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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        (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