# Week 3 ```Part 3: Cost-Volume-Profit (CVP) Relationship/Analysis
Cost Volume Profit Analysis is based on six assumptions:
1. A firm’s total revenue changes in direct proportion to changes in its unit sales volume. That is, the average sale price per unit of
product is constant. (Linear Relationship concept)
2. Total costs can be separated into fixed costs and variable costs.
3. Total variable costs change in direct proportion to changes in sales volume. That is, the average variable cost per unit remains
constant over the relevant range.
4. Total fixed costs (per month or per year) remain constant over the range of sales volume being considered.
5. Sales mix remains constant over the range of sales volume being considered.
6. Sales volume equals production volume; that is, inventory levels remain constant.
The discussion deals with the relationship between cost, volume and profits and the various changes in the respective values
dependent on the level of activity or volume of sales.
An important element in the discussion of CVP is the concept of contribution margin.
Contribution Margin – also known as marginal income or profit volume
- it is used to recover fixed expenses and any excess are treated as profits.
Formula: Sales – Variable Costs = Contribution Margin
Sales
Xxx
Less: Cost of Sales
Xxx
Gross Profit
Xxx
Less: Operating Expenses
Xxx
Net Income
xxx
Contribution Margin Income statement (Variable Costing)
Per unit
Totals
Ratio
Sales
Xx
XXXX
100%
Less:Variable Cost
Xx
XXXX
(VC/Sales)
Contribution Margin
Xx
XXXX
(CM/Sales)
Less: Fixed Cost
XXXX
Net Income
XXXX
Illustration: 01
Alpha
Bravo
Charlie
Selling Price
40
80
25
Units Sold
4,875
4,000
15,000
VC %
60%
75%
70%
CM %
40%
25%
30%
CM Peso Value
78,000
80,000
112,500
Fixed cost
60,000
90,000
62,500
Income/Loss
18,000
(10,000)
50,000
Cost Volume Profit Analysis – also known as Break-even Analysis
Break-even point - a situation wherein
a. Total Revenues = Total Costs; therefore NO LOSS, NO PROFIT.
b. Total Sales = Total Variable Costs + Total Fixed Costs
c. Total Sales – Total Variable Costs = Total Fixed Costs
d. Total Contribution Margin = Total Fixed Costs
Breakeven point (expressed in units)
= Total Fixed Costs/Unit Contribution Margin
Breakeven point (expressed in Pesos)
= Total Fixed Costs/CM ratio OR
= Breakeven units X Sales Price
As mentioned earlier, Contribution Margin is used to recover fixed costs. The point where all fixed costs are recovered is known as
the break even point.
Any additional sale beyond the breakeven point will mean Profit represented by the Contribution Margin since the fixed cost have
been fully recovered (paid for) by the CM at break even point.
Sales with a desired profit
Sales (in units) = Total fixed cost + Target Profit
------------------------------------CM / unit
Sales (in Pesos) =Total Fixed Cost + Target Profit
-------------------------------------CM ratio
Effects of Income Tax on Break-even Sales
At break-even point, income taxes are irrelevant or have no effect on the break-even sales because there are no profits at this level
of sales.
However, income tax will increase the desired sales volume if we include in our computation a target profit. The new formula will
therefore be:
Sales (in Pesos) =Total F Cost + Target Profit / (1-Tax rate)
--------------------------------------------------CM ratio
Whereby the Target Profit will be the Pre-tax Net Income.
Illustration: 02
The Rapido Muncho Restaurant has two outlets that are open 24 hours a day. Fixed costs for the two restaurants together total
P450,000 per year. Service varies from a cup of coffee to full meals. The average sales check per customer is P100. The average cost
of food and other variable costs for each customer is P60. The income tax rate is 30%. Target net income is P105,000.
