) ÷ (uP - uVC)
BEP(Qf) = (250 + 100) ÷ (15 - 10)
BEP(Qf) = (350) / (15 - 10)
BEP(Qf) = 70
BEP(Vf) = BEP(Qf) x uP
BEP(Vf) = 70 x 15
BEP(Vf) = 1050

------------------------------------------------
* (3) Break-Even Point Target Profit before Tax:
* if Target Profit after Tax = 100
* if Tax Rate = 20%

Target Profit before Tax = Target Profit after Tax ÷ (1 - Tax Rate)
Target Profit before Tax = 100 ÷ (1 - 0.20)
Target Profit before Tax = 100 / (1 - 0.20) = 125

BEP(Qft) = (TFC + Target Profit before Tax) ÷ (uP - uVC)
BEP(Qft) = (250 + 125) ÷ (15 - 10)
BEP(Qft) = (375) / (15 - 10)
BEP(Qft) = 75

BEP(Vft) = BEP(Qft) x uP
BEP(Vft) = 75 x 15
BEP(Vft) = 1125

(2) (BEPm) Break-Even Point (Multiple Products

* Definition:

* A multi-product project means that a project sells two or more products. The procedure of computing break-even point of a multi product project is a little more complicated than that of a single product project.

* Formula:
BEPm(Q) = TFC ÷ (P_w - uVC_w)
BEPm(Q) = TFC ÷ CM_w
BEPm(V) = BEPm(Q) x P_w
BEPm(V) = BEPm(Q) ÷ [CM_w/P_w]
BEPm(V) = BEPm(Q) ÷ CMR_w
BEPm(V) = TFC ÷ [1 - (uVC_w/P_w)]

where:
BEPm(Q) = Multiple Products Break-Even Point in Quantity (Units)
BEPm(V) = Multiple Products Break-Even Point in Value (Sales)
TFC = Total Fixed Cost
uP = Unit Price
uP_w = Weighted Average Unit Price
uP_w = (uP1 × R1) + (uP2 × R2) + (uP3 × R3) +...

uVC = Unit Variable Cost
uVC_w = Weighted Average Unit Variable Cost
uVC_w = (uVC1 × R1) + (uVC2 × R2) + (uVC3 × R3) +...

Ri = Unit Price Percentage (%) of Product (i)

Weighted Average Contribution Margin =
CM_w = (uP_w - uVC_w)

Weighted Average Contribution Margin Ratio =
CMR_w = (uP_w - uVC_w) ÷ uP_w

* For computing Break-Even Point of a company with two or more products, we must know the sales percentage of individual products in the total sales mix. This information is used in computing weighted average selling price and weighted average variable costs.

* Example:
* A Project has 3 products (A,B,C).
* Total Fixed Costs (TFC) = $50000
Unit Price ($), Unit Variable Costs ($), and Unit Price Percentage (%)

----------------------------------------------------
Product A B C
----------------------------------------------------
Unit Price (uP) ($) 200 100 50
Unit Variable Costs (uVC) ($) 100 75 25
Unit Price Ratio (R) (%) 20 30 50
----------------------------------------------------

* Solution:

** Total Fixed Costs:
(TFC) = 50000

** Weighted Average Unit Price (P_w):
(P_w) = (200 × 0.20) + (100 × 0.30) + (50 × 0.50)
= 40 + 30 + 25
(P_w) = 95

** Weighted Average Unit Variable Cost (uVC_w):
(uVC_w) = (100 × 0.20) + (75 × 0.30) + (25 × 0.50)
= 20 + 22.50 + 12.50
(uVC_w) = 55

BEPm(Q) = TFC ÷ (P_w - uVC_w)
BEPm(Q) = 50000 ÷ (95 – 55)
= 50000 ÷ 40
BEPm(Q) = 1250 (Units)

The Project will have to sell (1250) units to break-even.

to compute the number of units of each product to be sold:

