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ACC80008! Managerial!Accounting! Topic!3! Cost-Volume-Profit!(CVP)!Analysis!! Note:&These&solutions&were&taken&from&the&textbook&solutions&manual.& 4.2

Explain how to calculate a weighted average contribution margin per unit. (LO3) The weighted average contribution margin per unit is calculated only when performing CVP analysis for multiple products. There are two ways to calculate it:

(1)

Calculate the total contribution of all products by subtracting total variable costs from total revenues. Then calculate the weighted average contribution margin per unit by dividing the total contribution margin by the total number of units (the sum of units for all products).

(2)

Calculate the sales mix for each product by dividing the number of units sold for that product by the total number of units sold for all products. Calculate the contribution margin per unit for each product by subtracting that product’s variable cost from its revenues and dividing the result by that product’s number of units sold. Then calculate the weighted average contribution margin per unit by summing the following computation for all products: Each product’s sales mix percentage times its contribution margin per unit.

4.3 An organisation experiences a 20 per cent increase in pre-tax profits when revenues increase 20 per cent. Assuming linearity, what do you know about the organisation’s cost function? (LO6) The firm has only variable costs and no fixed costs. If there were fixed costs, income would increase by more than 20% when sales increase by 20%.

4.4

What is the effect on an entity’s breakeven point of a lower income tax rate? (LO3 and 4) None. The firm does not pay income taxes at the breakeven point.

4.5

To estimate revenues, costs and profits across a range of activity, we usually assume that the cost and revenue functions are linear. What are the specific underlying assumptions for linear cost and revenue functions, and how reasonable are these assumptions? (LO5) Assumptions: Fixed costs remain fixed, variable costs per unit or as a percentage of revenue remain constant, selling prices per unit remain constant, the sales mix remains constant, and operations are within a relevant range where all of these assumptions are met. These are very strong assumptions. There is always some variation in fixed costs because they include costs such as electricity that varies Page 1 of 6

with weather. In addition, organisations often get or give volume discounts, so variable costs and prices per unit may change at high volumes. However, results using these assumptions are accurate enough for general planning and decision making purposes.

4.8

Explain the term sales mix in your own words. How does sales mix affect the contribution margin? (LO4) Sales mix is the specific proportion of total sales of each type of good or service that is sold. A simple example was presented in the chapter for an ice-cream store. Usually about 15% of revenue was from beverages and the rest from ice-cream products. As the proportion of specific products sold changes, the contribution margin ratio changes because the contribution per unit is different for the different products in the sales mix.

4.10 Can the margin of safety ever be negative? Explain your answer. (LO6) By definition, the margin of safety is the difference between expected unit sales and breakeven unit sales. If expected unit sales are below breakeven unit sales, the margin of safety will be negative.

4.11 Describe three uses for CVP analysis. (LO1) CVP analysis can be used for planning purposes such as budgets, product emphasis, setting prices, setting activity levels, setting work schedules, purchasing raw materials, setting levels for discretionary costs such as advertising and research and development. It can also help with monitoring operations, and analysing the operating leverage of an organisation.

4.12 Explain how CVP analysis can be used to make decisions about increases in advertising costs. (LO4) To make decisions about advertising costs, accountants predict the amount of cost to be incurred and predict the increase in sales. CVP analysis is then used to determine whether the increase in cost is equal to or greater than the increase in contribution margin from additional units sold.

4.13 Under what circumstances will managers want sensitivity analysis results relating to a CVP analysis? (LO7)

Good managers are likely to always ask for sensitivity analysis because uncertainty about sales volumes and other factors always exists. However, when unanticipated changes in the business environment or consumer preferences arise, managers will be even more interested in sensitivity analysis. By analysing a variety of scenarios, managers can respond more quickly to unanticipated changes.

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Exercises 4.14

Cost function; selling price; profit; contribution margin Find the missing figures for each of the independent cases. (LO3)

Selling

Variable

Units

Contribution

Fixed

Profit

Price/unit

Costs/unit

Sold

Margin (total)

Costs

(loss)

$80

60

10 000

$200 000

$120 000

$80 000

$15

$10

5 000

$25 000

$25 000

$0

$4

$2

1 000

$2 000

$3 000

($1 000)

$100

$75

500

$12 500

$8 000

$4 500

$10

$6

1 000

$4 000

$6000

($2 000)

4.16 Target profit; not-for-profit breakeven

(a)$

The variable cost per gift basket is $2, fixed costs are $5000 per month, and the selling price of a basket is $7. How many baskets must be produced and sold in a month to earn a pre-tax profit of $1000? (b)$ The Community Clinic (a not-for-profit medical clinic) received a lump-sum grant from the City of Sydney of $460 000 this year. The fixed costs of the clinic are expected to be $236 000. The average variable cost per patient visit is expected to be $7.64 and the average fee collected per patient visit is $4.64. What is the breakeven volume in patient visits? (LO3) (a)

