Chapter 04 - Short-Term Decision Making
Chapter 4: Short-Term Decision Making
QUESTIONS
1.Short-term decisions differ in three primary ways. First, we assume that capacity is fixed. Second, these decisions are ad hoc and cannot be planned in advance. Last, these decisions are unique to the circumstances at the time.
2.In CVP analysis activity is measured as units produced and sold.
3.The five assumptions of CVP are: (1) selling price is constant per unit sold, (2) variable cost is constant per unit, (3) fixed cost is constant in total, (4) the number of units produced (purchased) equals the number of units sold, and (5) the sales mix is constant.
4.The breakeven point in units is the number of units that must be sold in order to cover both the fixed and variable costs. At breakeven, the company’s profits are zero. The breakeven point in dollars is the dollar amount of sales that must be generated to cover both the fixed and variable costs. If we take the breakeven point in units and multiple it by the selling price we can determine the breakeven point in dollars.
5.The contribution margin per unit is the selling price per unit minus the variable costs per unit while the contribution margin ratio is the contribution margin per unit divided by the selling price per unit.
6.Before-tax profit is calculated as the after-tax profit divided by 1 minus the tax rate.
7.We can use CVP to determine the number of units that must be sold to achieve a certain profit after taxes by using the following formula: (SP * Q – VC * Q) – FC = P / (1 –tax rate).
8.A product cost is incurred to manufacture a product while a nonproduct cost is incurred to sell the product or administer the company.
9.The three product costs are direct materials, direct labor, and manufacturing overhead. Direct materials are traced to the product, direct labor is involved in making the product, and manufacturing overhead is all the remaining product costs other than direct materials and direct labor.
10.Unit-related costs vary with units produced or sold, for example, packaging. Batch-related costs vary with the number of batches, regardless of how many units are in each batch, for example, ordering costs. Product-sustaining costs vary with the number of product lines, for example, advertising. Facility-sustaining costs do not vary with activity in the short run, for example, rent on the facilities.
11.A relevant variable must occur in the future and differ among alternatives.
12.A sunk cost is a past cost. Since the past cannot be changed, sunk costs are irrelevant.
13.An opportunity cost is a benefit forgone. Since we give up something to have something else, an opportunity cost is relevant.
14.Incremental means additional. Incremental revenues, costs, and profits are relevant, if and only if, they differ among alternatives.
15.The steps in a relevant variable analysis are: (1) identify the alternatives, (2) determine the relevant revenues, costs, and/or profits, and (3) choose the best alternative.
16.A special order decision occurs when a customer wants a reduced price, usually for buying in large volume. The selling price, the number of units desired, the unit-related costs, and the batch-related costs are relevant and the product-sustaining costs may be relevant.
17.Qualitative factors such as other customers must be considered.
18.A make-or-buy decision is an outsourcing decision where the company must decide whether to do something internally or pay someone externally to do it. Typically revenues are irrelevant in these decisions. The unit-related costs, batch-related costs, and number of units are relevant. Product-sustaining costs may also be relevant.
19.Opportunity costs arise if the company can use the space released for another activity if the primary activity is outsourced.
20.Qualitative factors such as quality and timeliness of delivery must be considered.
21.In a keep-or-drop decision the company must decide whether a product line should be discontinued. In these decisions all variables are relevant except facility-sustaining costs.
22.Qualitative factors such as related sales must be considered.
EXERCISES
E4.1$65 * Q - $24 * Q - $260,000 = Profit
E4.2LineAB is the total cost line.
Line CD is the total revenue line.
Point E is the breakeven point.
Area AEC is the loss area.
Area DEB is the profit area.
Line segment FG is the relevant range.
E4.3a.$120 - $30 = $90
b.$900,000/$90 = 10,000
c.$90/$120 = 0.75 or 75%
d.$900,000/0.55 = $$1,200,000 or
10,000 units * $120 = $1,200,000
E4.4a.0.45 = (1 – .55)
b.$1,333,333 = $600,000/0.45
c.($600,000 + $50,000)/0.45 = $1,444,444.44
E4.5a.$800,000/$40 = 20,000
b.($800,000 + $35,000)/$40 = 20,875
c.($720,000 + $35,000)/$80 = 18,875
E4.6a.$80,000/$3.25 = 24,615.38 (24,616 cans)
b.CM% = $3.25/$4.00 = 81.25%
$80,000/0.8125 = $98,461.54
c.$15,000/(1 – 0.20) = $18,750
d.($80,000 + $18,750)/$3.25 = 30,384.6 or (30,385 cans)
E4.7a.$750,000/CM = 1,000; CM = $750
b.SP - $2,000 = $750; SP = $2,750
c.Total profit = contribution margin = $750
E4.8a.$90,000/$2.65 = 33,962.26 (33,963 units)
b.New contribution margin = $3.25 - $0.48 = $2.77
$96,000/$2.77 = 34,657.04 (34,658 units)
c.We must determine when the costs of the two machines are equal:
$2.65 * Q - $90,000 = $2.77 * Q - $96,000; Q = 50,000
If the company believes it will sell more than 50,000 units, it should purchase the new machine because the variable costs are less.
