Chapter 12
Differential Analysis: The Key to Decision
Making
Solutions to Questions
12-1 A relevant cost is a cost that differs in
change in cost (or benefit) that will result from
some proposed action. An opportunity cost is
12-3 No. Variable costs are relevant costs
in total amount in direct proportion to changes
12-8 Not necessarily. An apparent loss may
be the result of allocated common costs or of
as a result of dropping the product is less than
12-9 Allocations of common fixed costs can
12–10 If a company decides to make a part
internally rather than to buy it from an outside
are machine time, direct labor time, floor space,
12–13 Joint products are two or more products
The Foundational 15
1. The total traceable fixed manufacturing overhead for Alpha and Beta is
computed as follows:
Alpha
Beta
Traceable fixed overhead per unit (a) ……..
$16
$18
Level of activity in units (b) …………………..
100,000
100,000
Total traceable fixed overhead (a) × (b) ….
$1,600,000
$1,800,000
2. The total common fixed expenses is computed as follows:
Alpha
Beta
Common fixed expenses per unit (a) ………
$15
$10
Level of activity in units (b) …………………..
100,000
100,000
Total common fixed expenses (a) × (b) …..
$1,500,000
$1,000,000
The company’s total common fixed expenses would be $2,500,000.
3. The profit impact is computed as follows:
Per
Total
Unit
10,000 units
Incremental revenue ……………………….
$80
$800,000
Incremental costs:
Variable costs:
Direct materials ………………………….
30
300,000
Direct labor ……………………………….
20
200,000
Variable manufacturing overhead …..
7
70,000
Variable selling expenses ……………..
12
120,000
Total variable cost ………………………..
$69
690,000
Incremental net operating income ………
$110,000
The Foundational 15 (continued)
4. The profit impact is computed as follows:
Per
Unit
Incremental revenue ……………………….
$39
Incremental costs:
Variable costs:
Direct materials ………………………….
12
Direct labor ……………………………….
15
Variable manufacturing overhead …..
5
Variable selling expenses ……………..
8
Total variable cost ………………………..
$40
Incremental net operating income ………
$ (5,000)
5. The profit impact is computed as follows:
Incremental revenue
(10,000 units × $80) (a) …………………….…….
$800,000
Incremental variable costs:
Direct materials (5,000 units × $30) ………………….
$150,000
Direct labor (5,000 units × $20) ……………………….
100,000
Variable manufacturing overhead
(5,000 units × $7) ………………………..…
35,000
Variable selling expenses
(5,000 units × $12) …………………………..
60,000
Total incremental variable cost (b) ………..…………….
345,000
Foregone sales to regular customers
(5,000 units × $120) (c) …………………….…….
600,000
Incremental net operating income
(a) − (b) – (c) ………………………………….…………….
$(145,000)
Note to instructors: Emphasize to students that the variable costs
related to 5,000 units of production are irrelevant to the decision
because they will be incurred whether the special order is accepted or
rejected.
The Foundational 15 (continued)
6. The profit impact of dropping the Beta product line is computed as
follows:
Contribution margin lost if the Beta product line is
dropped* ………………………………………………………..
$(3,600,000)
Traceable fixed manufacturing overhead …………………..
1,800,000
Decrease in net operating income if Beta is dropped ……
$(1,800,000)
* Beta’s contribution margin per unit is $40 ($80 − $40). Therefore, the
decrease in contribution margin if Beta is dropped would be $3,600,000
(90,000 units × $40).
Note to instructors: Emphasize that the traceable fixed manufacturing
overhead is avoidable and the common fixed expenses are not.
7. The profit impact of dropping the Beta product line is computed as
follows:
Contribution margin lost if the Beta product line is
dropped* ………………………………………………………....
$(1,600,000)
Traceable fixed manufacturing overhead …………………....
1,800,000
Increase in net operating income if Beta is dropped ……..