Required:
1. Compute for Breakeven sales in units and in pesos assuming that the target net income is before taxes.
a. BEP units
b. BEP pesos
2. Compute for Breakeven sales in units and in pesos assuming that the target net income is after taxes.
a. BEP units
b. BEP peso
Sales with Multiple Cost Drivers
Bep = Cost Driver x Activty + Cost Driver x Activity + Other Fixed Cost
Contribution Margin / unit or CM %
In the previous examples, units produced has been used as the cost driver (cause of the incurrence) of all fixed costs. However,
there are certain costs that may be variable in nature but whose cost driver may not be based on the units produced but on other
cost drivers; thus should be treated as fixed cost taking into consideration that units produced serves as the primary cost driver.
In this instance, we need to compute first the total cost of the fixed cost based on each cost driver to be able to get the Total Fixed
Cost to be allocated to each unit produced.
Illustration: 03
Sam Choy is a distributor of sticker books. For 200A, he plans to purchase sticker books for P30 each and sell them for P45 each.
Sam’s fixed costs for 200A are expected to be P240,000. Sam’s only other costs will be variable costs of P60 per shipment for
preparing the invoice and delivery documents, organizing the delivery and following up for collecting accounts receivable. The P60
cost will be incurred each time Sam ships an order of sticker books, regardless of the number of sticker books in the order.
Required: Suppose Sam anticipates making 500 shipments in 200A, how many sticker books must Sam sell to breakeven in 200A?
CVP Indifference Point
CVP Analysis can compare alternative cost structures or selling prices such as:
1. high salary/low commission vs. lower salary/higher commission for sales persons
2. highly automated production process with low variable cost per unit vs. lower technology with higher variable costs per unit and
lower fixed costs
Indifference point between alternatives is the level of sales in units or sales pesos where the profits of the alternatives are equal
Profit (A) = Profit (B)
Formula:
CM/unit (A) * Qty - Fixed Cost (A) = CM/unit (B) * Qty – Fixed Cost (B)
Illustration: 04
Phoenix Company is involved in the importation and distribution of bottled health drinks. These drinks are sold for P200 each.
Variable costs per bottle is P80. Salaries of sales person is fixed at P80,000 which is included in the total fixed costs of P360,000.
Phoenix is considering an alternative compensation scheme where salaries are decreased to P20,000 and the commission per item
sold is 20% of sales price.
Required:
1. Compute for the breakeven points of the current and proposed salary scheme.
a. Current: BEP
b. Proposed BEP
2. Compute for the indifference point. Which is the more favorable salary scheme assuming current demand is at 2,000 units?
Note:
1. The product/process with the higher contribution margin/unit is favorable if demand is greater than indifference point. It is
because we are able to sell more help in the recovery of fixed cost.
2. The product/process with the lower fixed cost is favorable if demand is less than the indifference point. It is because we are selling
less, it is better to have lower fixed cost that is needed to recover.
Margin of Safety Concept
Margin of Safety - excess of sales over breakeven that will bring forth profit; therefore all contribution margin derived from the
margin of safety is regarded as profit.
Formula:
Total Budgeted (or Actual) Sales
Less: Breakeven Sales
Margin of Safety
Margin of Safety Ratio =
Break Even Ratio =
PXX
PXX
PXX
Margin of Safety/Actual or budgeted sales
Break Even Sales/Actual or budgeted Sales
Illustration: 05
Actual or Budgeted Sales
Less Break Even Sales
Margin of Safety
CM Ratio
NI Ratio
300
Qty.
Peso Value
1,000
P10,000
100%
700
P7,000
70%
-------- ---------------P3,000
30%
x 40%
------------P1,200
12%
=====
====
%
40%
Based on the illustration, we could derive a new formula for Margin of Safety Ratio which is
Margin of Safety Ratio = Net Income Ratio/CM Ratio
Break-even ratio = FC /CM
Complementary ratios – ratios that combine to make a whole
Variable Cost ratio
Break-even ratio
Contribution Margin ratio
Margin of Safety ratio
Total Sales (100%)
Total Sales (100%)
==============
=============
Net income ratio MOSR x CM ratio  Net Income
Fixed Cost ratio Breakeven Sales % x CM ratio  FC
------------------------------Contribution Margin Ratio
===============
Illustration: 06
Three independent situations involving cost volume profit situations follow. In each case you are to determine the amount where
blank spaces appear.