E4.9
E4.10a.MOHb.DLc.MOH
d.MOHe.DMf.MOH
g.MOH h.MOH (DM)i.MOH
j.MOHk.MOHl.MOH
m.MOHn.MOHo.MOH
p.MOH
E4.11a.Bb.Uc.P
d.Be.Uf.P
g.Bh.Ui.F
j.Fk.Ul.P
m.Fn.Po.F
p.F
E4.12a.Pb.Pc.P
d.Pe.NPf.P
g.Ph.NPi.NP
j.Pk.Pl.NP
m.NPn.Po.P
E4.13Selling price$ 215
Less unit costs($90 + $70 + $50) 210
Contribution margin$ 5
* Quantity 1,500
Total contribution margin$7,500
Less batch costs (4 * $1,500) 6,000
Profit on order$1,500Accept
E4.14Selling price$ 120
Less unit costs 110
Contribution margin$ 10
* Quantity 1,000
Total contribution margin$10,000
Accept. Although the companyis only making $10 per person, the total is $10,000 and the client is important so building relationships and future business should be weighted heavily.
E4.15Reject the order. Since there is no excess capacity Gashler would give up regular customers paying $25 for special order customers paying only $20, thus, Gashler would be giving up $5 per case of oil.
If 20,000 cases of capacity exits, then only 10,000 cases of regular sales are lost:
Profit on special order ($20 - $15) * 30,000 $150,000
Profit lost on regular orders ($25 - $15) * 10,000 100,000
Additional profit if special order is accepted$ 50,000
The special order should be accepted because the profits will increase.
E4.16Make:
$115,000 ($20,000 + $55,000 + $35,000 + $5,000)
50,000 (opportunity cost)
$165,000
Buy:
$175,000 (1,000 * $175)Make
E4.17Use direct labor:
$2(labor)
1(unit-related overhead)
$3
Outsource direct labor:
$2.50(contractor’s fee)
0.30(unit-related overhead)
$2.80Accept offer
Consider quality. Also consider the dependability of contracted labor and the possible ill will caused by the layoff.
E4.18Make:
$ 8 (unit cost)
* 5,000
$40,000 (total unit cost)
5,000 (batch cost--tablecloths)
4,500 (opportunity cost: CM from additional napkin production)
200 (incremental batch cost)
$49,700
Buy:
$ 9.50
* 5,000
$47,500Buy
Consider quality.
E4.19Product C:
Revenues lost$12,000
Costs saved 10,000
Profit lost$ 2,000Keep
Consider related sales. Would sales of A or B increase if C were dropped?
E4.20Full Service:
Revenues lost$60,000
Costs saved 42,000
Profit lost$18,000Keep
Consider related sales
E4.21Profit lost (above)$18,000
Opportunity cost 11,520 ($28,800 * .4) Costs will increase also.
Profit lost$ 6,480 Keep
PROBLEMS
P4.1
a.The minimum selling price must allow Example Company to break even on the special order. The costs of the special order are $6.86 per unit and $1,500 per batch. Since the customer wants 50,000 units and we will use 2 batches the total costs of the special order are $346,000 ($6.86 * 50,000 + $1,500 * 2). Therefore the minimum selling price per unit would be $6.92 ($346,000/50,000).
b.With this option we run into a capacity problem and, therefore, will incur an opportunity cost.
Profit from special order ($1.14 * 100,000 – 2 * $1,500)$ 111,000
Opportunity cost (revenue lost) ($12 - $6.86) * 50,000 257,000
Profit from special order (146,000)
Do not accept the offer.
c.Other customers, Continuing relationship with special order customer. Long-term effects
P4.2
a.$1.05 per unit ($0.50 direct materials + $0.25 direct labor + $0.30 unit-related overhead) + $1,000 additional batch cost.
b.Selling price$ 1.75
Less unit cost 1.05
Contribution margin$ 0.70
* Quantity 5,000
Total contribution margin$3,500
Less batch cost 1,000
Profit on special order$2,500Accept
c.Other customers may want the same deal.
d.If another similar customer is not given the same price the company could be accused of price discrimination.