Information is given on a per unit basis, so use the following equation: Profit = (p – v ) q – F $1000 = ($7 per gift basket – $2 per gift basket) × Q – $5000 $6000 = ($5 per gift basket) × Q Q = $6000/$5 per gift basket = 1200 gift baskets

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(b)

This problem is about a not-for-profit organisation. Many not-for-profit organisations provide services or sell products at a loss and use donations or grants to cover the losses. As students approach problems in this textbook, they should think briefly about the type of organisation in the problem to help them solve it. This problem is a breakeven problem with a unit cost of $7.64 and unit revenue of $4.64, or a unit contribution margin (loss) of $(3.00). In a for-profit organisation, these numbers would indicate that the company loses money on each unit it sells. In a not-for-profit, it may be appropriate to sell services at a loss, as long as another source of funds covers the loss. In this problem, the clinic receives a grant from the city, so there is “fixed” revenue in addition to the fees collected.

Taking the grant into account, the breakeven is: 0 = ($4.64 – $7.64) × Q + $460 000 grant – $236 000 fixed cost 0 = –$3×Q + $224 000

Solving for Q: 3Q = $224 000 Q = 74 667 patients

4.19

Cost function; breakeven; profit

Ryans Music provides individual music lessons in the homes of clients. The following data is provided with respect to the last 12 months of activity ending 30 June 2016:

Each unit is equal to one half-hour lesson. Required (a) Assuming selling prices and costs remain the same as for 2016 calculate the number of lessons that are required to be sold in 2017 to break even. (b) If 4000 lessons were ‘conducted’ in 2017, what profit would be achieved? (c) For 2017, Ryans expects the unit labour cost to increase by $2 but, because of local competitive forces, Ryans does not wish to increase the lesson selling price. With some careful management, Ryans hopes to reduce annual fixed costs to $15 000. Calculate the number of music lessons that would need to be performed in 2017 in order to match the 2016 profit. (LO2) (a)

Break even = $18 000/($45 – $33) = 1500 units

(b)

(4000 units × $12) – $18 000 = $30 000 profit Contribution margin = $45 - $33 = $12

(c)

($15 000 + $30 000)/ $10 = 4 500 units

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4.34

Breakeven; target profit; margin of safety SS Vines and Daughter manufactures and sells swimsuits for $40 each. The estimated income statement for 2017 is as follows:

Required

(a)$ (b)$ (c)$ (d) (e) (f) (g)

Calculate the contribution margin per swimsuit and the number of swimsuits that must be sold to break even. What is the margin of safety in the number of swimsuits? Suppose the margin of safety was 5000 swimsuits in 2016. Are operations more or less risky in 2017 as compared to 2016? Explain. Calculate the contribution margin ratio and the breakeven point in revenues. What is the margin of safety in revenues? Suppose next year’s revenue estimate is $200 000 higher. What would be the estimated pre-tax profit? Assume a tax rate of 30 per cent. How many swimsuits must be sold to earn an after-tax profit of $180 000?

(LO6) (a)

Estimated sales in number of swimsuits = $2 000 000/$40 = 50 000 swimsuits

Variable cost per unit = $1 100 000/50 000 swimsuits = $22 per swimsuit

Contribution margin = $40 – $22 = $18 per swimsuit

Breakeven in units:

$765 000/$18 = 42 500 swimsuits

(b)

Margin of safety is 50 000 – 42 500 = 7500 swimsuits

(c)

If the margin of safety was 5000 swimsuits in 2016 and increases to 7500 swimsuits in 2017 (calculated in Part B), then operations will be less risky in 2017. A larger margin of safety means that the company is operating further beyond the breakeven point; swimsuit sales can drop by a larger amount before the company incurs a loss.

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(d)

Contribution margin ratio = $18/$40 = 0.45

Breakeven in revenues: $765 000/0.45 = $1 700 000

(e)

Margin of safety in revenue = $2 000 000 – $1 700 000 = $300 000

(f)

An increase in revenues of $200 000 is expected to increase pre-tax profits by $90 000 in profits ($200 000 × 0.45 contribution margin ratio) because fixed costs have been covered at this point. Total pre-tax is estimated to be:

$135 000 + $90 000 = $225 000

(g)

Pre-tax profit = $180 000/(1 – .30) = $257 143

CVP calculation: ($765 000+$257 143)/$18 = 56 786 swimsuits

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