Decison-analysis_i.pdf

Decision Analysis - I CMA Part 2

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Cost-Volume-Profit Analysis

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Cost-Volume-Profit Analysis ▪ CVP is used mostly for short-run decisions. ▪ CVP analysis enables a company to find the level of production and sales, both in units and in dollars, required for the company to break even or achieve a specified profit. ▪ Since prices and costs are usually fixed in the short run, the product profitability depends mostly upon the quantity sold.

▪ CVP analysis is used to calculate the effect on profitability of changes in the product mix and in quantities sold. ▪ CVP analysis examines what happens to total revenues, total costs and operating income in response to changes in the output level, product mix, selling price, variable costs per unit and fixed costs.

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Assumptions in CVP Analysis 1.

All costs are either fixed or variable (no mixed costs).

2.

Within the relevant range, total costs and revenues are predictable with a linear functional relationship to output.

3.

Total fixed costs, the selling price per unit, variable cost per unit, and the selling mix remain constant over the relevant range. (the range of output that is analyzed).

4.

Production is equal to sales (no changes in inventory).

5.

The time value of money is ignored.

▪ Though these may seem very strict, since we are looking at short-term decision making, it is much more likely that these conditions exist in the short-term.

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Unit Contribution Margin ▪ The unit contribution margin (UCM) is how much of the sales price is available to cover fixed costs and then to provide profits after the fixed costs are covered.

▪ It is calculated as follows: Selling price per unit

–

Variable costs per unit

=

Contribution margin per unit

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Total Contribution Margin Calculation ▪ The total contribution margin is the total amount of contribution that is received from all sales. ▪ Total contribution margin can be calculated two ways:

Unit contribution margin x

Number of units sold

=

Total contribution margin

OR Total revenue

-

Total variable cost

=

Total contribution margin

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Contribution Margin Ratio ▪ If unit contribution margin is expressed as a percentage of the sales price, it is the contribution margin ratio, or contribution margin percentage.

▪ The ratio is calculated as follows: Contribution Margin per Unit

Selling Price per Unit ▪ The contribution margin ratio can also be calculated using total amounts. contribution margin and total revenues instead of per unit amounts: Total Contribution Margin Total Revenue

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Contribution Margin Income Statement ▪ In a contribution margin income statement, the income statement is presented in such a way that it shows variable costs together and fixed costs together. which then shows a key item that does not appear on the standard income statement, contribution margin, as follows: Revenues -

Variable costs

=

Contribution margin

-

Fixed costs

=

Operating income

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▪ Example: Carl Company sells its product for $100 per unit. Fixed costs are $120,000, and the variable cost is $60 per unit. The unit contribution margin is $40 per unit ($100 − $60). This is the contribution to the coverage of fixed costs made by the sale of each unit. The following shows how the contribution margin increases as sales volume increases and more of the fixed costs are recovered, and operating income goes from negative to positive:

Sales Volume:

1,000

2,000

3,000

4,000

5,000

$100,000

$200,000

$300,000

$400,000

$500,000

Variable Costs @ $60

60,000

120,000

180,000

240,000

300,000

Contribution Margin

$ 40,000

$ 80,000

$120,000

$160,000

$200,000

120,000

120,000

120,000

120,000

120,000

$ 40,000

$ 80,000

Revenues @ $100

Fixed Costs Operating Income

$( 80,000) $( 40,000)

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$

-0-

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▪ Example: Carl Company sells its product for $100 per unit. Fixed costs are $120,000, and the variable cost is $60 per unit. The unit contribution margin is $40 per unit ($100 − $60). This is the contribution to the coverage of fixed costs made by the sale of each unit. The following shows how the contribution margin increases as sales volume increases and more of the fixed costs are recovered, and operating income goes from negative to positive:

Sales Volume:

1,000

2,000

3,000

4,000

5,000

$100,000

$200,000

$300,000

$400,000

$500,000

Variable Costs @ $60

60,000

120,000

180,000

240,000

300,000

Contribution Margin

$ 40,000

$ 80,000

$120,000

$160,000

$200,000

120,000

120,000

120,000

120,000

120,000

$ 40,000

$ 80,000

Revenues @ $100

Fixed Costs Operating Income

$( 80,000) $( 40,000)

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$

-0-

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Graphic Representation

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Calculating Breakeven Point ▪ The breakeven point (BEP) is the point where operating income is $0. The BEP may be calculated in respect to the number of units that must be sold or the dollar value of the revenue at which operating income will be $0. BEP in units = Fixed Costs Unit Contribution Margin

BEP in revenue = Fixed Costs

Contribution Margin Ratio

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▪ Example: Ray Company, a manufacturer of cell phones, sells them to wireless service providers for $60 each. Ray Company’s variable cost is $35 per phone. Calculate the Breakeven Point in Units. ▪ Ray’s unit contribution margin is: $60 − $35 = $25

▪ Ray Company’s fixed costs total $150,000. Ray’s breakeven point in units is: Breakeven point in units

= $150,000 / $25 = 6,000 units

▪ We can prove this by using the standard profit formula, which is Profit = Total Revenue – Total Variable Costs – Total Fixed Costs. Profit

= (6,000 × $60) – (6,000 × $35) − $150,000

= $360,000 − $210,000 − $150,000 =

$0

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▪ Example: With the same contribution margin and fixed costs as in the previous example, Ray Company’s breakeven point in dollars of revenue is calculated as follows. Calculate the breakeven point in revenue. ▪ Ray Company’s Contribution Margin Ratio is .416667 ($25 ÷ $60): Breakeven point in revenue

$150,000 =

$360,000

.416667 ▪ Proof: BEP in units =

Profit

$360,000 / $60

=

6,000 units

= (6,000 × $60) – (6,000 × $35) – $150,000

= $360,000 –

$210,000 – $150,000

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=

$0

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▪ Example: Given a selling price of $4.00 and variable costs of $2.20, what is the breakeven point in units if fixed costs are $4,600?

