Week 4 tutorial 3 solution Ch4 PDF

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4 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 $$4...

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4.20

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

Selling Price/unit

Variable Costs/unit

Units Sold

Contribution Margin (total)

Fixed Costs

Profit (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)

4.33

Breakeven; target profit; cost changes; selling price Laraby Company produces a single product. It sold 25 000 units last year with the following results.

In an attempt to improve its product, Laraby’s managers are considering replacing a component part that costs $2.50 with a new and better part costing $4.50 per unit during the coming year. A new machine would also be needed to increase plant capacity. The machine would cost $18 000 and have a useful life of six years with no salvage value. The company uses straight-line depreciation on all plant assets. Required (a) What was Laraby Company’s breakeven point in units last year?

(b)

How many units of product would Laraby Company have had to sell in the past year to earn $77 000 in after-tax profit? (c) If Laraby Company holds the sales price constant and makes the suggested changes, how many units of product must be sold in the coming year to break even? (d) If Laraby Company holds the sales price constant and makes the suggested changes, how many units of product will the company have to sell to make the same after-tax profit as last year? (e) If Laraby Company wishes to maintain the same contribution margin ratio, what selling price per unit of product must it charge next year to cover the increased materials costs? (LO2 and 3) (a)

Selling price per unit: = $625 000/25 000 units= $25/unit Variable cost per unit: = $375 000/25 000 units= $15/unit Breakeven point: $25×Q – $15×Q – $150 000 = $0 Q = 15 000 units

(b)

Adjust the after-tax income target to a before-tax income target. Income before tax × (1 – .45) = $77 000 Income before tax × 0.55 = $77 000 Income before tax = $140 000 Then solve for units at target profit: $25Q – 15Q – 150 000 = $140 000 Q = 29 000 units

(c) Current variable cost Less old component Plus new component New variable cost

$15.00 (2.50) 4.50 $17.00

Current fixed cost Plus depreciation on new machine $18 000/6 New fixed cost

Solve for breakeven where: $25×Q – $17×Q – $153 000 = $0 Q = 19 125 units (d)

Solve for target profit where: $25×Q – $17×Q – $153 000 = $100 000 (before tax)

$150 000 3 000 $153 000

Q = 31 625 units (e)

Current contribution margin ratio = ($25 – $15)/$25 = 40% New price: P – $17 = 0.40×P Rearrange terms: 0.60×P = $17 P = $28.33

4.43 Sales mix; multiple product breakeven; uncertainties; quality of information Dreamtime produces two products: regular boomerangs and premium boomerangs. Last month 1200 units of regular and 2400 units of premium were produced and sold. Average prices and costs per unit for the month are displayed here.

Product line fixed costs can be avoided if the product line is dropped. Corporate fixed costs can be avoided only if the entity goes out of business entirely. You may want to use a spreadsheet to perform calculations. Required (a) Assuming the sales mix remains constant, how many units of premium will be sold each time a unit of regular boomerangs is sold? (b) What are the total fixed product line costs for each product? (c) What are the total corporate fixed costs? (d) What is the overall corporate breakeven in total revenue and for each product, assuming the sales mix is the same as last month’s? (e) What is the breakeven in revenues for regular boomerangs, ignoring corporate fixed costs? (f) Why is the breakeven for regular boomerangs different when we calculate the individual product breakeven versus the combined product breakeven? (g) When managers monitor the profitability of regular boomerangs, are corporate fixed costs relevant? Explain. (h) CVP analysis assumes that the sales mix will remain constant. Explain why managers generally cannot know for certain what their sales mix will be. (i) What is the effect of uncertainty about the sales mix on the quality of the information obtained from CVP analyses?

(LO4) (a)

Last month 1200 regular and 2400 premium boomerangs were sold. Assuming the sales mix remains constant, two premium boomerangs are sold for each regular boomerang.

(b)

Total fixed product line costs: Regular: 1200 units × $8.17 = $9804 Premium: 2400 units × $24.92 = $59 808

(c)

Total corporate fixed costs: $5.62 × (1200 + 2400) units = $20 232

(d)

To calculate the overall breakeven, it is easiest to first calculate the weighted average contribution margin ratio using an income statement approach:

Units Revenue Variable cost Contribution margin

Regular 1 200 $26 580 5 172 $21 408

Premium Total 2 400 3 600 $108 720 $135 300 16 584 21 756 $ 92 136 $113 544

Weighted average contribution margin ratio ($113 544/$135 300)

83.92%

Overall corporate breakeven (recall that there are three fixed costs): Revenues = ($9804 + $59 808 + $20 232)/83.92% = $107 059 Breakeven for Regular based on sales mix in revenues: $107 059×($26 580/$135 300)

$ 21 032

Breakeven for Premium based on sales mix in revenues: $107 059×($108 720/$135 300) Total corporate sales at breakeven (e)

86 027 $107 059

Breakeven for regular boomerangs ignoring corporate fixed costs: Revenues = $9804/[($22.15 – $4.31)/$22.15] = $9804/0.8054 = $12 173

(f)

When regular boomerangs is required to cover only its own fixed costs, the company does not need to sell as many units to breakeven. The breakeven revenue for boomerangs is higher when it covers both its own

and corporate fixed costs ($21 032) than when it only covers its own fixed costs ($12 173). (g)

Corporate fixed costs are not usually under the control of the individual product managers. Therefore, corporate fixed costs generally are not considered when evaluating individual product profitability. However, the company as a whole needs to cover all of its fixed costs, so it is important to take corporate fixed costs into account when planning overall operations.

(h)

The actual sales mix can differ from plans for many reasons. For example, customer preferences can change, altering the number and prices of units. Competitor’s prices and products could affect the sales mix. Consumer buying patterns change when the economy changes. Sometimes an unforeseen event will greatly alter consumer behaviour. These changes cannot easily be predicted.

(i)

When the sales mix is more uncertain, the quality of information from CVP analysis is lower because the CVP assumptions are more likely to be violated. Therefore, the likelihood that the sales mix will remain constant must be evaluated. Sensitivity analysis should also be performed to examine a larger range of operations that incorporate possible changes in sales mix. The quality of the CVP analysis is negatively affected by higher uncertainty about any of the variables used....