Case A
Selling price
Variable cost
Fixed cost
CM per unit
Total fixed costs
BEP in units
BEP in sales
CMR
MOS unit
NI(loss)
Units sold
Case B
P2.00
P2.10
P0.60
P.90
P180.000
Case C
P8.00
P3.00
P200,000
P600,000
P90,000
100%
8,000
P16,000
12,000
25%
4,000
Illustration: 07
Additional Exercises: Based on the scanty information given in each problem below, determine the amount of each item required:
Case A: Breakeven % is 64%, Net Profit is 12% of sales, Fixed Costs P128,000
Required:
Actual Sales
Case B: Net profit is 7.5% of sales, Variable ratio is 70%, Breakeven sales volume is P150,000 30%CMR, 7.5%NI.
Required:
Actual Sales
Case C: Net Profit is 7% of sales, Breakeven % is 80%, Variable costs P260,000.
Required:
a. Margin of Safety Figure
b. Fixed Costs
Case D: Variable ratio is 65%, Breakeven % is 60%, Net Profit is P56,000
Required:
a. Margin of Safety Figure
b. Fixed Costs
LEVERAGE
In physics, leverage implies the use of a lever to raise a heavy object with a small amount of force. In politics, people have leverage if
they can accomplish a great deal with their influence by simply making a phone call. We apply this concept of leverage in business as
well taking into account a small increase in sales will generate a large effect on income.
Operating Leverage - measure of how sensitive net income is to % change in sales.
-serve as a multiplier effect as it measures at a given level of sales, how a percentage change in sales will affect profit
Operating leverage results from the presence of fixed operating costs in a firm's income stream. The extent of the presence of fixed
operating costs in a firm's income stream is measured by the degree of operating leverage (DOL).
Degree of operating leverage =
Contribution Margin
Net Income
Note:
The DOL will never be less than 1 because CM will always be equal or greater than Net Income. Thus it is considered as a multiplier.
% Change in Sales x Operating Leverage = % Change in NI
Illustration:
Markov Company has the following income statement for the year just ended expressed in ‘000s:
Sales
Variable Cost
Contribution Margin
Less Fixed Cost
Net income
100
60
40
30
10
The operating leverage would be:
Contribution Margin: 40/10 = 4  This simply means for every % change in sales volume, NI% will change 4 times.
Therefore: if Sales Volume increases by 10%, Net income will improve not by 10% but by 40% (10% x 4 times)
Sales
Variable Cost
Contribution Margin
Less Fixed Cost
Net income
100
60
40
x 110% =
x 110%
110
=
10
x 140% =
30
14
30
66
44
It should be noted that companies with higher fixed cost levels will have a higher degree of operating leverage. Thus, other than
providing ease in computation of projected net income, it serves as an indicator on the level of usage of fixed cost in generating
sales.
Relationship between Operating Leverage and Margin of Safety
These two functions are inversely proportional to each other.
Operating leverage = Contribution Margin / Net Income
Margin of Safety = Net Income / Contribution Margin
Thus:
Operating leverage = 1/ Margin of Safety
Margin of Safety = 1/ Operating leverage
Illustration: 08
Fiesta Corporation is a manufacturer of fish crackers with catsup dip. Each pack of fish crackers with catsup dip sells for P35. Variable
cost of producing one pack averages P15. Fixed costs are estimated to be at P1,000,000. For the previous year, sales reached
P3,500,000. After careful market analysis, sales volume for the current year is targeted to increase by 10%.
Required:
1. Determine the Net Income and Operating Leverage for Fiesta Corporation for the previous year.
2. Determine the Net Income and the Operating Leverage for the current year.
3. Determine the Margin of Safety and BEP in peso for the current year.
Sales Mix Analysis
- break-even analysis involving more than one product or involving multi products
There may exist two scenarios in a Sales Mix situation whereby the product mix may be composed of:
1. Independent products.
2. Package (Composite) Products.
A. Independent Products Scenario
Break even units = Total Fixed Cost
-------------------------*Weighted CM/ unit  Using the Quantity Mix
*Weighted contribution margin per unit is obtained by multiplying the individual Sales Mix Proportions (usually expressed as a
percentage based on the Quantity) to the corresponding Contribution Margin per Unit.