▪ The unit contribution margin is $1.80 per unit ($4.00 – $2.20). This is the contribution to cover fixed costs that is made by the sale of each unit.

Breakeven Point in units =

Fixed Costs Contribution Margin Per Unit

Breakeven Point in units = $4,600 / $1.8 = 2,555.55 = 2,556 units

▪ With $4,600 of fixed costs, the number of units that must be sold to break even is 2,556. Actually, the math of $4,600/$1.80 is equal to 2,555.55; however, since it is not possible to sell .55 of a unit, we must round this answer to the next highest whole number.

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Breakeven in Decisions Making ▪ Used to make decisions about: • •

How many units need to be sold to justify an expense – marketing, buying a fixed asset, hiring a person? What is the effect of changing prices?

▪ In book are examples of increasing fixed marketing costs and determining the impact of reduced sales price.

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Calculating Profit Points

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Two Types of Profit Calculations 1.

A target dollar amount of profit.

2.

A target percent of sales price profit.

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1. Target $ Amount of Profit ▪ We use the break even formula for units to calculate the # of units to sell to achieve a specific profit value.

▪ The required dollar amount of profit is treated as an additional fixed cost that must be covered by the contribution margin. •

This makes sense since management says that both fixed costs and the target profit amount of profit need to be met. It is treated as a fixed cost since the target profit amount does not change as the level of production changes.

▪ The formula to calculate the number of units to achieve the specified profit is:

Fixed Costs + Required Pre-Tax Profit Contribution Margin Per Unit

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2. Target Percent of Sales Profit ▪ When the required profit is shown as a percentage of sales, the profit amount is treated like a variable cost. “Contribution” = Revenue - VC – Pre-tax Profit %

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Calculating PRE-Tax Profit ▪ In order to calculate the number of units to sell in order to achieve a specific dollar amount of after-tax profit, after-tax profit must be converted to a pre-tax profit.

▪ This is done with the following calculation: Target AFTER-tax income (1 – tax rate)

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▪ Let us assume the same information as in the previous example (a selling price of $4.00, variable costs of $2.20, and fixed costs of $4,600), and add that the company must achieve a minimum pre-tax profit of $5,000. What is the required sales level to achieve this?

Sales Volume for $5,000 pre-tax profit = $4,600 + $5,000= 5,333.33 $1.80 5,334 units

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▪ Let us assume the same facts as the previous example, but change the profit requirement to 35% of sales.

▪ The amount of pre-tax profit needed from each sale is $4.00 × .35, or $1.40. This required pre-tax profit will be an adjustment (a decrease) to the contribution margin per unit that we use in the denominator, so the adjusted contribution margin per unit is going to be lower than the contribution margin per unit. ▪ The variable costs now consist of the actual variable costs of $2.20 per unit as well as the required pre-tax profit, which is 35% of the sales price of $4.00, or $1.40 per unit. The adjusted contribution margin per unit is $.40, calculated as follows: $4.00 − $2.20 VC − $1.40 P = $.40. ▪ Thus, the number of units of sales required to achieve a pre-tax profit of 35% of sales is:

Target Sales Volume for pre-tax profit of 35% of sales = ($4.00 − $2.20 − $1.40)

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$4,600

= 11,500

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▪ For our company with a sale price per unit of $4.00, variable costs of $2.20, fixed costs of $4,600, and a tax rate of 40%, an after-tax net income requirement of $5,000 would require how many units of sales?

Contribution margin per unit: $4.00 − $2.20 = $1.80 Target pre-tax net income: $5,000 / (1 − .40) = $8,333 Target sales volume in units: ($4,600 + $8,333) / $1.80 = 7,185 Target revenue: Contribution margin ratio = $1.80 / $4.00 = .45 Target revenue = ($4,600 + $8,333) / .45 = $28,740

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▪ For a company with a sale price per unit of $4.00, variable costs of $2.20, and fixed costs of $4,600, now has an after-tax net income requirement of 20% of revenue and the tax rate is 30%. How many units does the company need to sell? 1.

Calculate the target pre-tax net income needed per unit: Required after-tax percentage of revenue × Sale price per unit = .20 × $4.00 (1 − tax rate) .70 = $1.1429 This means that each unit sold must include $1.1429 of pre-tax net income in order for the company to have an after-tax net income equal to 20% of sales.

2.

Calculate the adjusted contribution margin per unit: Adjusted contribution margin per unit = $4.00 − $2.20 − $1.1429

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= $.6571

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3.

Calculate the target sales volume needed to achieve a 20% after-tax net income:

Target Sales Volume in number of units = $4,600 / .6571 = 7,000 units

4.