* BEPm(Q) = Multiple Products Break-Even Point in Quantity (Units)
-——------------------------------—--
Product No. of Units
-——------------------------------—--
(A) (1250 × 0.20) = 250
(B) (1250 × 0.30) = 375
(C) (1250 × 0.50) = 625
-——------------------------------—--
Total = 1250
-——------------------------------—--
Break-Even Point in Units = 1250
-——------------------------------—--

* As number of units of each individual product to be sold have been computed, break even point in Value, can be computed as follows:

* BEPm(V) = Multiple Products Break-Even Point in Value (Sales):
-——------------------------------—--
Product No. of dollars
-——------------------------------—--
(A) (250 × 200) = 50000
(B) (375 × 100) = 37500
(C) (625 × 50) = 31250
-——------------------------------—--
Total = 118750
-——------------------------------—--
Break-Even Point in Value = $118750
-——------------------------------—--

(3) Contribution Margin

* It can be verified by preparing a Contribution Margin income statement as follows:

Weighted Average Total Variable Cost =

TVC_w = (BEPm(Q1) x uVC1) + (BEPm(Q2) x uVC2) + (BEPm(Q3) x uVC3) + ...

TVC_w = (250 × 100) + (375 × 75) + (625 × 25)
= $68750

Total Contribution Margin = Total Revenue - Total Variable Cost

TCM_w = sum(uP_w - uVC_w)
= 118750 - 68750 = 50000

Net Profit = Total Revenue - Total Variable Cost - Total Fixed Cost

Net Profit = Total Contribution Margin - Total Fixed Cost
= 50000 - 50000
= 0

----------------------------------------------
** Weighted Contribution Margin:

+--------------------------+
| CM MCR CMR |
|--------------------------|
| 40 57.895 42.105 |
|--------------------------|

* Total Weighted Average Unit Price (uPw) = 95.000
* Total Weighted Average Unit Variable Cost (uVCw) = 55.000
* Total Weighted Contribution Margin (CMw) = 40.000
* Total Weighted Marginal Cost Ratio (MCRw) = 57.895
* Total Weighted Contribution Margin Ratio (CMRw) = 42.105
* Total Break-Even Point (Units) (BEP[Q]) = 1250.000
* Total Break-Even Point (Value) (BEP[V]) = 118750.000
----------------------------------------------------------------------
* CMw = Total Weighted Contribution Margin
= (uPw - uVCw)
= (95 - 55)
CMw = 40 $
----------------------------------------------
* MCRw = Total Weighted Marginal Cost Ratio
= (uVCw ÷ uPw) x 100
= (55 ÷ 95) x 100
= (55 / 95) * 100
MCRw = 57.895 %
----------------------------------------------
* CMRw = Total Weighted Contribution Margin Ratio
= 1- MCRw (%)
= (uPw - uVCw) ÷ uPw
= (95 - 55) ÷ 95
= 40 / 95 * 100
CMRw = 42.105 %
----------------------------------------------

(4) Safety Margin

* Definition:

* Safety Margin is the amount of the increase in the target or actual sales from sales that achieve Break-Even Point

* Safety Margin is the amount that can be reduced without losses in sales

* Safety Margin is a measure of risk. It represents the amount of drop in sales which a company can tolerate.
Higher the safety margin, the more the company can withstand fluctuations in sales. A drop in sales greater than safety margin will cause net loss for the period.

* Formula:

Safety Margin of Quantity = [Expected Quantity - BEP(Q)]
SM(Q) = [Q^ - BEP(Q)]

Safety Margin of Value = [Expected Value - BEP(V)]
SM(V) = [V^ - BEP(V)]

Safety Margin Ratio of Quantity = [Expected Quantity - BEP(Q)] ÷ Expected Quantity × 100
SMR(Q) = [Q^ - BEP(Q)] ÷ Q^ × 100