Break even sales can be derived by determining the break even units per product line and then multiply by the corresponding sales
prices
Or
TOTAL FIXED COST
Weighted Average CM%  Using the Revenue Mix
*Weighted contribution margin % = Total CM
Total REVENUES
Illustration: 09
Marvel Heroes Company is planning to sell two lines of stuffed toys, Fantastic Four and Avengers in the coming Holiday Season. The
company budgets the following sales figures:
Units Sold
Revenues P200 and P100 per unit
Variable Costs P120 and P70 per unit
Contribution Margin P80 and P30
Fixed Costs
Operating Income
Fantastic Four
600
P120,000
P72,000
P48,000
Avengers
400
P40,000
P28,000
P12,000
Total
1,000
P160,000
P100,000
P60,000
P45,000
P15,000
Required: Determine the following:
1. Breakeven point in units:
2. Breakeven point in sales pesos:
B. Package / Composite Units
Certain products are sold in packages or components with a corresponding mix or ratio that has to be observed. Example would be a
Gift Pack that must contain 1 bottle of champagne, 3 canned goods and 6 boxes of herbs and spices.
Formula to compute for the break-even units will then be:
Break even units = Total Fixed Cost
-------------------------*Composite CM/ unit
Composite Unit is computed as Sum of CM per unit * Product Mix (usually expressed in Qty.)
Illustration: 10
* A company sells two products, X and Y. The sales mix consists of a composite unit of two units of X for every five units of Y (2:5).
Fixed costs are P49,500. The unit contribution margins for X and Y are P2.50 and P1.20, respectively.
1. Considering the company as a whole, the number of composite units to breakeven is?
2. Compute the quantity of X and Y that must be produced to meet break-even sales.
* HP Inc. formulates and sells three major chemicals: Supercali, Fragilistic, and Expialidocious. It sells to industrial users who use and
buy these chemicals in the following ratio: three (3) measures of Supercali for (1) measure of Fragilistic, and (2) measures of
Fragilistic per (1) measure of Expialidocious. The company makes the following contribution margin per measure: RPCPA
Supercali:
P30
Fragilistic:
P45
Expialidocious: P90
Fixed costs amounted to P1.8 million.
1. How many (in units) of Supercali would be sold?
2. How many (in units) of Fragilistic would be sold?
3. How many (in units) of Expialidocious would be sold?
Problem Solving:
IP-1 (Moderate)
The Soda Factory sells high energy bars to supermarkets for P80 per bar. Variable cost is P45 per bar and annual fixed cost are P854,
000.
1. Determine the breakeven point in units and pesos.
2. Determine the number of units required to earn a before tax profit of P120, 000.
3. Determine the required earn an after 40% tax profit of P120, 000.
4. Determine the volume required to earn a before tax return on sales of 13.25%.
5. Determine the volume required to earn an after tax return of 8.4%. (Assume 40% tax rate)
6. If the body Fit can sell 40, 000 bars, what price would it have to charge to earn a before tax profit of P260, 000.
IP-2 (Moderate)
Marcoleta &amp; Co., makes a sign pen that sells for P20.00 per unit. Variable costs are P8.00 per unit, and fixed cost total P1, 800,000
per year.
1. What is the product’s ratio?
2. Use the CM ratio to determine the break-even point in peso sales.
3. Due to an increase in demand, the company estimates that sales will increase by P1, 200,000 during the next year. By how much
should net operating income (or net operating loss) charge, assuming that fixed cost do not change?
Assume that the operating results for last year were:
Sales ……………………………………………………… P4, 000, 000
Less variable expenses …………………………… 1, 600, 000
Contribution margin …………………………………. 2, 400, 000
Less fixed expenses ………………………………… 1, 800, 000
Net operating income ……………………………. P 600, 000
4. Compute the degree of operating leverage at the level of sales last year.
5. The president expects sales to increase by 20% next year. By what percentage should net operating income increase?
6. Refer to the original data. Assume that the company sold 180, 000 units last year. The sales manager is convinced that a 10%
reduction in the selling price, combined with a 90, 000 increases in advertising, would cause annual sales in units to increase by one
fourth. Prepare two contribution income statements, one showing the results of operation if these changes are made. Would you
recommend that the company do as the sales manager suggest?
