P 4-5. Break-Even , “What if”
a. Number of trips
(6 per week × 52 weeks)
Revenue per trip ($360 x 4 passengers)
Total revenue ($1,440 per trip x 312 trips)
312
$1,440
$449,280
Variable costs:
Fuel
Maintenance
Total variable costs
$147,976
127,920
$275,896
Variable costs per trip ($275,896 ÷ 312)
$884.28
Contribution margin per trip ($1,440 − $884.28)
$555.72
Fixed costs:
Salary
$ 70,000
Depreciation of plane
25,000
Depreciation of office equipment
2,800
Rent
40,000
Insurance
20,000
Miscellaneous
Total fixed costs
7,500
$165,300
Breakeven number of trips is ($165,300 ÷ $555.72) = 297 trips.
b. If Michael draws a salary of $110,000, fixed costs will increase by $40,000 to
$205,300. In this case, the breakeven number of trips is ($205,300 ÷ $555.72)
369. Note that this number of trips is not feasible if Michael can only fly one
round trip per day, unless he adds a seventh day.
c. The average before tax profit per round trip is $8,084 ÷ 312 = $25.91.
d. The incremental profit associated with adding a round trip is the contribution
margin per trip, which is $555.72.
P 4-11. Break-Even Analysis, Margin of Safety, Increase in Profit
a.
Total
Sales ($1,200 x 1,500 apps)
Per unit
Percent
$1,800,000
$1,200
100%
Less variable expenses
1,100,000
$740
61.67%
Contribution margin
$690,000
$460
38.33%
Less fixed expenses
300,000
Operating income
$390,000
Breakeven point (in number of apps) = $300,000 / $460 = 652 units (rounded)
Contribution margin ratio = $460 / $1,200 = 38.33%
Breakeven point (in sales dollars) = $300,000 / 38.33% = $782,677 (rounded)
b. Margin of safety in units = 1,500 – 652 = 848 units
Margin of safety in dollars = $1,800,000 - $782,677 = $1,017,326
c. Target profit (in units) = ($300,000 + $450,000) / $460 = 1,630 units
Target profit (in dollars) = ($300,000 + $450,000) / 38.33% = $1,956,692 (rounded)
d.
New income statement:
Sales
Less variable expenses
Contribution margin
Less fixed expenses
Operating income
$
Total
Per unit
Percent
$2,124,000
$1,200
100%
1,309,800
$740
61.67%
814,200
$460
38.33%
380,000
$434,200
Yes, they should increase their advertising, since their operating income will rise to
$434,200 from $390,000 in the original scenario.
P 4-12. Multiproduct CVP
a.
Contribution margin
Sales
Audio
Video
Car
$1,120,000
$ 460,000
$ 614,400
3,200,000
1,920,000
1,280,000
0.3500
0.2395
0.4800
Contribution margin ratio
(CM ÷ sales)
b. A $125,000 increase in Audio sales would increase profit by $43,750 while the
effect for Video would be $29,938 and $60,000 for the Car product line. All else
equal, it would be better to increase sales of Car products.
c. The weighted average contribution margin ratio is $2,194,400 ÷ $6,400,000 =
.342875
The break-even level of sales is:
(Direct fixed + common fixed) ÷ contribution margin ratio = $4,360,190.
($785,000 + 710,000) ÷ .342875 = $4,360,190
d. Sales need to achieve a profit of $1,800,000 is
($1,800,000 + $785,000 + $710,000) ÷ .342875 = $9,609,916.
e. Audio sales = ($3,200,000 ÷ 6,400,000) × $9,609,916 = $4,804,958
Video sales = ($1,920,000 ÷ 6,400,000) × $9,609,916 = $2,882,975
Car sales = ($1,280,000 ÷ 6,400,000) × $9,609,916 = $1,921,983