Safety Margin Ratio of Value = [Expected Value - BEP(V)] ÷ Expected Value × 100
SMR(V) = [V^ - BEP(V)] ÷ V^ × 100

where:
SM(Q) = Safety Margin of Quantity
SM(V) = Safety Margin of Value
SMR(Q) = Safety Margin Ratio of Quantity
SMR(V) = Safety Margin Ratio of Value
Q^ = Expected Quantity
V^ = Expected Value

------------------------------------------------
* Example:
TFC = 250
uVC = 10
uP = 15

* (1) Break-Even Point:

TR = TVC + TFC = 0
TR - TVC - TFC = 0
(uP x Q) - (uVC x Q) - TFC = 0

uP x Q = uVC x Q + TFC
15 x Q = (10 x Q) + 250

250 = (15 x Q) - (10 x Q)
250 = Q x (15 - 10)

----------------------------------------------
* BEP(Q) = TFC ÷ (uP - uVC)
= 250 / (15-10)
= 50
BEP(Q) = 50

----------------------------------------------
* BEP(V) = BEP(Q) x uP
= 50 x 15
BEP(V) = 750

----------------------------------------------
** Contribution Margin

+--------------------------+
| CM MCR CMR |
|--------------------------|
| 5 66.67 33.33 |
|--------------------------|

----------------------------------------------
* CM = Contribution Margin
= (uP - uVC)
= (15 - 10)
CM = 5 $
----------------------------------------------
* MCR = Marginal Cost Ratio
= (uVC ÷ uP) x 100
= (10 ÷ 15) x100
= (10 / 15)*100
MCR = 66.67 %
----------------------------------------------
* CMR = Contribution Margin Ratio
= 1- MCR (%)
= (uP - uVC) ÷ uP
= (15 - 10) ÷ 15
= 5 / 15
CMR = 33.33 %
----------------------------------------------

----------------------------------------------
** Safety Margin

+------------------------------------------+
| TFC uP uVC BEP(Q) BEP(V) |
|------------------------------------------|
| 250 15 10 50 750 |
|------------------------------------------|
+------------------------------------------------------------+
| Qh SM_Q SMR_Q Vh SM_V SMR_V |
|------------------------------------------------------------|
| 70 20 28.5714 1050 300 28.5714 |
+------------------------------------------------------------+

* Qh = Expected Quantity = 70

----------------------------------------------
* SM_Q = Safety Margin of Quantity
= [Qh - BEP(Q)]
SM_Q = 70 - 50
SM_Q = 20
----------------------------------------------
* SMR_Q = Safety Margin Ratio of Quantity
= [Qh - BEP(Q)] ÷ Qh × 100
= (70 - 50) ÷ 70 × 100
= (70 - 50) / 70 * 100
SMR_Q = 28.5714
----------------------------------------------
* Vh = Expected Value
= [Qh × uP]
= 70 x 15
Vh = 1050
----------------------------------------------
* SM_V = Safety Margin of Value
= [Vh - BEP(V)]
= 1050 - 750
SM_V = 300
----------------------------------------------
* SMR_V = Safety Margin Ratio of Value
= [Vh - BEP(V)] ÷ Vh × 100
= [1050 - 750] ÷ 1050 × 100
= (1050 - 750) / 1050 * 100
SMR_V = 28.5714
----------------------------------------------

(5) (WACC) Weighted Average Cost of Capital

* Formula:
WACC = (W1 x R1) + (W2 x R2) + (W3 x R3) +...+ (WJ x RJ)

where:
Wi = Relative Weights for Project (i)
Ri = Discount Rate for Project (i)
J = Number of Projects

* Assume investor who would like to determine rate of return on 3 investment projects:

* Assume the investments are proportioned accordingly: 25% in investment A, 25% in investment B, and 50% in investment C. The rate of return is 5% for investment A, 6% for investment B, and 2% for investment C.

* (WACC) which would return a total weighted average of 3.75% on the total amount invested. If the investor had made the mistake of using the Arithmetic Average, the incorrect return on investment calculated would have been 4.33%.