7. Refer to the original data. Assume again that the company sold 180, 000 units last year. The president does not want to change
the selling price. Instead, he wants to increase the sales commission by P1.25 per unit. He thinks that this move, combined with
some increase in advertising be increase annual sales by 20%. By how much could advertising be increased with profits remaining
unchanged? Do not prepare an income statement; use incremental analysis approach.
8. Assume that in the coming year there will be no change in the cost structure. The company can sell 220, 000 units next year. What
selling price is required to have the company earn P 664, 000 before tax profit?
IP-3 (Moderate)
Mystery Company operates a chain of fancy pendant shops around the country. The shops carry many styles of pendants that are all
sold at the same price. Sales personnel in the shops are paid a substantial commission on each pendant sold (in addition to small
basic salary) in order to encourage them to be aggressive in their sales efforts.
The following cost and revenue data relate to Shop 30 and are typical of one of the company’s many outlets:
Per pendant
Selling price
P 50.00
Variable expenses:
Invoice cost
Sales commission
Total variable expenses
Fixed Expenses:
Rent
Salaries
Total fixed expenses
P 26.50
1.00
P 27.50
P 56, 000
122, 000
182, 000
P 360, 000
Required:
1. Calculate the annual break-even point in pesos sales and in unit sales for Shop 30.
2. If 15, 000 pendants are sold in a year, what would be Shop 30’s net operating income or loss?
3. The company is considering paying the store manager Shop 30 an incentive commission of P2.50 per watch (in addition to the
salesperson’s commission). If this change is made, what will be the new break-even point in pesos sales and in unit sales?
4. Refer to the original data. As an alternative to (3) above, the company is considering paying the store manager at P4.00
commission on each pendant sold in excess of the break-even point. If this change is made, what will be the shop’s net operating
income or loss if 17, 500 pendants are sold?
5. Refer to the original data. The company is considering eliminating sales commission entirely in its shops and increasing fixed
salaries by P11,300 annually. If this change is made, what will be the new break-even point in pesos sales and in unit sales for Shop
30? Would you recommend that the change be made?
IP-4 (fractional) - moderate
Laurente &amp; Co. of Bacolod makes two products, Mini and Giga. Present revenue, cost, and sales data on the two products follow:
Mini
Giga
Selling price per unit
P 10.00
P 5.00
Variable expenses per unit
P 4.00
P 3.00
Number of units sold annually
30, 000
40, 000
Fixed expenses total P 228,000 per year.
Required:
1. Assuming the sales mix given above, do the following:
a. Prepare a contribution income statement showing both pesos and percent columns for each product and for the company as a
whole.
2. The company has just developed a new product, Mega. Assume that the company could sell 5, 000 units at P20.00 each. The
variable expenses would be P15.00 each. The company’s fixed expenses would not change.
a. Prepare another contribution income statement, including sales of Mega (Sales of the other two products would not
change). Carry percentage computations to one decimal place.
IP-5 (Difficult) (RPCPA)
Great Wall Ski Company recently expanded its manufacturing capacity, which will allow it to produce up to 15, 000 pairs of cross
country skis of the mountaineering model or the touring model. The sales department assures management that it can sell between
9, 000 pairs and 13, 000 pairs either product this year. Because the models are very similar, Great Wall will produce only one of the
two models.
The following information was complied by the accounting department.
Selling price
Variable cost
Per-Unit (pair) Data
Mountaineering Touring
P88.00
P 80.00
P 52.80
P 52.80
Fixed cost will total P 369, 600 if the mountaineering model is produced but will be only P 316, 800 if the touring model is produced.
Siberian Ski is subject to a 40% income tax rate.
Required:
1.Compute the contribution margin for each product line.
2. If the Great Wall desires an after-tax net income of P22,080, how many pairs of touring skis will the company have to sell?