P4.3HINT:200,000 * $2.25 = $450,000; of this total $200,000 is facility sustaining overhead and $100,000 is batch-related overhead. The remaining $150,000 is unit-related overhead, so unit-related overhead is $150,000/200,000 = $0.75 per unit.
a.Relevant costs to make are $6.25 per unit ($2.00 direct labor + $3.50 direct material + $0.75 unit-related overhead.
b.Relevant costs to buy:
Direct labor$1.50($2.00 * 0.75)
Direct material 1.40($3.50 * 0.4)
Unit-related overhead 0.60($0.75 * 0.8)
Purchase price 1.60
Total relevant costs$5.10
c.Total relevant costs to buy are less than the total relevant costs to make, so Hahn should buy the tubes.
d.Relevant costs to buy would be $6.50 ($1.50 + $1.40 + $0.60 + $3.00), so Hahn should make the tubes.
e.Relevant costs to make are $6.25 * 200,000 + $60,000 = $1,310,000 while the relevant costs to buy are $6.50 * 200,000 = $1,300,000. Therefore, Hahn should buy the tubes.
f.Quality and reliability
P4.4
a.Relevant costs to make are $50,000 ($7,000 direct materials + $8,000 direct labor + $5,000 unit-related overhead + $30,000 batch-related overhead). Relevant costs to buy are $48,000 ($48 * 1,000). The company should continue to buy XJ7.
b.Relevant costs to make are $32,000 ($7,000 direct materials + $8,000 direct labor + $5,000 unit-related overhead + $12,000 batch-related overhead ($30,000 * 2/5)). Relevant costs to buy are $48,000 ($48 * 1,000). The company should make XJ7.
c.Quality should be considered as well as timeliness.
P4.5
a.$175 * Q - $65 * Q - $90,000 = 0.1 ($175*Q)
b.$110 * Q - $90,000 = $17.50 * Q
$92.50 Q = $90,000
Q = 972.97 or 973
c.$210 * Q - $65 * Q - $90,000 = 0.1 * $210 * Q
$145 * Q - $90,000 = $21 * Q
$124 * Q = $90,000
Q = 725.8 or (726 offices)
d.Volume may go down because customers are upset with the increase in price.
P4.6Variable cost per unit = $3 ($24,000/8,000); contribution margin per unit = $15
a.$78,000/$15 = 5,200
b.($78,000 + $44,000)/$15 = 8,133.33 (8,134 widgets)
c.Before-tax profit = $44,000/0.7 = $62,857.14
($78,000 + $62,857.14)/$15 = 9,390.48 (9,391 widgets)
d.$15 * Q - $78,000 = 0.2 * $18 * Q
$15 * Q - $78,000 = $3.60 * Q
$11.40 * Q = $78,000
Q = 6,842.11 (6,843 widgets)
e.Before-tax profit = (0.2 * $18 * Q)/0.7 = $5.14 * Q
$15 * Q - $78,000 = $5.14 * Q
$9.86 * Q = $78,000
Q = 7,910.75 (7,911 widgets)
P4.7Selling price per client = $1,925 ($800 + $75 * 15). Variable costs per client = $380 ($80 + $20 * 15). The contribution margin per client = $1,545
a.$9,000/$1,545 =5.83 (6 clients)
b.($9,000 + $8,000)/ $1,545 = 11
c.(50 * $1,545) - $9,000 = $68,250
d.New selling price per client = $2,045 ($800 * 1.15 + $75 * 15) and, therefore, the new contribution margin per client = $1,665 ($2,045 - $380).
$9,000/$1,665 = 5.41 (6 clients)
e.(40 * $1,665) - $9,000 = $57,600. The price should not be increased.
f.New variable cost per client = $350 ($80 + $18 * 15) and, therefore, the new contribution margin is $1,575 ($1,925 - $350).
$9,000/$1,575 = 5.71 (6 clients)
g.(55 * $1,575) - $9,000 = $77,625
P4.8
a.Selling price per unit = $20 ($16,000,000/800,000)
b.Variable cost per unit = $2.50 ($2,000,000/800,000)
c.Contribution margin per unit = $17.50 ($20 - $2.50)
d.Contribution margin ratio = 87.5% ($17.50/$20)
e.$8,000,000/$17.50 = 457,142.8571 (457,143 units)
f.$8,000,000/0.875 = $9,142,857.14 (or 457,143 * $20 = $9,142,860 rounding error)
P4.9Cost of goods sold = $631,000. Unit-related costs are $225,000 ($0.75 * 300,000), batch-related costs are $96,000 (300,000/2,500 * $800), product-sustaining costs are $10,000 (research & development) and, therefore facility-sustaining costs are $300,000. Selling & administrative costs are $225,000. Unit-related costs are $45,000 ($0.15 * 300,000), product-sustaining costs are $120,000 (advertising) and, therefore, facility-sustaining costs are $60,000.
a.Revenues lost$837,000
Cost of goods sold saved:
Unit-related$225,000
Batch-related 96,000
Product-sustaining 10,000
Selling & administrative costs saved:
Unit-related 45,000
Product-sustaining 120,000
Total costs saved$496,000
TexMex should keep the product line since the relevant revenues lost exceed the relevant costs saved.