* Arithmetic Average =(0.05 + 0.06 + 0.02)/3 = 0.0433 = 4.33%

* Example:
Project Wi Ri
-----------------------------
(A) 25 5%
(B) 25 6%
(C) 50 2%
-----------------------------

WACC = (W1 x R1) + (W2 x R2) + (W3 x R3) +...+ (WJ x RJ)
WACC = (0.25 * 0.05) + (0.25 * 0.06) + (0.50 * 0.02) = .0375 = 3.75%

References

Frank J. Fabozzi & Pamela P. Peterson (2003)
"Financial Management and Analysis, 2nd Edition",
John Wiley & Sons, Inc..

Examples:

clear all

sysuse fbep.dta, clear

fbep up uvc , tfc(stfc) pf(sprofit) tax(stax) qh(qh) pcm list mp id(id) ratio(ratio)

fbep up uvc , tfc(mtfc) pf(mprofit) tax(mtax) qh(qh) pcm list mp id(id) ratio(ratio)

clear all

sysuse fbep.dta, clear

fbep up uvc , tfc(mtfc) pf(mprofit) tax(mtax) qh(qh) pcm list mp id(id) ratio(ratio) save(D:\fbep)

===========================================================================
*** Multiple Products Break-Even Point Analysis (BEP) ***
===========================================================================

---------------------------------------------------------------------------
** Contribution Margin

+-----------------------------------+
| id _CM _MCR _CMR |
|-----------------------------------|
1. | 1 5 66.666667 33.333333 |
|-----------------------------------|
2. | 2 20 50 50 |
3. | 2 7.5 75 25 |
4. | 2 12.5 50 50 |
|-----------------------------------|
5. | 3 20 66.666667 33.333333 |
6. | 3 5 75 25 |
7. | 3 10 50 50 |
|-----------------------------------|
8. | 4 600 62.5 37.5 |
+-----------------------------------+
* CM = Contribution Margin = (uPw - uVCw)
* MCR = Marginal Cost Ratio = (uVCw ÷ uPw) × 100
* CMR = Contribution Margin Ratio = (uPw - uVCw) ÷ uPw × 100

---------------------------------------------------------------------------
** (1) Multiple Products Break-Even Point (BEP)
---------------------------------------------------------------------------
* Product ( 1 )
* Total Weighted Average Unit Price (uPw) = 15.000
* Total Weighted Average Unit Variable Cost (uVCw) = 10.000
* Total Weighted Contribution Margin (CMw) = 5.000
* Total Weighted Marginal Cost Ratio (MCRw) = 66.667
* Total Weighted Contribution Margin Ratio (CMRw) = 33.333
* Total Break-Even Point (Units) (BEP[Q]) = 50.000
* Total Break-Even Point (Value) (BEP[V]) = 750.000
----------------------------------------------------------------------
* Product ( 2 )
* Total Weighted Average Unit Price (uPw) = 95.000
* Total Weighted Average Unit Variable Cost (uVCw) = 55.000
* Total Weighted Contribution Margin (CMw) = 40.000
* Total Weighted Marginal Cost Ratio (MCRw) = 57.895
* Total Weighted Contribution Margin Ratio (CMRw) = 42.105
* Total Break-Even Point (Units) (BEP[Q]) = 1250.000
* Total Break-Even Point (Value) (BEP[V]) = 118750.000
----------------------------------------------------------------------
* Product ( 3 )
* Total Weighted Average Unit Price (uPw) = 100.000
* Total Weighted Average Unit Variable Cost (uVCw) = 65.000
* Total Weighted Contribution Margin (CMw) = 35.000
* Total Weighted Marginal Cost Ratio (MCRw) = 65.000
* Total Weighted Contribution Margin Ratio (CMRw) = 35.000
* Total Break-Even Point (Units) (BEP[Q]) = 28.571
* Total Break-Even Point (Value) (BEP[V]) = 2857.143
----------------------------------------------------------------------
* Product ( 4 )
* Total Weighted Average Unit Price (uPw) = 1600.000
* Total Weighted Average Unit Variable Cost (uVCw) = 1000.000
* Total Weighted Contribution Margin (CMw) = 600.000
* Total Weighted Marginal Cost Ratio (MCRw) = 62.500
* Total Weighted Contribution Margin Ratio (CMRw) = 37.500
* Total Break-Even Point (Units) (BEP[Q]) = 8.333
* Total Break-Even Point (Value) (BEP[V]) = 13333.333
----------------------------------------------------------------------