Calculate the target revenue needed to achieve a 20% after-tax net income:

Adjusted Contribution margin ratio = $.6571 / $4.00 = .16428 Target revenue = $4,600 / .16428 = $28,000

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Proof: Revenue: 7,000 × $4.00 Variable costs: 7,000 × $2.20 Contribution margin Fixed Costs Net Income before tax Effective Income Tax @ 0.30 Net Income after tax

$28,000 15,400 $12,600 4,600 $ 8,000 2,400 $ 5,600

$5,600 ÷ $28,000 = 0.20 or 20%.

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Breakeven Analysis for Multiple Products

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Breakeven for Multiple Products ▪ When more than one product the assumption that the sales mix is constant is critical. • •

It is important to know that for each different product mix there is a different breakeven point. This is because the contribution from the mix will be different in each case.

▪ In order to calculate the BEP with multiple products, basket that consists of the minimum integer numbers of units of all products sold is used.

▪ BEP is calculated in terms of baskets instead of units.

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Multiple Product Calculations A.

Sales Quantity Mix (Dollar amount of contribution per basket)

B.

Sales Revenue Mix (Contribution margin ratio for the Basket)

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A. Sales Quantity Mix 1.

Calculate the dollar amount of contribution for the basket.

2.

Calculate BEP for number of baskets

▪ 2 ways to visualize this 1.

Either full units

2.

Or one full unit that is some % of each product.

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▪ Let us assume that the contribution of the products are:

Product A: $10

Product B: $12

Product C: $15

Product D: $17

▪ The calculation of contribution per basket:

A: $10 * .10 = $1.00 B: $12 * .20 = $2.40 C: $15 * .30 = $4.50 D: $17 * .40 = $6.80 Total $14.70 ▪ Remember that each basket that is sold has only .10 of a unit of Product A, .20 of a unit of Product B, .30 of a unit of Product C, and only .40 of a unit of Product D.

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One Basket that is Made Up of A Number of Units of Each Product

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▪ Let us assume that the contribution of the products are:

Product A: $10

Product B: $12

Product C: $15

Product D: $17

▪ The calculation of contribution per basket:

A: $10 * 1 = $10.00 B: $12 * 2 = $24.00 C: $15 * 3 = $45.00 D: $17 * 4 = $68.00 Total $147.00 ▪ Now each basket has 1 unit of Product A, 2 units of Product B, 3 units of Product C, and 4 units of Product D.

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▪ Example: Assume that the sales revenue of a company is made up of 40% of Product A and 60% of Product B. The following is information about each product:

Selling price Variable costs Contribution dollar amount Contribution margin

Product A $4.00 $2.50 $1.50 37.5%

Product B $3.00 $1.75 $1.25 41.7%

▪ Fixed costs for the company are $75,000. ▪ How many of each product needs to be sold to break even?

▪ Contribution margin per BASKET: (.40 × $1.50) + (.60 × $1.25) = $1.35 ▪ Breakeven point in BASKETS: $75,000 / $1.35 = 55,555.55 BASKETS.

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▪ The last step is to determine how many units of each product are in the 55,555.55 baskets that are sold at the breakeven point.

▪ Product A: 55,555.55 × .40 = 22,222.22, or 22,223 units of Product A ▪ Product B: 55,555.55 × .60 = 33,333.33, or 33,334 units of Product B

▪ The calculations may also be done with 4 units of A and 6 units of B in each basket that is sold.

▪ (4 x $1.50) + (6 x $1.25) = $13.50 contribution per BASKET. ▪ $75,000 / $13.50 = 5,555.55 BASKETS and the breakeven point. ▪ Product A: 5,555.55 × 4 = 22,222.22, or 22,223 units of Product A ▪ Product B: 5,555.55 × 6 = 33,333.33, or 33,334 units of Product B

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▪ Example: A company’s basket of sales consists of 25 units of Product A, 5 units of Product B, and 20 units of Product C. The company’s fixed costs are $50,000. Selling prices and variable costs are as follows:

Selling price/unit Variable cost/unit Contribution margin/unit Number of units

Item A 10.00 5.00 5.00 25

Item B 6.00 4.00 2.00 5

Item C 8.00 4.50 3.50 20

▪ The total contribution margin for the basket is $205.

($5 × 25) + ($2 × 5) + ($3.50 × 20) ▪ The breakeven point in baskets is 243.90

$50,000 / $205

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▪ Each basket consists of 25 units of A, 5 units of B, and 20 units of C.

Product A: 243.90 × 25 Product B: 243.90 × 5 Product C: 243.90 × 20 Total breakeven quantity

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= = =

6,098 units 1,220 units 4,878 units 12,196 units

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B. Sales Revenue Mix ▪ Uses the weighted average contribution margin for the basket.

▪ Calculates the BEP for baskets.

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▪ Example: Assume that the sales revenue of a company is made up of 40% of Product A and 60% of Product B. The following is information about each product:

Selling price Variable costs Contribution dollar amount Contribution margin

Product A $4.00 $2.50 $1.50 37.5%

Product B $3.00 $1.75 $1.25 41.7%

▪ Fixed costs for the company are $75,000. ▪ How many of each product needs to be sold to break even?

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▪ WAVG Contribution Margin Ratio per BASKET =

(.40 × .375) + (.60 × .417) = .40 ▪ The fixed costs divided by the WAVG contribution margin ratio gives the total breakeven revenue.

$75,000 / .40 = $187,500 ▪ The last step is to determine the 40% and 60% of the total breakeven revenue for Product A and Product B:

Revenue for A = $187,500 × .40 = $75,000 Revenue for B = $187,500 × .60 = $112,500

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▪ Note: Because the selling prices of the two products are different, the percentage breakdown by product in units sold will not be the same as the percentage breakdown by product in revenue— 40% and 60%. ▪ Breakeven revenue for A is $75,000 and the unit price of A is $4. Therefore, the breakeven quantity for A is $75,000 ÷ $4, or 18,750 units.