$ 200,000
* Beta’s contribution margin per unit is $40 ($80 − $40). Therefore, the
decrease in contribution margin if Beta is dropped would be $1,600,000
(40,000 units × $40).
8. The profit impact of dropping the Beta product line is computed as
follows:
Contribution margin lost if the Beta product line is
dropped …………………………………………………………...
$(2,400,000)
Traceable fixed manufacturing overhead …………………....
1,800,000
Contribution margin on additional Alpha sales* …………
765,000
Increase in net operating income if Beta is dropped ……..
$ 165,000
* Alpha’s contribution margin per unit is $51 ($120 − $69). Therefore,
the increase in Alpha’s contribution margin if Beta is dropped would be
$765,000 (15,000 units × $51).
The Foundational 15 (continued)
9. The profit impact of buying 80,000 Alphas from a supplier rather than
making them is computed as follows:
Make
Buy
Cost of purchasing (80,000 units × $80) ……..
$6,400,000
Direct materials (80,000 units × $30) …………
$2,400,000
Direct labor (80,000 units × $20) ………………
1,600,000
Variable manufacturing overhead
(80,000 units × $7) ……………………………..
560,000
Traceable fixed manufacturing overhead ……..
1,600,000
Total costs ……………………………………………
$6,160,000
$6,400,000
Difference in favor of continuing
to make the Alphas ……………….
$240,000
Note to instructors: Emphasize that the variable selling expenses are
irrelevant to this decision because they will be incurred regardless of
whether the company makes or buys its Alphas.
10. The profit impact of buying 50,000 Alphas from a supplier rather than
making them is computed as follows:
Make
Buy
Cost of purchasing (50,000 units × $80) ……..
$4,000,000
Direct materials (50,000 units × $30) …………
$1,500,000
Direct labor (50,000 units × $20) ………………
1,000,000
Variable manufacturing overhead
(50,000 units × $7) ……………………………..
350,000
Traceable fixed manufacturing overhead ……..
1,600,000
Total costs ……………………………………………
$4,450,000
$4,000,000
Difference in favor of buying
Alphas from the supplier ……..…
$450,000
Note to instructors: Emphasize that the variable selling expenses are
irrelevant to this decision because they will be incurred regardless of
whether the company makes or buys its Alphas.
The Foundational 15 (continued)
11. The pounds of raw material per unit are computed as follows:
Alpha
Beta
Direct material cost per unit (a) ……………………….
$30
$12
Cost per pound of direct materials (b) ……………….
$6
$6
Pounds of direct materials per unit (a) ÷ (b) ……….
5
2
12. The contribution margins per pound of raw materials are computed as
follows:
Alpha
Beta
Selling price per unit………………………….
$120
$80
Variable cost per unit ………………………..
69
40
Contribution margin per unit (a) …………..
$ 51
$40
Pounds of direct material required to
produce one unit (b) ……………………….
5 pounds
2 pounds
Contribution margin per pound (a) ÷ (b) .
$10.20
$20.00
13. The optimal number of units to produce would be computed as
follows:
Product
Pounds
Per Unit
Units
Produced
Total
Pounds
Beta ……………………………..
2
60,000
120,000
Alpha …………………………….
5
8,000
40,000
Total pounds available ………
160,000
The Foundational 15 (continued)
14. The total contribution margin would be computed as follows:
Alpha
Beta
Number of units produced (a) ………………………….
8,000
60,000
Contribution margin per unit (b) ……………………….
$51
$40
Total contribution margin (a) × (b) …………..……….
$408,000
$2,400,000
The company’s total contribution margin would be $2,808,000
($408,000 + $2,400,000).
15. The maximum price per pound is computed as follows:
Alpha
Regular direct material cost per pound ………………………..
$ 6.00
Contribution margin per pound of direct materials ………….
10.20
Maximum price to be paid per pound…………………………..
$16.20
Because the company has satisfied all demand for Betas, it would use
additional raw materials to produce Alphas.