Chapter 11 Class Problem
James R. Martin, Ph.D., CMA
Professor Emeritus, University of South Florida
Chapter 11 | MAAW's Textbook Table of Contents
The Micro Company produces a single product that has the following costs:
Direct material per unit $30.
Direct labor per unit 24.
Variable overhead per unit 21.
Variable selling & administrative per unit 25.
Fixed cost are $60,000 for manufacturing and $15,000 for selling & administrative.
The product sells for $200 per unit.
1. What is Micro Company’s break-even point in units?
CM per unit = P-V = 200 - (75+25) = 100.
X = 75,000 ÷ 100 = 750 units.
2. How many units would Micro Company need to sell to earn $20,000 net income before taxes?
X = (75,000 + 20,000) ÷ 100 = 950 units.
The Bibb Company produces a single product with the following sales price and costs:
Price = $160.
Variable manufacturing costs per unit = $53.
Variable selling & administrative costs per unit = $22.
Fixed manufacturing costs = $60,000.
Fixed selling & administrative costs = $46,000.
The tax rate is 40 percent.
3. How many units would Bibb Company need to sell to earn $29,985 after taxes?
Contribution per unit = P -V = 160 - (53 + 22) = 85
85X = 106,000 + (29,985 ÷ .6)
(Dividing by 1-T or .6 converts desired NIAT to desired NIBT).
85X = 106,000 + 49,975
X = 1,835 units
4. How many units would Bibb Company need to sell to earn a 20% return on sales before taxes (i.e., NIBT ÷ Sales$ = .20)?
85X = 106,000 + .2(160X)
85X = 106,000 + 32X
53X = 106,000
X = 2,000 units
5. How many units would Bibb Company need to sell to earn a 12% return on sales after taxes (i.e., NIAT ÷ Sales$ = .12)?
85X = 106,000 + [.12(160X)] ÷ .6
(Dividing by .6 converts desired NIAT to desired NIBT).
85X = 106,000 + 32X
X = 2,000 units
Deskjet Company produces color printers.
The product sells for $300,
has a variable cost ratio (V/P) of .60 and
total fixed costs of $600,000.
6. What is Deskjet’s break-even point in dollars?
Since V/P = .60, the contribution margin ratio = 1 - V/P = 1 - .60 = .40.
This is because (P-V)/P + V/P = 1.
$600,000 ÷ .40 = $1,500,000
7. What is Deskjet’s break-even point in units?
Divide the BEP in Sales$ by the price to find the BEP in units:
$1,500,000 ÷ $300 = 5,000 units
or use CM per unit in the equation: 300 - .6(300) or .4(300) = 120 CM per unit.
$600,000 ÷ $120 = 5,000 units
Pool Company has total fixed costs of $156,000 and sells two products as follows:
| Product | Price | Variable cost | Budgeted Sales Mix in Units |
| P1 | $10 | $5 | 60% |
| P2 | 20 | 8 | 40% |
8. How many mixed units would Pool Company need to sell to break-even based on the budgeted mix?
The contribution margin per unit for P1 is 10-5 = $5, and 20-8 = $12 for P2.
Then calculate the weighted average contribution margin using the mix ratios as the weights:
W = ($5)(.6) + ($12)(.4) = $7.8
X = $156,000 ÷ 7.8 = 20,000 mixed units.
9. How many mixed units would Pool Company need to sell to generate $46,800 net income after taxes based on the budgeted mix? Assume the tax rate is 40%.
7.8X = $156,000 + (46,800 ÷ .6)
(Dividing by .6 converts desired NIAT to desired NIBT).
7.8X = 156,000 + 78,000
X = 234,000 ÷ 7.8 = 30,000 mixed units
10. How many units of each product would be needed to generate $78,000 net income before taxes based on the budgeted mix?
(This is the same as question 9, but stated in terms of desired NIBT).
(156,000 + 78,000) ÷ 7.8 = 30,000 mixed units
P1 = .6(30,000) = 18,000 units of P1
P2 = .4(30,000) = 12,000 units of P2
11. How many mixed units would Pool Company need to sell to generate a 40% return on sales before taxes?
The weighted average price is (.6)(10) + (.4)(20) = $14
7.8X = 156,000 + .4(14X)
X = 70,909.09 mixed units
12. How many mixed units would Pool Company need to sell to generate a 30% return on sales after taxes?
7.8X = 156,000 + [.3(14X) ÷ .6]
(Dividing by .6 converts desired NIAT to desired NIBT).
X = 195,000
13. Assume Pool Company’s non-cash fixed costs are $46,800. What is their cash flow break-even point in mixed units before considering taxes?
7.8X = 156,000 - 46,800 (Note that this would result in an accrual accounting loss of 46,800,
7.8X = 109,200 but the cash inflow only needs to be $109,200 to cover the outflow).
X = 14,000 mixed units
14. What is Pool Company’s cash flow break-even point after taxes in mixed units?
We can use the after tax equation:
(1-.4)(7.8)X = (1-.4)(156,000) - 46,800
4.68X = 93,600 - 46,800
X = 10,000 mixed units
Check: TCM
(7.8)(10,000) 78,000
Less TFC
156,000
Before tax
Loss
(78,000)
Add tax savings .4(78,000) 31,200
Loss after
tax
(46,800)
Add
depreciation
46,800
Cash flow after
taxes
0
Note the after tax loss is 78,000 - 31,200 = 46,800.
Note: We can also use the following approach, although it is perhaps more confusing.
7.8X = 156,000 - (46,800 ÷
.6)
7.8X = 156,000 -
78,000
(This converts the 46,800 to the before tax loss of 78,000).
7.8X = 78,000
X = 10,000 mixed units.
15. How many mixed units would Pool Company need to produce and sell to generate an after tax cash flow of $56,160?
4.68X = 93,600 - 46,800 + 56,160 Using the after tax
equation.
4.68X = 93,600 + 9,360
X = 102,960 ÷ 4.68
X = 22,000 mixed units
Check: TCM
(7.8)(22,000) 171,600
Less TFC
156,000
NIBT
15,600
Less tax
(.4)(15,600) -
6,240
NIAT
9,360
Add
depreciation
46,800
Cash flow after
taxes $56,160