▪ Breakeven revenue for B is $112,500 and the unit price of B is $3, so the breakeven quantity for B is $112,500 ÷ $3, or 37,500 units. ▪ The total breakeven quantity is 18,750 + 37,500, or 56,250 units. Units sold of A are 33.33% of the total 56,250 units, while units sold of B are 66.67% of the total.

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Effect of Changes in Sales Mix ▪ Increasing the % of sales of the higher contribution goods is the goal.

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CVP and Conditions of Risk and Uncertainty

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CVP and Risk and Uncertainty ▪ Since CVP analysis is used for decision-making, it necessarily involves assumptions about the future. This introduces the elements of risk and uncertainty into the process.

▪ Risk relates to the probability that an outcome has been predicted correctly. As the probability of an event’s occurring nears 100%, the amount of risk decreases, and vice versa. ▪ Uncertainty occurs when there is no basis to draw a conclusion one way or another.

▪ Several methods can be used to address risk and uncertainty when using CVP analysis.

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Sensitivity Analysis and CVP ▪ Sensitivity analysis is an effective method of dealing with uncertainty that might arise in decisionmaking. Sensitivity analysis answers the question, “If some underlying assumption changes or is not achieved, what will happen to the result?” ▪ By looking at how much the results change as an assumption changes, the decision-maker can identify critical factors that must be controlled as much as possible.

▪ With CVP analysis, the underlying assumptions will include sales volume, selling prices, and costs. Sensitivity analysis can determine the changes in operating income that could take place if sales levels change, if prices change, or if costs change.

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▪ Example 1: The following is an example of a sensitivity analysis using CVP analysis, where the number of units sold, the price, and the fixed cost are held constant but the variable cost per unit changes. Variable Cost Per Unit = $20 Sales: 6,000 units @ $50 per unit $300,000 Variable cost for 6,000 units 120,000 Contribution margin $180,000 Fixed Cost 100,000 Operating income $ 80,000

$25

$30

$35

$300,000

$300,000

$300,000

150,000 $150,000 100,000 $ 50,000

180,000 $120,000 100,000 $ 20,000

210,000 $90,000 100,000 $(10,000)

▪ For each $5 increase in variable cost per unit, the variable cost for 6,000 units increases by $30,000 (6,000 × $5) and operating income decreases by $30,000 until at a variable cost per unit of $35, a loss results.

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▪ Example 2: The following is an example of a sensitivity analysis where the number of units sold changes while the sales price, the variable cost per unit, and the fixed costs remain the same. The changing volume affects sales revenue, variable cost, and the contribution margin. Number of Units Sold = Sales @ $50 per unit Variable cost @ $25 per unit

6,000 $300,000

5,000 $250,000

4,000 $200,000

3,000 $150,000

150,000 Contribution margin ($25 per unit) $150,000 Fixed Cost 100,000 Operating income $50,000

125,000

100,000

75,000

$125,000 100,000 $25,000

$100,000 100,000 $ 0

$ 75,000 100,000 $(25,000)

▪ The unit contribution margin is $50 − $25, or $25. The contribution margin ratio is $25 ÷ $50, or 50%. Each one-unit change in sales volume affects operating income (upward or downward) by $25, because for each 1,000-unit decline in sales volume operating income declines by $25,000.

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Margin of Safety ▪ The margin of safety, another aspect of sensitivity analysis, is The excess amount of actual or planned sales over the breakeven level of sales.

▪ In other words, the margin of safety measures the amount by which sales can fall from their actual or budgeted level without the company becoming unprofitable. ▪ The margin of safety may be expressed as either revenue or units. If expressed in revenues, it is the actual or planned sales revenue minus the sales revenue at the breakeven point. If expressed in units, it is the actual or planned sales volume minus the breakeven volume.

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Margin of Safety Formula

=

Actual or planned sales (units or revenue) Breakeven sales (units or revenue) Margin of safety

÷ =

Margin of safety Actual or planned sales Margin of safety ratio

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▪ Example: Following is the sensitivity analysis from the preceding Example 2 showing changes in operating income that occur with changes in number of units sold. It is followed by a calculation of the margin of safety at the level of 6,000 units of sales. Number of Units Sold = 6,000 Sales @ $50 $300,000 Variable cost @ $25 150,000 Contribution margin ($25 per unit) $150,000 Fixed Cost 100,000 Operating income $ 50,000

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5,000 $250,000 125,000

4,000 $200,000 100,000

3,000 $150,000 75,000

$125,000 100,000 $ 25,000

$100,000 100,000 $ 0

$ 75,000 100,000 $(25,000)

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▪ The breakeven sales level is 4,000 units ($100,000 fixed costs divided by the contribution margin of $25 per unit). At a sales level of 4,000 units, operating income is zero.

▪ The margin of safety in units at the sales level of 6,000 units is 2,000 units. 6,000 – 4,000 = 2,000 units. ▪ The margin of safety in revenue at the level of 6,000 units is (6,000 – 4,000) × sales price of $50 = $100,000. ▪ Note that $100,000 is also the difference between sales revenue at the level of 6,000 units ($300,000) and sales revenue at the level of 4,000 units ($200,000). Therefore: 1. The margin of safety ratio in units at 6,000 units = (6,000 – 4,000) ÷ 6,000 = 33 1/3% 2. The margin of safety ratio in revenue at 6,000 units = ($300,000 − $200,000) ÷ $300,000 = 33 1/3%

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Other Decisions

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Other Decisions 1.

