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Appendix A
Pricing Products and Services
Solutions to Questions
A-1 In cost-plus pricing, prices are set by
unit sales of a product with elastic demand
are
sensitive to the price charged for the product.
A-3 The profit-maximizing price should de-
Fixed costs are relevant in a decision of whether
to offer a product or service at all, but are not
A-4 The markup over variable cost depends
on the price elasticity of demand. A product
the product. Full cost is an alternative approach
A-6 The absorption costing approach as-
sumes that consumers do not react to prices at
all—consumers will purchase the forecasted unit
sales regardless of the price that is charged.
A-7 The protection offered by full cost pric-
ing is an illusion. All costs will be covered only if
A-8 Target costing is used to price new
products. The target cost is the expected selling
price of the new product less the desired profit
Exercise A-1 (30 minutes)
1. Maria makes more money selling the ice cream cones at the lower price,
as shown below:
$1.89 Price
$1.49 Price
Unit sales ......................
1,500
2,340
Sales .............................
$2,835.00
$3,486.60
Cost of sales @ $0.43 .....
645.00
1,006.20
Contribution margin .......
2,190.00
2,480.40
Fixed expenses ..............
675.00
675.00
Net operating income .....
$1,515.00
$1,805.40
2. The price elasticity of demand, as defined in the text, is computed as
follows:
d =
ln(1+% change in quantity sold)
ln(1+% change in price)
2,340-1,500
ln(1+ )
1,500
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Exercise A-1 (continued)
3. The profit-maximizing price can be estimated using the following formu-
la from the text:
d
d
ε
Profit-maximizing price = Variable cost per unit
1+ε
-1.87
= $0.43
1+(-1.87)
= 2.1494 × $0.43 = $0.92
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This price is much lower than the prices Maria has been charging in the
past. Rather than immediately dropping the price to $0.92, it would be
prudent to drop the price a bit and see what happens to unit sales and
to profits. The formula assumes that the price elasticity is constant,
which may not be the case.
Exercise A-2 (15 minutes)
1.
( )
( )
Required ROI Selling and administraive
+
× Investment expenses
Markup percentage =
on absorption cost Unit sales × Unit product cost
12% × $750,000 + $50,000
= 14,000 units × $25 per unit
$140,000
= = 4
$350,000 0%
2.
Unit product cost ...............
$25
Markup (40% × $25).........
10
Selling price per unit ..........
$35
Exercise A-3 (10 minutes)
Sales (300,000 units × $15 per unit) ........
$4,500,000
Less desired profit (12% × $5,000,000) ...
600,000
Target cost for 300,000 units ...................
$3,900,000
Problem A-4 (45 minutes)
1. The postal service makes more money selling the souvenir sheets at the
lower price, as shown below:
$7 Price
$8 Price
Unit sales ...............................
100,000
85,000
Sales ......................................
$700,000
$680,000
Cost of sales @ $0.80 per unit .
80,000
68,000
Contribution margin ................
$620,000
$612,000
2. The price elasticity of demand, as defined in the text, is computed as
follows:
d =
ln(1 + % change in quantity sold)
ln(1 + % change in price)
85,000 - 100,000
ln(1 + )
100,000
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Problem A-4 (continued)
3. The profit-maximizing price can be estimated using the following formu-
d
1+ε
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=
-1.2163 $0.80
1+(-1.2163)
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Problem A-4 (continued)
The critical assumption in these calculations is that the percentage in-
crease (decrease) in quantity sold is always the same for a given per-
centage decrease (increase) in price. If this is true, we can estimate the
Problem A-4 (continued)
The profit at each price in the above demand schedule can be computed
as follows:
Price
(a)
Quantity
Sold (b)
Sales
(a) × (b)
Cost of Sales
$0.80 × (b)
Contribution
Margin
$8.00
85,000
$680,000
$68,000
$612,000
$7.00
100,000
$700,000
$80,000
$620,000
$6.13
117,647
$721,176
$94,118
$627,058
$5.36
138,408
$741,867
$110,726
$631,141
$4.69
162,833
$763,687
$130,266
$633,421
$4.10
191,569
$785,433
$153,255
$632,178
$3.59
225,375
$809,096
$180,300
$628,796
$3.14
265,147
$832,562
$212,118
$620,444
$2.75
311,937
$857,827
$249,550
$608,277
$2.41
366,985
$884,434
$293,588
$590,846
Problem A-4 (continued)
The contribution margin is plotted below as a function of the selling price:
$580,000
$590,000
$600,000
$610,000
$620,000
$630,000
$640,000
$2.00 $3.00 $4.00 $5.00 $6.00 $7.00 $8.00
Selling Price
Contribution Margin