b.Related sales, future research & development
P4.10GammaOmegaLambda
Sales in units 1,800 400 1,500
Selling price per unit $0.50 $3.00 $1.00
Unit-related COGS 0.45 1.50 0.83
Unit-related S & A** 0.03 0.17 0.06
Contribution margin per unit $0.02 $1.33 $0.11
**(Amount given less $150) divided by the number of units
a.Alternative #1:
Increase in contribution margin from Lambda
(1,500 * 0.2 * $0.11)$ 33.00
Increase in advertising cost (10.00)
Contribution margin lost from Gamma
(1,800 * $0.02) (36.00)
Increase in profits$(13.00)
Alternative #2:
Increase in contribution margin from Omega
(400 * 0.4 * $1.33)$212.80
Contribution margin lost from Gamma & Lambda
(1,800 * $0.02) + (1,500 * $0.11)(201.00)
Increase in profits$ 11.80
Alternative #3:
Increase in contribution margin from Gamma
(1,800 * 0.15 * $0.02)$ 5.40
Increase in contribution margin from Lambda
(1,500 * 0.1 * $0.11) 16.50
Increase in promotion costs (50.00)
Increase in profits$(28.10)
Alternative #2 is best.
b.Related sales, long-term product mix
CASES
C4.1Answers depend on the company chosen by the students.
C4.2
a.The relevant variables are direct materials, direct labor, and unit-related overhead. Also, the offered selling price and the freight expense are relevant. Finally, the additional batch-related cost is relevant.
b.Additional revenue (30,000 valves * $19)$570,000
Direct materials (30,000 valves * $5) (150,000)
Direct labor (30,000 valves * $6)(180,000)
Unit-related overhead (30,000 valves * $6)(180,000)
Freight expense (30,000 valves * $1) (30,000)
Additional batch-related cost (12,000)
Profit on order(per month)$ 18,000
Accept the order
c.Other customers, long-term relationships
CRITICAL THINKING
CT4.1Answers vary depending on the assumptions made by the students. A cost guideline follows.
Hamburger ($1.25 * 12 * 0.1)$1.500 (a)
Crushed tomatoes 1.700
Tomato sauce ($0.51 * 5) 2.550
Red beans ($1.32 * 2) 2.640
Seasonings 0.450
Total cost of ingredients per batch$8.840
Labor—cooking (10/60 * $3.49 * 0.1)$0.0582 (b)
Labor—chopping and mixing (10/60 * $3.49) 0.5817
Total labor cost per batch$0.6399
Total cost per batch ($8.84 + $0.6399)$9.4799
Cost per bowl ($9.4799/57)$0.1663
Cost of bowls 0.0350
Cost of lids 0.0250 (c)
Cost of spoons 0.0100
Total cost per bowl$0.2363
(a) Assuming that hamburger is only purchased 10 percent of the time.
(b) Assuming an average of the wage rate for assistants managers and crew members.
(c) Assuming that lids will be used for dine-in also.
CT4.2Selling price per unit = $500 ($5,000,000/10,000), variable cost per unit = $100 ($1,000,000/10,000), and contribution margin per unit = $400 ($500 - $100). Contribution margin ratio = 80% ($400/$500).
a.$1,500,000/$400 = 3,750; $1,500,000/0.80 = $1,875,000
b.Before-tax profit = $2,000,000/0.60 = $3,333,333.33
($1,500,000 + $3,333,333.33)/$400 = 12,083.33
c.$600 * Q - $100 * Q – 2,250,000 = $2,500,000
$500 * Q = $4,750,000
Q = 9,500
d.Whether sales volume will drop.
e.$500 * Q - $80 * Q - $2,250,000 = 0
$420 * Q = $2,250,000
Q = 5,357.14
f.If the increase in volume is sufficient to offset the decrease in revenue per unit, it should consider it.
ETHICAL CHALLENGES
EC4.1This treatment is improper because in the short run the costs that are allocated to the production process could be captured in the cost of the inventory, which if not sold would be shown on the balance sheet, not the income statement.
EC4.2Answers depend on the student. This is a classic example of the role of business and how cost/benefit analysis can be misused if benefits are not correctly determined.
COMPUTER APPLICATIONS
CA4.1
Selling price / 300Variable cost / 100
Contribution margin / 200
Fixed cost / 40,000
Target profit / 3,000
Tax rate / 0.4
a. / 200
b. / 215
c. / 225
d. / 220
e. / 216.216
f. / 216.216
CA4.2
Selling price / 20Variable cost / 7
Contribution margin / 13
Fixed cost / 1,850
Target profit / 600
a. / 142.308
b. / 188.462
c. / 208.242
d. / 123.333
e. / 76.9231
4-1