Choosing between two cost options

2.

Choosing between two production options

3.

Using fixed versus variable inputs

4.

Product-mix decisions under constraints

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1. Choosing Between Two Cost Options ▪ In some cases, management must choose between two ways of accomplishing the same thing that have different costs. What is the best way to make this decision?

▪ To determine which of two cost options is preferable, begin by creating two cost functions, one for each option, with the same variables in both cost functions and using the same variable on the right side of both equations. ▪ Next, set the left sides of the two equations equal to one another and solve for the unknown that is common to both. ▪ The solution is the variable amount at which the two options are equal to each other.

▪ Management can use that information to make a decision between the two options based on the expected quantity.

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▪ Example: JJ Motors, Inc. employs 45 sales personnel to market its line of automobiles. The average car sells for $35,000 and a 6% commission is paid to the salesperson. JJ Motors is considering a change to a salary and commission arrangement in which each salesperson would be paid a salary of $2,000 per month plus a commission of 3% of his or her sales. Determine the amount of total monthly car sales revenue at which JJ Motors would be indifferent as to which plan it selects.

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▪ Solution: ▪ Under the existing system, the cost formula is:

0.06S

=C

▪ Under the proposed option, the cost formula is: (2,000 × 45) + 0.03S = C ▪ At this point it is not necessary to know the value of C. Since the question is the sales revenue at which C would be the same for both equations, C must have the same value for both equations. Therefore, Set the two left sides of the two equations equal to one another, and the two right sides (C) will be equal to one another as well. The result is an equation with just one unknown variable, “S,” which represents the level of sales revenue at which the compensation to the sales staff will be the same under both cost structures:

0.06S = (2,000 × 45) + 0.03S 0.03S = 90,000 S = $3,000,000

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▪ If JJ Motors expects that its level of sales revenue per month will be $3,000,000 or more, it would be better to offer the salespeople $2,000 per month plus a 3% commission, because the marginal commission cost for each car sold over the level of $3,000,000 would be only 3% of the sales price. Under the straight commission arrangement, JJ’s marginal cost for each car sold over the level of $3,000,000 would be 6% of the sales price. ▪ However, if JJ Motors expects that its level of sales per month will be less than $3,000,000, it would be better to offer the salespeople a straight sales commission of 6%. For example, if sales were $2,500,000, commission cost under the straight commission arrangement would be:

$2,500,000 × 0.06 = $150,000 ▪ Under the salary plus commission compensation schedule, total commission cost at a sales level of $2,500,000 would be:

($2,000 × 45) + (0.03 × $2,500,000) = $165,000

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2. Choosing Between Two Production Options ▪ CVP analysis and the concepts of marginal analysis can help a company decide which product to produce in order to maximize profits (or some other strategy) when it can produce only one product out of two possible products. ▪ These types of questions will most likely require candidates to determine either the level of revenue or the level of units of output at which the company will be indifferent to the available options (that is, the point at which the company will not care which option is selected). In other words, the point of indifference is the point at which the profit under each choice is the same.

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Two Variables / Two Formulas ▪ In any situation with two unknown values, as is the case in the following example, two formulas are needed in order to solve the problem.

▪ In the second formula, express one of the unknown values in terms of the other unknown value and then substitute this new value into the first equation to create an equation with only one unknown value. ▪ In a CVP analysis problem, the two formulas will probably be the profit formula and the revenue formula. ▪ EXAMPLE IN BOOK. LARGER THAN REASONABLE EXPECTATION FOR A QUESTION.

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3. Using Fixed or Variable Inputs ▪ This is fundamentally the same as the discussion for two cost options.

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4. Product Mix Decisions Under Constraints ▪ Decisions made under situations of constraint are usually short-run decisions. In the short run, managers do the best they can with the resources they have. In the long run, of course, capacity can be expanded and constraints eliminated, or at least reduced. ▪ A constraint or limiting factor may eliminate a number of possible solutions because they are not feasible in the short run due to the constraint. In the decision-making process, this limiting factor must be kept in mind and appropriately addressed. ▪ The Theory of Constraints addresses the issues, problems, and solutions associated with such limitations.

▪ When production is operating at capacity, operating income is maximized by maximizing the contribution margin per unit of the constrained resource. ▪ If a company has several different products and has more than one limiting factor, linear programming can be used to find the product mix that will maximize net income given the existing constraints. Linear programming is not tested on the CMA exams. ▪ Theory of Constraints is tested on the CMA Part 1 exam and is covered in HOCK study materials for the Part 1 exam.

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Decision Making

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Decision Making ▪ Decision-making involves selecting among different options that are available to a company. ▪ A decision-maker should select the option that maximizes the benefits and/or reduces costs to the company. ▪ Relevant factors in decision-making can be qualitative (characteristics, and more difficult to assess) as well as quantitative (numerical, and easier to assess).

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Typical Types of Short-Term Decisions ▪ Pricing What is the minimum price we can accept? • •

Should price be based upon costs, or upon the market target pricing? Will a new customer be profitable enough to justify aggressive pricing?

▪ Alternative manufacturing options • •

What is the most cost-efficient way to manufacture the product? What is the most profitable output level? Should a one-time special order be accepted?

