9.3 Multi-Product Calculations Flashcards
Due to a change in market conditions, a company finds that it can sell as many of each of its three main products as it can produce. Which one of the following is most important in determining which of the three products to produce and market?
A. Sales prices per unit.
B. Contribution margin per hour of production time available.
C. Sales price less full absorption cost per hour of production time available.
D. Contribution margin per unit.
B. Contribution margin per hour of production time available.
In the short run, many costs are fixed. Therefore, contribution margin (revenues - all variable costs) becomes the best measure of profitability. Moreover, certain resources also are fixed. Accordingly, when deciding which products to produce at full capacity, the criterion should be the contribution margin per unit of the most constrained resource. This approach maximizes total contribution margin.
A manufacturer plans to produce two products, Product C and Product F, during the next year, with the following characteristics.
Product C Product F
Selling price per unit $10 $15
Variable cost per unit $ 8 $10
Expected sales (units) 20,000 5,000
Total projected fixed costs for the company are $30,000. Assume that the product mix would be the same at the breakeven point as at the expected level of sales of both products. What is the projected number of units (rounded) of Product C to be sold at the breakeven point?
A. 11,538
B. 2,308
C. 9,231
D. 15,000
C. 9,231
The composite unit contribution margin (composite UCM) is the combined UCM of the individual products.
Composite UCM = {($10 – $8) × [20,000 ÷ (20,000 + 5,000)]} +
{($15 – $10) × [5,000 ÷ (20,000 + 5,000)]}
= ($2 × 80%) + ($5 × 20%)
= $1.60 + $1.00
= $2.60
The total breakeven point is then calculated.
Total BEP in units = Fixed costs ÷ Composite UCM
= $30,000 ÷ $2.60
= 11,538.46
The breakeven point for a single product is its proportion of the total.
BEP for Product C = 11,538.46 × 80%
= 9,230.77
A company produces three distinct products as follows:
Product Percentage of Total Sales in Units Sale Price
Quinoa bars 50% $1
Millet cookies 30% $1
Amaranth pops 20% $2
The contribution margin for the Quinoa Bars is 25% of sales. Millet Cookies and Amaranth Pops both have a 50% contribution margin. Calculate the breakeven point in sales dollars if fixed costs are $675,000.
A. $1,705,263
B. $1,800,000
C. $506,757
D. $675,000
A. $1,705,263
Weighted-average UCM is 0.475 {[($1 × .25%) × 50%] + [($1 × 50%) × 30%] + [($2 × 50%) × 20%]}. Weighted-average selling price is $1.20 [(50% × $1) + (30% × $1) + (20% × $2)]. Thus, weighted-average CMR is 0.3958333 (.475 ÷ $1.20). The breakeven point in sales dollars is $1,705,263 ($675,000 ÷ 0.3958333).
Siberian Ski Company recently expanded its manufacturing capacity to allow it to produce up to 15,000 pairs of cross-country skis of the mountaineering model or the touring model. The sales department assures management that it can sell between 9,000 pairs and 13,000 pairs (units) of either product this year. Because the models are very similar, Siberian Ski will produce only one of the two models. The information below was compiled by the accounting department.
Selling price per unit
Mountaineering: $88.00
Touring: $80.00
Variable costs per unit
Mountaineering: 52.80
Touring: 52.80
Fixed costs will total $369,600 if the mountaineering model is produced but will be only $316,800 if the touring model is produced. Siberian Ski is subject to a 40% income tax rate.
If Siberian Ski Company desires an after-tax net income of $24,000, how many pairs of touring model skis will the company have to sell?
A. 13,118 pairs.
B. 12,529 pairs.
C. 13,853 pairs.
D. 4,460 pairs.
A. 13,118 pairs.
The breakeven sales volume equals total fixed costs divided by the unit contribution margin (UCM). In the breakeven formula, the desired profit should be treated as a fixed cost. Because the UCM is stated in pretax dollars, the targeted profit must be adjusted for taxes. Thus, the targeted after-tax net income of $24,000 is equivalent to a pretax profit of $40,000 [$24,000 ÷ (1.0 – 0.40 tax rate)]. The sum of the pretax profit and the fixed costs is $356,800 ($316,800 + $40,000). Consequently, the desired sales volume is 13,118 pairs of touring skis [$356,800 ÷ ($80 selling price – $52.80 unit variable cost)].