---------------------------------------------------------------------------
** (1-1) Safety Margin of Multiple Products (BEP)

+-----------------------------------------------------------------------+
| id _Qh _SM_Q _SMR_Q _Vh _SM_V _SMR_V |
|-----------------------------------------------------------------------|
1. | 1 70 20 28.571429 1050 300 28.571429 |
|-----------------------------------------------------------------------|
2. | 2 300 50 16.666667 60000 10000 16.666667 |
3. | 2 300 -75 -25 30000 -7500 -25 |
4. | 2 300 -325 -108.33333 15000 -16250 -108.33333 |
|-----------------------------------------------------------------------|
5. | 3 200 188.57143 94.285714 30000 28285.714 94.285714 |
6. | 3 200 194.28571 97.142857 20000 19428.571 97.142857 |
7. | 3 200 188.57143 94.285714 10000 9428.5714 94.285714 |
|-----------------------------------------------------------------------|
8. | 4 3900 3891.6667 99.786325 6240000 6226666.7 99.786325 |
+-----------------------------------------------------------------------+
* Qh = Expected Quantity
* SM(Q) = Safety Margin of Quantity [Qh - BEP(Q)]
* SMR(Q) = Safety Margin Ratio of Quantity [Qh - BEP(Q)] ÷ Qh × 100
* Vh = Expected Value [Qh × _uP]
* SM(V) = Safety Margin of Value [Vh - BEP(V)]
* SMR(V) = Safety Margin Ratio of Value [Vh - BEP(V)] ÷ Vh × 100
---------------------------------------------------------------------------

+-----------------------------------------------------------------+
| id _TFC _uP _uVC _uPw _uVCw _BEP_Q _BEP_V |
|-----------------------------------------------------------------|
1. | 1 250 15 10 15 10 50 750 |
|-----------------------------------------------------------------|
2. | 2 50000 200 100 40 20 250 50000 |
3. | 2 50000 100 75 30 22.5 375 37500 |
4. | 2 50000 50 25 25 12.5 625 31250 |
|-----------------------------------------------------------------|
5. | 3 1000 150 100 60 40 11.428571 1714.2857 |
6. | 3 1000 100 75 20 15 5.7142857 571.42857 |
7. | 3 1000 50 25 20 10 11.428571 571.42857 |
|-----------------------------------------------------------------|
8. | 4 5000 1600 1000 1600 1000 8.3333333 13333.333 |
+-----------------------------------------------------------------+
* TFC = Total Fixed Cost
* uP = Unit Price
* uVC = Unit Variable Cost
* uPw = Weighted Average Unit Price
* uVCw = Weighted Average Unit Variable Cost
* BEP_Q = Break-Even Point in Quantity (Units)
* BEP_V = Break-Even Point in Value (Sales)

---------------------------------------------------------------------------
** (2) Multiple Products Break-Even Point Target Profit (BEPf)
---------------------------------------------------------------------------
* Product ( 1 )
* Total (BEP) Target Profit (Units) = 70.000
* Total (BEP) Target Profit (Value) = 1050.000
----------------------------------------------------------------------
* Product ( 2 )
* Total (BEP) Target Profit (Units) = 1275.000
* Total (BEP) Target Profit (Value) = 121125.000
----------------------------------------------------------------------
* Product ( 3 )
* Total (BEP) Target Profit (Units) = 42.857
* Total (BEP) Target Profit (Value) = 4285.714
----------------------------------------------------------------------
* Product ( 4 )
* Total (BEP) Target Profit (Units) = 91.667
* Total (BEP) Target Profit (Value) = 146666.667
----------------------------------------------------------------------