▪ Research and development what new products? ▪ Outsourcing decisions – should we make or buy?

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Relevant Revenues and Costs ▪ Relevant revenues and costs are the expected future revenues and costs that differ among alternatives.

▪ Only relevant revenues and costs are considered in the decision-making process. ▪ This is because: • • • •

Must focus on the future (nothing can change the past). Costs resulting from past decisions and that cannot be changed are called sunk costs. These costs are irrelevant to the decision process since they remain the same for all options taken. If costs or revenues are not different between options, they do not matter in the process of selecting an option because they are the same no matter what is done. Revenues and costs that do not differ are irrelevant and are not included in the decision making process.

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Differential vs. Incremental ▪ Relevant revenues and costs are further classified as incremental revenues and costs or differential revenues and costs. •

The terms “incremental” and “differential” are often used interchangeably; however, they are not the same.

▪ Differential revenues and costs are those that differ between two alternatives.

▪ Incremental revenues and costs are incurred additionally as a result of an activity.

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▪ Example: The following illustrates the factors involved in differential and incremental costs. ▪ A company’s machine has worn out, cannot be repaired, and must be replaced (that is, keeping it is not an option). Management has two choices: it can either replace the worn-out machine with an updated model of the same type or it can upgrade to a fully automated, totally different system. The difference in costs between the replacement machine and the upgraded machine is the differential cost. (The cost of doing nothing is not relevant because it is not an option.) ▪ On the other hand, if the machine had not yet worn out, then the choice would be between keeping it at its existing cost or upgrading to a new machine. The relevant cost is the difference between the current cost for the old machine and the cost for the upgraded machine. The additional cost of the upgraded machine, over and above the current cost for the existing machine, represents incremental cost. It is the cost the company would incur by upgrading that is in addition to the present cost of keeping the old machine.

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Avoidable vs. Unavoidable Costs ▪ An avoidable cost is a cost that can be avoided if a particular option is selected. It is a cost that would go away. • •

For example, if production is outsourced, the variable cost to produce the product in-house will go away and be replaced by the cost to purchase the product externally. Avoidable costs are relevant costs to the decision-making process because they will continue if one course of action is taken but they will not continue if another course of action is taken.

▪ An unavoidable cost is an expenditure that will not be avoided regardless of which course of action is taken. •

a payment on a non-cancelable lease for production equipment that would continue even if production were outsourced.

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▪ Example: A decision to close a plant. ▪ Avoidable and unavoidable costs are important to a decision to close a plant or other business unit. If closing the unit would avoid certain costs, those avoidable costs are relevant to the decision. Unavoidable costs, however, are irrelevant because they do not differ between the two alternatives. If some of the fixed plant costs would continue even if the plant were closed, those costs are unavoidable costs and they are not relevant to the decision. ▪ A central administrative cost that has been allocated to a division is another example of an unavoidable cost that would continue if the division were closed. Even if that division were to be closed, the cost would continue to be incurred by central administration. It would simply be allocated to another division or divisions. So for the company as a whole, the central administrative cost would not differ between the two alternatives of closing the division or keeping it open. ▪ Only costs that would be avoided (costs that would go away) if the division were closed are relevant to the decision to close a division or not to close it.

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Sunk Costs ▪ A cost for which the money has already been spent and cannot be recovered. ▪ Sunk costs are not relevant to decision-making because they will not be any different regardless of what decision is made.

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Explicit and Implicit Costs ▪ An explicit cost is a cost that can be identified and accounted for. Explicit costs represent obvious cash outflows from a business.

▪ On the other hand, an implicit cost is an implied cost. It is more difficult to identify, and it does not clearly show up in the accounting records, although it is there.

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Opportunity Costs ▪ Opportunity costs are examples of implicit costs. ▪ An opportunity cost is the contribution to income that is forgone by not using a limited resource in its best alternative use. ▪ The relevant portion of the opportunity cost is the difference between the contribution to income that could be earned on the alternative item and the contribution to income that can be earned on the item to be produced.

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Opportunity Costs ▪ The opportunity cost is calculated only from the revenues that would not be received and expenditures that would not be made for the other available alternatives.

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Imputed and Post-ponable Costs ▪ An imputed cost is one that does not show up in the accounting records and does not entail a cash outlay, but it represents a cost that must be considered in decision making. An opportunity cost is a type of imputed cost. For example, if a business uses space for its own production activities that it could have rented out to a tenant, the rent that it could have received and did not receive is an imputed cost of production.

▪ A postponable cost is a cost that may be delayed to a future period with very little, if any, effect on the current operations and efficiency of the company. For example, employee training costs may be, and commonly are, delayed during a difficult financial period because training has a longterm rather than a short-term impact. ▪ Whether or not these items are relevant will depend on the different options available.

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Marginal Analysis Measures ▪ Marginal revenue ▪ Marginal cost ▪ Marginal profit ▪ Marginal product The additional output that is produced by adding one additional unit of input.

▪ Marginal resource cost The change in the total cost that results from using one additional unit of a resource. ▪ Marginal revenue product The change in total revenue that arises from using one additional unit of a resource. ▪ THERE IS AN EXAMPLE IN THE BOOK THAT GOES THROUGH THIS, but you do not need to know the details of this, just what this means for a company in terms of making decisions.

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Income Taxes in Decision Making ▪ Income taxes are relevant in decision making only when they are different between different options.