Siberian Ski Company recently expanded its manufacturing capacity to allow it to produce up to 15,000 pairs of cross-country skis of the mountaineering model or the touring model. The sales department assures management that it can sell between 9,000 pairs and 13,000 pairs (units) of either product this year. Because the models are very similar, Siberian Ski will produce only one of the two models. The information below was compiled by the accounting department.
Selling price per unit
Mountaineering: $88.00
Touring: $80.00
Variable costs per unit
Mountaineering: 52.80
Touring: 52.80
Fixed costs will total $369,600 if the mountaineering model is produced but will be only $316,800 if the touring model is produced. Siberian Ski is subject to a 40% income tax rate.
If the Siberian Ski Company Sales Department could guarantee the annual sale of 12,000 pairs of either model, Siberian Ski would
A. Produce 12,000 pairs of touring skis because they have a lower fixed cost.
B. Be indifferent as to which model is sold because each model has the same variable cost per unit.
C. Produce 12,000 pairs of mountaineering skis because they have a lower breakeven point.
D. Produce 12,000 pairs of mountaineering skis because they are more profitable.
D. Produce 12,000 pairs of mountaineering skis because they are more profitable.
Preparing income statements determines which model will produce the greater profit at a sales level of 12,000 pairs. Thus, as indicated below, the mountaineering skis should be produced.
Mountain / Touring
Sales $1,056,000 / $960,000
Variable costs (633,600) / (633,600)
Fixed costs (369,600) / (316,800)
Operating Income $ 52,800 / $ 9,600
Siberian Ski Company recently expanded its manufacturing capacity to allow it to produce up to 15,000 pairs of cross-country skis of the mountaineering model or the touring model. The sales department assures management that it can sell between 9,000 pairs and 13,000 pairs (units) of either product this year. Because the models are very similar, Siberian Ski will produce only one of the two models. The information below was compiled by the accounting department.
Selling price per unit
Mountaineering: $88.00
Touring: $80.00
Variable costs per unit
Mountaineering: 52.80
Touring: 52.80
Fixed costs will total $369,600 if the mountaineering model is produced but will be only $316,800 if the touring model is produced. Siberian Ski is subject to a 40% income tax rate.
The total sales revenue at which Siberian Ski Company would make the same profit or loss regardless of the ski model it decided to produce is
A. $880,000
B. $422,400
C. $924,000
D. $686,400
A. $880,000
The sales revenue at which the same profit or loss will be made equals the unit price times the units sold for each kind of skis. Accordingly, if M is the number of units sold of mountaineering skis and T is the number of units sold of touring skis, this level of sales revenue may be stated as $88M or $80T, and M is therefore equal to ($80 ÷ $88)T. Moreover, given the same profit or loss, the difference between sales revenue and total costs (variable + fixed) will also be the same for the two kinds of skis. Solving the equation below by substituting for M yields sales revenue of $880,000 [(11,000 × $80) or (10,000 × $88)].
SalesM – VCM – FCM = SalesT – VCT – FCT
$88M – $52.80M – $369,600 = $80T – $52.80T – $316,800
$35.2M – $52,800 = $27.2T
$35.2($80 ÷ $88)T = $27.2T + $52,800
T = 11,000 units
M = 10,000 units
MultiFrame Company has revenue and cost budgets for the two products it sells as shown to the right.
The budgeted unit sales equal the current unit demand, and total fixed overhead for the year is budgeted at $975,000. Assume that the company plans to maintain the same proportional mix. In numerical calculations, MultiFrame rounds to the nearest cent and unit.
