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Chapter 11 Class Problem

James R. Martin, Ph.D., CMA

Professor Emeritus, University of South Florida

**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
(This produces an after tax loss equal to 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__ (Note the after
tax loss is 78,000 - 31,200 = 46,800).

Loss after
tax
(46,800)

Add
depreciation
46,800

Cash flow after
taxes
0

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