▪ May be relevant in decisions about location of an office or factory. ▪ May be relevant in pricing decisions. (transfer pricing and sales to other jurisdictions)

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Make-or-Buy Decisions

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Make-or-Buy Decisions ▪ Make-or-buy decisions Usually involve whether the company should produce something itself or buy it from outside.

▪ The only costs that need to be considered are the relevant costs which usually consist of the variable costs and avoidable fixed costs. ▪ If the cost to purchase the product from outside is lower than the avoidable cost of internal production, the company should buy the product from the outside.

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Make-or-Buy: Relevant Costs ▪ The purchasing costs (purchase price, ordering costs, carrying costs, etc.) for the purchase from an outsider are all relevant variable costs and must be included in the cost of purchasing the item.

▪ Only avoidable fixed and variable costs of in-house production are compared to the cost to buy. ▪ If we would avoid more than it would cost to buy, we should buy.

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Make-or-Buy: Maximum Price ▪ The maximum price a company would usually be willing to pay for purchasing outside the company is – =

Total internal production costs Unavoidable costs (fixed and variable) Maximum price to pay (avoidable costs)

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Other Qualitative Factors ▪ Other qualitative considerations for the decision are: • • • •

Quality Reliability and flexibility of delivery terms Public relations with the community in which the factory is located Service

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▪ Example: Medina Co. produces football goal posts for sale to college and professional football teams. The variable and fixed costs to produce a goal post are as follows:

Direct materials Direct labor Indirect variable costs Fixed costs Selling and administrative Total

$200 per goal post $150 per goal post $75 per goal past $125 per goal post $100 per goal post $650 per goal post

▪ Butler Corp. has recently approached Medina with an offer to supply Medina with finished goal posts that Medina would then resell under the Medina name. The price of one goal post from Butler is $490.

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▪ If Medina purchased goal posts from Butler, all of its fixed costs would continue to be incurred, but Medina would be able to eliminate half of the selling and administrative costs that are associated with the production and sale of their own goal posts. The other variable costs would not be incurred because they would not need to pay any production costs if they purchase goal posts from an outside supplier. ▪ The two questions that we need to look at are whether or not Medina should accept the offer, and if not, what is the maximum price they would pay to Butler.

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▪ Should Medina accept Butler’s offer, and if not, at what price would Medina be willing to accept the offer?

▪ Medina should not accept the offer from Butler. If they accept the offer, their total costs incurred would be $665 per goal post.

Goal Post itself Fixed Costs Selling and Admin Costs Total Cost

$490 125 50 $665

▪ What is the maximum price Medina would be willing to pay? ▪ Given that Medina will have $175 of costs that will continue even if they purchase from Butler, the maximum price that they would be willing to pay is $175 less than their cost of production, or $475.

▪ Other Considerations?

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Special Order Decisions

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Special Order Decisions ▪ When a company has a request for a special, one-time order and it must determine the minimum price to charge.

▪ There are two factors to consider about this price: 1.

Direct costs of production (avoidable costs if the company does not produce)

2.

Level of capacity at which the company is operating

▪ The minimum price charged in a special order decision must include all of the costs that will be incurred directly as a result of this specific order. •

These would be the costs that would be avoidable if the company did not produce this order.

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Direct Costs of Production ▪ Generally direct costs includes the variable costs of production – direct materials, direct labor and variable overheads. ▪ Nonmanufacturing costs and fixed manufacturing costs will usually continue, even if this order is not produced.

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Capacity Status ▪ The minimum price to charge in a special order decision is affected by the percentage of capacity at which the company is operating.

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Operating at Less than Full Capacity ▪ If the company is operating at less than full capacity and there is sufficient capacity to produce this new order, then only the avoidable (direct) costs of production are used to determine the minimum price for the order.

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Operating at Full Capacity ▪ If the company is operating at full capacity, it must also include the opportunity cost of producing the order as a cost to be charged to the new order. •

Since the company is producing at full capacity, it is going to have to not produce something else in order to produce this special order. As a result, it will lose the contribution that would have been earned from the other sale.

▪ Therefore the company needs to recover not only the direct (avoidable) costs of producing this order, but also the contribution that is lost from the products that are not going to be sold as a result of accepting this order.

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▪ Scenario: Athens Co. produces two products – refrigerators and microwave ovens. Athens has the following information in respect to each unit produced of each product:

Units produced Sales price Variable costs Contribution per unit Fixed costs per unit Profit per unit

Refrigerator 500 $ 300 (100) 200 ( 75) $ 125

Microwave 500 $ 200 ( 75) 125 ( 50) $ 75

▪ All of the variable costs will be avoided if a unit is not produced. However, all of the fixed costs will continue if a unit is not produced, because fixed costs do not change in total as production volume changes (as long as production remains within the relevant range). Since the fixed costs will continue without change, they will simply be allocated to other units produced.

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▪ Example 1: Assume that a one-time customer comes to Athens and offers to buy 200 refrigerators if Athens is able to provide the refrigerators at a lower price than other companies. At this time, Athens is operating at 60% capacity and has the ability to produce these refrigerators and all of what is currently being produced. ▪ The minimum price that Athens should charge for the 200 refrigerators is $100.01. This is the amount of the variable costs that will be incurred to produce this order, plus $.01. If the price were only $100.00, then Athens would be indifferent to producing the refrigerators because there would be no additional contribution from them.