---------------------------------------------------------------------------
** (2-1) Safety Margin of Multiple Products Target Profit (BEPf)

+---------------------------------------------------------------------+
| id _Qh _SM_Qf _SMR_Qf _Vh _SM_Vf _SMR_Vf |
|---------------------------------------------------------------------|
1. | 1 70 0 0 1050 0 0 |
|---------------------------------------------------------------------|
2. | 2 300 45 15 60000 9000 15 |
3. | 2 300 -82.5 -27.5 30000 -8250 -27.5 |
4. | 2 300 -337.5 -112.5 15000 -16875 -112.5 |
|---------------------------------------------------------------------|
5. | 3 200 182.85714 91.428571 30000 27428.571 91.428571 |
6. | 3 200 191.42857 95.714286 20000 19142.857 95.714286 |
7. | 3 200 182.85714 91.428571 10000 9142.8571 91.428571 |
|---------------------------------------------------------------------|
8. | 4 3900 3808.3333 97.649573 6240000 6093333.3 97.649573 |
+---------------------------------------------------------------------+
* Qh = Expected Quantity
* SM(Qf)= Safety Margin of Quantity [Qh - BEP(Qf)]
* SMR(Qf)= Safety Margin Ratio of Quantity [Qh - BEP(Qf)] ÷ Qh × 100
* Vh = Expected Value [Qh × _uP]
* SM(Vf)= Safety Margin of Value [Vh - BEP(Vf)]
* SMR(Vf)= Safety Margin Ratio of Value [Vh - BEP(Vf)] ÷ Vh × 100
---------------------------------------------------------------------------

+------------------------------------------------------------+
| id _Profit _TFC _uP _uVC _BEP_Qf _BEP_Vf |
|------------------------------------------------------------|
1. | 1 100 250 15 10 70 1050 |
|------------------------------------------------------------|
2. | 2 1000 50000 200 100 255 51000 |
3. | 2 1000 50000 100 75 382.5 38250 |
4. | 2 1000 50000 50 25 637.5 31875 |
|------------------------------------------------------------|
5. | 3 500 1000 150 100 17.142857 2571.4286 |
6. | 3 500 1000 100 75 8.5714286 857.14286 |
7. | 3 500 1000 50 25 17.142857 857.14286 |
|------------------------------------------------------------|
8. | 4 50000 5000 1600 1000 91.666667 146666.67 |
+------------------------------------------------------------+
* Profit = Target Profit
* TFC = Total Fixed Cost
* TFC = Total Fixed Cost
* uP = Unit Price
* uVC = Unit Variable Cost
* BEP_Qf = Break-Even Point Target Profit (Units)
* BEP_Vf = Break-Even Point Target Profit (Value)

---------------------------------------------------------------------------
** (3) Multiple Products Break-Even Point Target Profit before Tax (BEPx)
---------------------------------------------------------------------------
* Product ( 1 )
* Total (BEP) Target Profit before Tax (Units) = 72.222
* Total (BEP) Target Profit before Tax (Value) = 1083.333
----------------------------------------------------------------------
* Product ( 2 )
* Total (BEP) Target Profit before Tax (Units) = 1281.250
* Total (BEP) Target Profit before Tax (Value) = 121718.750
----------------------------------------------------------------------
* Product ( 3 )
* Total (BEP) Target Profit before Tax (Units) = 46.429
* Total (BEP) Target Profit before Tax (Value) = 4642.857
----------------------------------------------------------------------
* Product ( 4 )
* Total (BEP) Target Profit before Tax (Units) = 96.053
* Total (BEP) Target Profit before Tax (Value) = 153684.211
----------------------------------------------------------------------

---------------------------------------------------------------------------
** (3-1) Safety Margin of Multiple Products Target Profit before Tax (BEPx)

