Cost-Volume-Profit

Analysis

Prof. Jason R. Radam

Basic Principles

Cost and expenses are segregated into fixed and

variable elements

Profit = Sales – Cost and expenses

Profit = Sales – Fixed costs – Variable costs

Basic Principles

Basic assumptions within the relevant range:

Linearity – The behavior of sales and costs are linear

Behavior of sales, costs, and expenses:

Sales – it changes directly in relation to the level of units sold

Fixed costs (total) – is constant regardless to the change in the level of units of production and sales

Fixed costs (per unit) – changes inversely with the level of production

Variable cost (total) – change in direct proportion with the level of production

Variable cost (per unit) – is constant regardless to the change in the level of units of production and sales

Basic Principles

Selling price – assumed to be constant

Work in process (WIP) inventory – disregarded; there is

no WIP inventory

Finished goods (FG) inventory – no change;

production = sales

Product and sales mix:

There is only one product, or

If there are two or more products produced and sold, the

sales mix is assumed to be constant

Marginal Income Statement

Condensed format

Sales P x

Less: Variable cost and expenses x

Contribution margin P x

Less: Fixed cost and expenses x

Income before income tax P x

Expanded format

Sales P x

Less: Variable cost of goods sold x

Manufacturing margin P x

Less: Variable expenses x

Contribution margin P x

Less: Fixed cost and expenses x

Income before income tax P x

Basic Principles

Variable production costs refer to direct materials,

direct labor, and variable overhead

Variable expenses are those expenses incurred not

related to production; examples are delivery expenses,

salesmen’s commission, and packing supplies

Fixed costs and expenses can be direct or indirect;

examples are rent of factory and office building, salaries

expense, and taxes and insurances

Relevant formulas

Contribution margin (CM) = ?

CM = Sales – Variable costs

CM = Sales x CMR

CM Ratio (CMR) = ?

CMR = 100% - VC Ratio

CMR = UCM / USP

Unit CM (UCM) = ?

UCM = USP – UVC

UCM = FC / BEP (units)

UCM = CM / Quantity sold

Profit (EBIT) = ?

Profit = CM – Fixed costs

Profit = Sales x ROS

∆Profit = ∆CM - ↑ in FC

∆Profit = ∆CM + ↓ in FC

Break-even point (BEP) = ?

BEP (units) = FC / UCM

BEP (pesos) = FC / CMR

Comp. BEP (units) = FC / Ave.

UCM

Comp. BEP (pesos) = FC / Ave.

CMR

Relevant formulas

At BEP:

Profit (loss) = 0

Sales = Total costs

Contribution margin = Total

fixed costs

Fixed costs (FC) = ?

FC = CM – Profit

FC = BEP (units) x UCM

VC Ratio (VCR) = ?

VCR = VC / Sales

VCR = UVC / USP

VCR = 100% - CMR

VCR = ∆Costs / ∆Sales

Margin of Safety (MS) = ?

MS = Actual sales – Actual

breakeven sales

MS = Budgeted sales – Budgeted

breakeven sales

MS = Sales x MS Ratio (MSR)

Relevant formulas

MSR = MS / Actual (budgeted)

sales

MSR = 1 – (BE Sales / Actual

sales)

Degree of operating leverage (DOL):

DOL = CM / EBIT

DOL = %∆ in EBIT / %∆ in Sales

Exercise Problems

Matador Company produces a merchandise that has the following data:

Unit sales price P80 per unit

Unit variable costs P48 per unit

Total fixed costs P640,000 per year

Units sold during the current year 25,000 units

Required:

a. Unit contribution margin, contribution margin ratio, and variable cost ratio

b. Break-even point in units and in pesos

c. Margin of safety in units and in pesos, and margin of safety ratio

d. Net profit ratio (ROS)

e. The amount of profit using the margin of safety

f. If sales increase by P300,000, how much would you expect income to increase?

Solution Guide

a.

UCM = P32 ; CMR = 40% ; VCR = 60%

b. BEP (units) = FC / UCM = P640,000 / P32 = 20,000 units

BEP (pesos) = FC / CMR = P640,000 / 40% = P1,600,000

To prove: Contribution margin (P1,600,000 x 40%) P640,000

Less: Fixed costs 640,000

Profit 0

Units Unit price Amount Rate

Sales 25,000 P80 P2,000,000 100%

Less: Variable costs 25,000 48 1,200,000 60%

Contribution margin 25,000 P32 P 800,000 40%

Less: Fixed costs 640,000

Income before income tax P 160,000

Solution Guide

c.

d. Net profit ratio (ROS) = P160,000 / P2,000,000

= 8%

e. Profit = MS x CMR = P400,000 x 40% = P160,000

f. Increase in CM (increase in profit) = increase in sales x CMR

= P300,000 x 40% = P120,000

Amount Units Rate

Actual sales P2,000,000 25,000 100%

Less: Break-even sales 1,600,000 20,000 80%

Margin of safety P 400,000 5,000 20%

Exercise Problems

Emperador Corporation produces three products, namely, products L, B and M.

Multi-product sales mix are based on units. The following data are related to the

three products:

Total fixed costs = P800,000

Required:

a. Weighted average unit contribution margin (WAUCM)

b. Composite BEP in units and allocation of CBEP

c. Composite BEP in pesos

d. Sales per mix and composite BEP

e. The number of units to be sold if the company wants a profit of P400,000.

L B M

Unit sales price P 200 P 50 P 120

Unit variable costs 120 20 90

Sales mix 2 5 3

Solution Guide

a.

b. Composite BEP (units) = FC / WAUCM = P800,000 / P40

= 20,000 units

Allocation of Comp. BEP (units):

L = 20,000 x 2/10 = 4,000 units

B = 20,000 x 5/10 = 10, 000 units

M = 20,000 x 3/10 = 6,000 units

UCM Sales mix ratio WAUCM

L P80 2/10 P16

B 30 5/10 15

M 30 3/10 9

P40

Solution Guide

c. Composite BEP (pesos) = FC / WACMR = P800,000 / P 39.604 = P 2,020,000

WACMR = WAUCM / WAUSP = P40 / P101 = P 39.604

WAUSP = ?

L = P200 x 2/10 = P 40

B = 50 x 5/10 = 25

M = 120 x 3/10 = 36

WAUSP P101

d. Sales per mix = FC / Comp. UCM = P800,000 / P400 = 2,000 units

UCM Sales mix WAUCM

L P80 2 P160

B 30 5 150

M 30 3 90

P400

Solution Guide

Composite BEP (units)

L = 2,000 x 2 = 4,000 units

B = 2,000 x 5 = 10,000 units

M = 2,000 x 3 = 6,000 units

Composite BEP (units) 20,000 units

e. Composite sales = FC + Target Profit / Ave. UCM

= (P800,000 + 400,000) / P40

= 30,000 units

Ω End Ω