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▪ Example 2: Assume that a one-time customer comes to Athens and offers to buy 200 refrigerators if Athens is able to provide the refrigerators at a lower price than other companies. At this time, Athens is operating at 100% capacity and in order to produce these 200 refrigerators they would need to not produce 300 microwaves. ▪ In this case, the minimum price that Athens must charge will include not only the variable costs of production, but also the contribution that will be lost by not producing the 300 microwaves. We already know that the variable costs are $100, so we will need to look at the lost contribution. ▪ The contribution per microwave is $125 per unit and since there are 300 microwaves that will not be produced, the lost contribution is $37,500. This is the amount of contribution that the 200 refrigerators will need to provide. Dividing this amount among the 200 refrigerators, we get an amount of $187.50 per refrigerator, bringing the total ‘cost’ to $287.50. ▪ Athens will need to charge at least $287.51 per refrigerator. in order to accept this order.

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▪ Proof of Example 2: ▪ Currently, Athens has $162,500 of total contribution.

Original refrigerators Remaining microwaves

500 units × $200 = 500 units × $125 =

$100,000 62,500

▪ If they were to set the price at $287.50 for the new refrigerator order, their contribution would still be exactly $162,500. It is calculated as follows:

Original refrigerators Remaining microwaves New refrigerator order Total contribution

500 units × $200 = 200 units × $125 = 200 units × $187.50 =

$100,000 25,000 37,500 $162,500

▪ If they were to sell the refrigerators for less than $287.50, their total contribution would be less than it currently is.

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Sell or Process Further

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Sell or Process Further Decisions ▪ Decisions need to be made when a product could be sold now or processed further and sold for a higher price. ▪ Relevant for joint production situations and inventory that is currently obsolete.

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Joint Production Process ▪ When joint costs have incurred for a product, management should not consider the joint costs allocated to the individual products. •

This is because these are sunk costs.

▪ The only factors that are relevant are incremental revenues and costs after the splitoff point. • •

The increased revenues attainable by processing further should be balanced against the increased costs to process further. The increase in net operating income as a result of the additional processing is the only basis for the decision.

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Obsolete Inventory ▪ With obsolete inventory, the original cost of the inventory is a sunk cost and is irrelevant. ▪ The revenue from selling the reworked inventory is compared to the costs of reworking the inventory.

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▪ Example 1: CCC has ten computers in inventory that are obsolete. CCC purchased the computers four years ago for its inventory at a cost of $800 but has never been able to sell them. The company has a customer who would buy them for $175 each if CCC upgrades them; or CCC could sell them to another customer “as is” for $100 each. The cost to upgrade the computers would be $100 per computer, including labor. CCC’s tax rate is 40%. Would the company be better off selling the computers now for $100 each or upgrading them and selling them for $175 each; and how much is the difference?

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Revenue Less: Cost to upgrade Cash flow from sale Less: Cost of goods sold Taxable income/(loss) Income tax benefit Net cash flow after tax

Sell Now $1,000 0 $1,000 $8,000 (7,000) 2,800 $3,800

Upgrade & Sell $1,750 1,000 $750 $8,000 (7,250) 2,900 $3,650

Difference +$ 750 + 1,000 −$ 250 0 − 250 + 100 −$ 150

▪ The tax loss is relevant to the decision only because they will shelter other income from tax. This means that this loss will be used to offset other profit and will reduce the total tax liability of the company. After tax considerations, CCC would be better off selling the computers now, because its net after tax cash flow would be $150 greater than if they upgrade and sell them.

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▪ Example 2: Assume the same facts as before, except CCC has no customer to purchase the computers in their present state. They could sell them to the same customer as above for the same $175 after upgrading them. CCC must get rid of the computers to make room for new merchandise. Since the computers contain toxic components, they would have to be sent to a recycling center that will charge $15 per computer to recycle them. Now, the choice is between upgrading and selling them, or paying a recycler. Which way is CCC better off, and by how much?

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Revenue Less: Additional cost Cash flow from sale Less: Cost of goods sold Taxable income/(loss) Income tax benefit Net cash flow after tax

Recycle $ 0 150 ($150) $8,000 (8,150) 3,260 $3,110

Upgrade & Sell $1,750 1,000 $750 $8,000 (7,250) 2,900 $3,650

Difference +$1,750 + 850 +$ 900 0 + 900 − 360 +$ 540

▪ Because CCC would have to pay to dispose of the computers, it is better off upgrading and selling them.

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Disinvestment Decisions

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Disinvestment Decisions ▪ Discuss what it is. ▪ In this decision-making process, it is critical to remember that some of the fixed costs of the division may not be avoided even if the division is terminated. •

•

This is because some of the fixed costs may be allocations of central fixed costs or are costs that cannot be terminated (such as a non-cancelable lease). Because those costs will simply be transferred to another division if the division in question is terminated, these are not avoidable costs.

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Disinvestment Decision Steps ▪ three main steps : 1.

Identify all unavoidable fixed costs that are allocated to or incurred by the division that would continue even if the division were terminated. These are the unavoidable costs that would simply be transferred to another division if this division were terminated.

2.

Identify all unavoidable variable costs that would continue even if the division were terminated. These are again the unavoidable variable costs that would be absorbed by another division after this one is closed.

3.

Identify all avoidable costs (both fixed and variable) that will be incurred only if the division continues to operate and compare this to the revenue of the division. If the revenue from this division is less than the avoidable costs of the division, the division should be terminated.

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Thank You!

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