Agenda:

• A little more vocabulary

• C-V-P analysis

• Thursday’s class

• Group problem solving

Vocabulary

• Gross Margin = Revenue - Cost of goods sold.

• Contribution margin = Revenue - Variable costs

• Gross margin percent = Gross margin/Revenue

• Contribution margin percent = Contribution margin/Revenue

Safety margin:

• The dollar amount by which sales exceed what is required to break even.

• The number of units by which sales exceed what is required to break even.

Cost-Volume-Profit Analysis: A Simple Model for Evaluating Decision Options

A model is always an abstraction. It is a representation, sometimes mathematical, of what are believed to be the relations among the relevant decision options.

Simple model:

• The fundamental accounting equation

Profit () = Revenues - Costs

Revenue = SP*units sold

SP = selling price

Costs = FC + VC(units manufactured)

FC = fixed cost

VC = unit variable costs.

Within this model:

We are assuming that units manufactured = units sold.

What if we want to know how much product we must sell to break even?

The breakeven point is the point where profit is zero,

so = 0

= SP*units sold - FC - VC*units sold

= (SP - VC)*units sold - FC

units sold = FC/(SP - VC)

We will call units sold at = 0: BEunits

Formula for breakeven point

Note: (SP - VC) = unit contribution margin (CM)

units sold at breakeven point = FC/CM

or

BEunits = FC/CM

Breakeven revenue

Breakeven units (BEunits) * SP, or

SP * BEunits = SP*(FC/CM)

Breakeven revenue = FC/(CM/SP)

Assumptions underlying CVP analysis

• In manufacturing firms, the inventory levels at the beginning and end of the period are the same. This implies that the number of units produced during the period equals the number of units sold.

• The behavior of total revenue is linear (straight line). This implies that the price of the product or service will not change as sales volume varies within the relevant range.

Assumptions underlying CVP analysis

• The behavior of costs is linear (straight line) over the relevant range. This implies the following more specific assumptions.

a. Costs can be categorized as fixed, variable, or semi-variable. Total fixed costs remain constant as activity changes, and the unit variable cost remains unchanged as activity varies.

b. The efficiency and productivity of the production process and workers remain constant.

• In multi-product organizations, the sales mix remains constant over the relevant range.

• In multi-product organizations, when we do a single CVP analysis, we assume the products all are sold in the same market. Substitutes.

• This means that the product mix does not change in response to changes in production/sales volume.

Assumptions underlying CVP analysis

Example 1: equation approach

• Movie theater: $48,000 monthly fixed costs

• $8 ticket price.

• $2 variable cost per ticket.

• Give breakeven units and revenue

Example 1

• Suppose practical capacity per month is 12,000 tickets and that the movie theater has operated at 60% capacity during December. It is now December 30.

• Has the theater made money in December?

• If they could capture 1,000 customers by lowering the ticket price to $7 for New Year’s Eve, should they do it?

Example 2

Data: Air Safety Systems company manufactures a component used in aircraft radar systems. The firm's fixed costs are $4,000,000 per year. The variable cost of each component is $2,000, and the components are sold for $3,000 each. The company sold 5,000 components during the prior year, and budgets 5,000 in sales for the coming year. (Ignore taxes)

Example 2

FC = $4,000,000; VC = $2,000; SP = $3,000; sold prior yr./budgeted this yr. = 5,000 units

1. Compute the breakeven point in units.

2. Compute the breakeven point in dollars.

Example 2

FC = $4,000,000; VC = $2,000; SP = $3,000; sold prior yr./budgeted this yr. = 5,000 units

What will be the new breakeven point if fixed costs increase by 10%?

Example 2

FC = $4,000,000; VC = $2,000; SP = $3,000; sold prior yr./budgeted this yr. = 5,000 units

What was the company's operating income for the prior year?

Example 2

The sales manager believes that a reduction in the sales price to $2,500 will result in orders for 1,200 more components each year. What will the new breakeven point be if the price is changed?

FC = $4,000,000; VC = $2,000; SP = $3,000; sold prior yr./budgeted this yr. = 5,000 units

Example 2

The sales manager believes that a reduction in the sales price to $2,500 will result in orders for 1,200 more components each year.

Should the price change be made?

FC = $4,000,000; VC = $2,000; SP = $3,000; sold prior yr./budgeted this yr. = 5,000 units

Example 2

FC = $4,000,000; VC = $2,000; SP = $3,000; sold prior yr./budgeted this yr. = 5,000 units

What is the company's current safety margin?

How many units will Air Safety Systems need to sell if they want to achieve a profit of $2,500,000?

Example 2

Suppose that due to a new labor contract variable costs increase by 10%. What is the new breakeven point?

What will operating income be if sales remain at the same level as last year?

FC = $4,000,000; VC = $2,000; SP = $3,000; soldprior yr./budgeted this yr. = 5,000 units

Multiple productsParry Sound Diskettes:

Economy Standard PremiumSelling price $10 $15 $25Less variable costs:

Direct materials 2 3 5Direct labor 2 4 6Mfg. Overhead 1 2 3Selling 2 2 2

Contribution margin $ 3 $ 4 $ 9

Product % of total sales 10% 50% 40%

Weighted average contrib. margin (WACM) = ?

What is expected profit?

Fixed costs:

Manufacturing costs $200,000

Advertising $100,000

Admin. costs $100,000

Total predicted sales 80,000 units

Capacity 100,000 units

Expected Profit = E() = ?

Suppose an advertising budget increase of $100,000 is expected to increase sales by 20,000. Should the firm spend $100,000 on additional advertising?

Compute the new expected profit:

= ?

Compare this to profit before the change.

An advertising budget increase of $150,000 is expected to change the sales mix to (.05, .30, .65). Should the advertising budget be increased?

New weighted average contribution margin:

?

E() = ?

A 2% selling commission increase is expected to increase overall demand by 10,000. Should they do it?

Selling commissions are variable costs, so unit contribution margins will decline.

Change in variable costs:Economy:

Standard:

Premium:

The new contribution margins are Economy:

Standard:

Premium:

Should Parry Disketts increase selling commissions?

New weighted average contribution margin:

?

E() = ?

Example 3: Kaplan Co.

(a) What is Kaplan’s breakeven point?

FC = $900,000

VC = $12 + $5 = $17

CM = $23 - $17 = $6

BEunits = $900,000/$6 = 150,000 units

(b) Unit sales at target income

= ($900,000 + $240,000)/$6

= 190,000 units

Example 3: Kaplan Co.

(a) Last year’s income = 185,000 x $6

- $900,000 = $210,000

= target income

(b) Contribution to date = 30,000 x $6

= $180,000

(c) Target contribution margin = $6.50

Target contribution margin:

Let CM* = target contribution margin

130,000 units = (($900,000-$85,000)+($210,000-$180,000))/CM*

CM* = $6.50

*CM

)000,180$000,210($)000,85$000,900($

Prestige

• Using CVP analysis.

• A spreadsheet is a good way to tackle the problem.

• In addition to the financial analysis, you are asked to consider factors such as mission, marketing, strategy, and financial flexibility.

Prestige

• I have made a worksheet available to you on the homepage to help structure your computations.

• Just use it as a guideline for your spreadsheet analysis.