Plastic Frames / Glass Frames
Sales price $10.00 / $15.00
Direct materials (2.00) / (3.00)
Direct labor (3.00) / (5.00)
Fixed overhead (3.00) / (4.00)
Net income per unit $ 2.00 / $ 3.00
Budgeted unit sales 100,000 / 300,000
The total number of units MultiFrame needs to produce and sell to break even is
A. 150,000 units.
B. 354,545 units.
C. 177,273 units.
D. 300,000 units.
A. 150,000 units.
The calculation of the breakeven point is to divide the fixed costs by the contribution margin per unit. This determination is more complicated for a multi-product firm. If the same proportional product mix is maintained, one unit of plastic frames is sold for every three units of glass frames. Accordingly, a composite unit consists of four frames: one plastic and three glass. For plastic frames, the unit contribution margin is $5 ($10 – $2 – $3). For glass frames, the unit contribution margin is $7 ($15 – $3 – $5). Thus, the composite unit contribution margin is $26 ($5 + $7 + $7 + $7), and the breakeven point is 37,500 packages ($975,000 FC ÷ $26). Because each composite unit contains four frames, the total units sold equal 150,000.
MultiFrame Company has revenue and cost budgets for the two products it sells as shown to the right.
The budgeted unit sales equal the current unit demand, and total fixed overhead for the year is budgeted at $975,000. Assume that the company plans to maintain the same proportional mix. In numerical calculations, MultiFrame rounds to the nearest cent and unit.
Plastic Frames / Glass Frames
Sales price $10.00 / $15.00
Direct materials (2.00) / (3.00)
Direct labor (3.00) / (5.00)
Fixed overhead (3.00) / (4.00)
Net income per unit $ 2.00 / $ 3.00
Budgeted unit sales 100,000 / 300,000
The total number of units needed to break even if the budgeted direct labor costs were $2 for plastic frames instead of $3 is
A. 154,028 units.
B. 144,444 units.
C. 156,000 units.
D. 146,177 units.
B. 144,444 units.
If the labor costs for the plastic frames are reduced by $1, the composite unit contribution margin will be $27 {($10 – $2 – $2) + [($15 – $3 – $5) × 3]}. Hence, the new breakeven point is 144,444 units [4 units × ($975,000 FC ÷ $27)].
MultiFrame Company has revenue and cost budgets for the two products it sells as shown to the right.
The budgeted unit sales equal the current unit demand, and total fixed overhead for the year is budgeted at $975,000. Assume that the company plans to maintain the same proportional mix. In numerical calculations, MultiFrame rounds to the nearest cent and unit.
Plastic Frames / Glass Frames
Sales price $10.00 / $15.00
Direct materials (2.00) / (3.00)
Direct labor (3.00) / (5.00)
Fixed overhead (3.00) / (4.00)
Net income per unit $ 2.00 / $ 3.00
Budgeted unit sales 100,000 / 300,000
The total number of units needed to break even if sales were budgeted at 150,000 units of plastic frames and 300,000 units of glass frames with all other costs remaining constant is
A. 171,958 units.
B. 418,455 units.
C. 153,947 units.
D. 365,168 units.
C. 153,947 units.
The unit contribution margins for plastic frames and glass frames are $5 ($10 – $2 – $3) and $7 ($15 – $3 – $5), respectively. If the number of plastic frames sold is 50% of the number of glass frames sold, a composite unit will contain one plastic frame and two glass frames. Thus, the composite unit contribution margin will be $19 ($5 + $7 + $7), and the breakeven point in units will be 153,947 [3 units × ($975,000 ÷ $19)].
A firm produces and sells two main products, with contribution margins per unit as follows.
- Product A: $10.00 per unit
- Product B: $8.00 per unit
Fixed costs for the year are budgeted at $264,480, and the firm calculated its breakeven point at 28,500 units. What percentage of units sold are expected to be Product A?
A. 64%
B. 56%
C. 44%
D. 36%
A. 64%
The first step is to find the average contribution margin of one unit, $9.28 ($264,480 ÷ 28,500). Then, set the average contribution margin equal to the proportion, X, of Product A, multiplied by Product A’s contribution margin plus the proportion, Y, of Product B, multiplied by Product B’s contribution margin ($9.28 = $10X + $8Y). As X and Y are proportions of 1, either is equal to 1 less the other (Y = 1 – X). Therefore, it is possible to solve for the proportion X algebraically by substituting the Y value in the earlier equation with the later equation, as follows:
$9.28 = $10X + $8Y; Y = 1 – X
$9.28 = $10X + $8 (1 – X)
$9.28 = $10X + $8 – $8X
$1.28 = $2X
X = .64
Thus, 64% of the contribution margin is contributed by Product A.