3. How much would the variable cost per unit of the touring model have to change before it had the same breakeven point in units
as the mountaineering model?
4. Suppose the variable cost per unit of touring skis decreases by 10 percent, and the total fixed cost of touring skis increases by 10
percent. Compute the new breakeven point.
5. Suppose management decided to produce both products. If the two models are sold in equal proportion, and total fixed cost
amount to P 343, 200, what is the firm’s breakeven point in units?
6. Suppose the Great Wall decided to produce only one model of ski. What is the total sales revenue at which great Wall make the
same profit or loss regardless of the ski model it decided to produce?
7. If the Great Wall sales department could guarantee the annual sale of 12, 000 pairs of either model, which model would the
company produce &amp; why? Mountaineering because of highest CM per unit
IP 8 (Easy, Moderate to Difficult)
Solve each as independent problem.
1. The Childers Co. sells widgets. At an annual sales volume of 75,000 units the company breaks even. At annual sales volume of 100,
000 units the company reports a profit of P200, 000. The annual fixed costs for the Childers Co. are? (M)
2. Batman Co. earned P40, 000 on sales of P400, 000. It earned P55, 000 on sales of P450, 000. Variable costs as a percentage of
sales and total fixed cost are? (M)
3. At a sales level of P90, 000, Violeta Company’s contribution margin is p24, 000. If the degree of operating leverage is 6 at a P90,
000 sales level, net income must be? (M)
4. The Siamese Company has an operating leverage of 2. Sales for 2005 are p2, 000, 000 with a contribution margin of P1, 000, 000.
Sales are expected to be P3, 000, 000 in 2006. Net income for 2006 can be expected to increase by what amount over year 2005?
(M)
5. The Makatao Marketing Co., is expecting an increase of the fixed costs by P78, 750 upon moving their place to business to the
downtown area. Likewise it is anticipating that the selling price per unit and the variable expenses will not change. At present, the
sales volume necessary to breakeven is P750, 000 but with the expected increase in fixed costs, the sales volume necessary to
breakeven would go up to P975, 000. Based on this projection, what was the total fixed cost before the increase of P78, 750? (D)
6. Alla Co. is considering dropping a product. Variable costs are P75.00 per unit. Fixed overhead costs, exclusive of depreciation, have
been allocated at a rate of p5.00 per unit and will continue whether or not production ceases. Depreciation on the equipment is P60,
000 a year. If production is stopped, the equipment can be sold for P140, 000. If production continues, however, it will be useless at
the end of 1st year and will have no salvage value. The selling price is P100 a unit. Ignoring the tax effect, what is the minimum unit
to be sold in the current year to breakeven on cash flow basis?
7. In 2004 Lucia Company had a net loss of P8, 000. The company sells one product with selling price of P80 and variable cost per
unit of P60. In 2005, the company would like to earn a before tax profit of P40, 000. How many additional units must the company
sell in 2005 than it sold in 2004? Assume that the tax rate is 40%. (M)
8. Mars Co. is considering two processes. The first process is highly manual with variable cost per unit of P24 and fixed costs of P640,
000 per annum. The second process is highly mechanized with variable cost of P15 and fixed costs of P1, 200, 000 per annum. The
selling price is P60. Compute the difference point. In quantity &amp; in peso (D)
9. ABE, Inc. sells a product for P8 per unit. The fixed costs are P160, 000 and the variable costs are 60% of the selling price. What
would be the amount of sales if ABE were to realize a profit of 12% of sales? (M)
10. Pyramid Company would like to market a new product at a selling price of P15 per unit. Fixed costs for this product are P1, 000,
000 for less than 500, 000 units of output &amp; P1, 500, 000 for 500, 000 or more units output. The contribution margin percentage is
20%. How many units of this product must be sold to:
a. Breakeven? (E)
b. Earn a target operating income of P1 million? (E)
11. Cadet Company had is a manufacturer of its only one product line. It had a sale of P400, 000 for 2006 with a contribution margin
ratio of 20 percent. Its margin of safety ratio was 10 percent. What was the company’s fixed cost? (E)
DONE!
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