+-------------------------------------------------------------------------+
| id _Qh _SM_Qx _SMR_Qx _Vh _SM_Vx _SMR_Vx |
|-------------------------------------------------------------------------|
1. | 1 70 -2.2222223 -3.1746032 1050 -33.333334 -3.1746032 |
|-------------------------------------------------------------------------|
2. | 2 300 43.75 14.583333 60000 8750 14.583333 |
3. | 2 300 -84.375 -28.125 30000 -8437.5 -28.125 |
4. | 2 300 -340.625 -113.54167 15000 -17031.25 -113.54167 |
|-------------------------------------------------------------------------|
5. | 3 200 181.42857 90.714286 30000 27214.286 90.714286 |
6. | 3 200 190.71429 95.357143 20000 19071.429 95.357143 |
7. | 3 200 181.42857 90.714286 10000 9071.4286 90.714286 |
|-------------------------------------------------------------------------|
8. | 4 3900 3803.9474 97.537112 6240000 6086315.8 97.537112 |
+-------------------------------------------------------------------------+
* Qh = Expected Quantity
* SM(Qx)= Safety Margin of Quantity [Qh - BEP(Qx)]
* SMR(Qx)= Safety Margin Ratio of Quantity [Qh - BEP(Qx)] ÷ Qh × 100
* Vh = Expected Value [Qh × _uP]
* SM(Vx)= Safety Margin of Value [Vh - BEP(Vx)]
* SMR(Vx)= Safety Margin Ratio of Value [Vh - BEP(Vx)] ÷ Vh × 100
---------------------------------------------------------------------------

+-------------------------------------------------------------------+
| id _Profit _Tax _TFC _uP _uVC _BEP_Qx _BEP_Vx |
|-------------------------------------------------------------------|
1. | 1 100 .1 250 15 10 72.222222 1083.3333 |
|-------------------------------------------------------------------|
2. | 2 1000 .2 50000 200 100 256.25 51250 |
3. | 2 1000 .2 50000 100 75 384.375 38437.5 |
4. | 2 1000 .2 50000 50 25 640.625 32031.25 |
|-------------------------------------------------------------------|
5. | 3 500 .2 1000 150 100 18.571429 2785.7143 |
6. | 3 500 .2 1000 100 75 9.2857143 928.57143 |
7. | 3 500 .2 1000 50 25 18.571429 928.57143 |
|-------------------------------------------------------------------|
8. | 4 50000 .05 5000 1600 1000 96.052632 153684.21 |
+-------------------------------------------------------------------+
* Profit = Target Profit
* Tax = Tax Rate
* TFC = Total Fixed Cost
* uP = Unit Price
* uVC = Unit Variable Cost
* BEP_Qx = Break-Even Point Target Profit before Tax (Units)
* BEP_Vx = Break-Even Point Target Profit before Tax (Value)
---------------------------------------------------------------------------

*** Save Break-Even Point Analysis ***
*** (BEP) Results File Has Been saved in:

Data Directory: D:\Stata\SSC

Open File: D:\fbep.csv
--------------------------------------------------

Authors

- Emad Abd Elmessih Shehata
Professor (PhD Economics)
Agricultural Research Center - Agricultural Economics Research Institute - Egypt
Email: emadstat@hotmail.com
WebPage at IDEAS: http://ideas.repec.org/f/psh494.html
WebPage at EconPapers: http://econpapers.repec.org/RAS/psh494.htm

- Sahra Khaleel A. Mickaiel
Professor (PhD Economics)
Cairo University - Faculty of Agriculture - Department of Economics - Egypt
Email: sahra_atta@hotmail.com
WebPage at IDEAS: http://ideas.repec.org/f/pmi764.html
WebPage at EconPapers: http://econpapers.repec.org/RAS/pmi764.htm

FBEP Citation

Shehata, Emad Abd Elmessih & Sahra Khaleel A. Mickaiel (2016)

FBEP: "Stata Module to Estimate Financial Break-Even Point Analysis (BEP) for Single and Multiple Products"

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