16–8
1. Before-tax income = $25,200/(1 – 0.40) = $42,000
2.
Units = ($150,000 + $42,000)/$0.80 = $192,000/$0.80 = 240,000
Before-tax income = $25,200/(1 – 0.30) = $36,000 Units = ($150,000 + $36,000)/$0.80 = $186,000/$0.80 = 232,500
Before-tax income = $25,200/(1 – 0.50) = $50,400 Units = ($150,000 + $50,400)/$0.80 = $200,400/$0.80 = 250,500 215,000 – 187,500 = 27,500 pans or
$526,750 – $459,375 = $67,375
3.
4.
528
16–9
Sales
Variable costs
Contribution margin Fixed costs
Operating income (loss)
Units sold Price/unit
Variable cost/unit
Contribution margin/unit Contribution margin ratio Break-even in units
A $ 5,000 4,000 $ 1,000 500* $ 500 1,000* $5 $4* $1* 20%* 500*
B $ 15,600* 11,700 $ 3,900 4,000 $ (100)* 1,300 $12* $9 $3 25%* 1,334*
C $ 16,250* 9,750 $ 6,500* 6,100* $ 400 125 $130 $78* $52* 40% 118*
D $9,000 5,400* $3,600* 750 $2,850 90 $100* $60* $40* 40%* 19*
*Designates calculated amount.
Note: When the calculated break-even in units includes a fractional amount, it has been rounded up to the next whole unit.
16–10
1. Variable cost ratio = Variable costs/Sales = $399,900/$930,000 = 0.43, or 43%
2. 3. 4.
Contribution margin ratio = (Sales – Variable costs)/Sales = ($930,000 – $399,900)/$930,000 = 0.57, or 57% Break-even sales revenue = $307,800/0.57 = $540,000 Margin of safety = Sales – Break-even sales = $930,000 – $540,000 = $390,000
Contribution margin from increased sales = ($7,500)(0.57) = $4,275 Cost of advertising = $5,000
No, the advertising campaign is not a good idea, because the company’s op-erating income will decrease by $725 ($4,275 – $5,000).
529
16–11
1. 2.
Income 0 0 $570,000 P
= Revenue – Variable cost – Fixed cost
= 1,500P – $300(1,500) – $120,000 = 1,500P – $450,000 – $120,000 = 1,500P = $380
$160,000/($3.50 – Unit variable cost) = 128,000 units Unit variable cost = $2.25
16–12
1. Contribution margin per unit = $5.60 – $4.20* = $1.40
*Variable costs per unit:
$0.70 + $0.35 + $1.85 + $0.34 + $0.76 + $0.20 = $4.20
Contribution margin ratio = $1.40/$5.60 = 0.25 = 25%
2. Break-even in units = ($32,300 + $12,500)/$1.40 = 32,000 boxes
3. 4. 5.
Break-even in sales = 32,000 ? $5.60 = $179,200 or = ($32,300 + $12,500)/0.25 = $179,200 Sales ($5.60 ? 35,000)
Variable costs ($4.20 ? 35,000) Contribution margin Fixed costs
Operating income
$ 196,000 147,000 $ 49,000 44,800 $ 4,200 Margin of safety = $196,000 – $179,200 = $16,800
Break-even in units = 44,800/($6.20 – $4.20) = 22,400 boxes New operating income = $6.20(31,500) – $4.20(31,500) – $44,800 = $195,300 – $132,300 – $44,800 = $18,200 Yes, operating income will increase by $14,000 ($18,200 – $4,200).
530
16–13
1. Variable cost ratio = $126,000/$315,000 = 0.40
Contribution margin ratio = $189,000/$315,000 = 0.60 2. $46,000 ? 0.60 = $27,600
3. Break-even revenue = $63,000/0.60 = $105,000 Margin of safety = $315,000 – $105,000 = $210,000 4. Revenue = ($63,000 + $90,000)/0.60 = $255,000
5.
Before-tax income = $56,000/(1 – 0.30) = $80,000
Note: Tax rate = $37,800/$126,000 = 0.30
Revenue = ($63,000 + $80,000)/0.60 = $238,333
Sales ............................................................................... Less: Variable expenses ($238,333 ? 0.40) ................. Contribution margin ...................................................... Less: Fixed expenses ................................................... Income before income taxes ........................................ Income taxes ($80,000 ? 0.30) ......................................
Net income ................................................................
531 $ 238,333
95,333 $ 143,000 63,000 $ 80,000 24,000 $ 56,000
16–14
1.
Operating income (0.20)Revenue (0.20)Revenue (0.40)Revenue Revenue = Revenue(1 – Variable cost ratio) – Fixed cost
= Revenue(1 – 0.40) – $24,000 = (0.60)Revenue – $24,000 = $24,000 = $60,000
$ 60,000 24,000 $ 36,000 24,000 $ 12,000
Sales ............................................................................... Variable expenses ($60,000 ? 0.40) .............................. Contribution margin ...................................................... Fixed expenses .............................................................. Operating income .....................................................
$12,000 = $60,000 ? 20%
2. If revenue of $60,000 produces a profit equal to 20 percent of sales and if the
price per unit is $10, then 6,000 units must be sold. Let X equal number of units, then:
Operating income 0.20($10)X $2X $4X X
0.25($10)X
$2.50X $3.50X
X
= (Price – Variable cost) – Fixed cost = ($10 – $4)X – $24,000 = $6X – $24,000 = $24,000
= 6,000 buckets = $6X – $24,000 = $6X – $24,000 = $24,000
= 6,857 buckets
$68,570 27,428 $41,142 24,000 $17,142
Sales (6,857 ? $10) ......................................................... Variable expenses (6,857 ? $4) ..................................... Contribution margin ...................................................... Fixed expenses .............................................................. Operating income ..................................................... $17,142* = 0.25 ? $68,570 as claimed *Rounded down.
Note: Some may prefer to round up to 6,858 units. If this is done, the operat-ing income will be slightly different due to rounding.
532