Final Exam Sample Problem
Price, Promotion, and Demand Elasticity
The group product manager for ointments at American Therapeutic
Corporation was reviewing price and promotion alternatives for two products:
Rash-Away and Red-Away. Both products were designed to reduce skin
irritation, but Red-Away was primarily a cosmetic treatment whereas RashAway also included a compound that eliminated the rash.
The price and promotion alternatives recommended for the two products by
their respective brand managers included the possibility of using additional
promotion or a price reduction to stimulate sales volume. A summary of the
current price, cost, contribution margin (CM), ad spend, and volume for the two
products follows:
Unit price
Variable costs
CM
Ad Spend
Volume
Rash-Away
$2.00
$1.40
$0.60
$200,000
1,000,000
Red-Away
$1.00
$0.25
$0.75
$150,000
1,500,000
Both brand managers included a recommendation to either invest an
incremental $150,000 in advertising or reduce price by 10 percent.
1. What level of unit sales and dollar sales will be necessary to recoup
the $150,000 incremental increase in advertising expenditures.
FC/(P – VC/unit)
FC/CM
= Q required to break even (BEQ)
= Q required to break even (BEQ)
Incremental Q + Original Q
$150,000
= 250,000 + 1,000,000
$0.60
Unit Sales
BER = BEQ * P
1,250,000 × $2.00
Dollar Sales
Rash-Away:
1,250,000
$2,500,000
Red-Away:
1,700,000
$1,700,000
$150,000
= 200,000 + 1,500,000
$0.75
1,700,000 × $1.00
2. What level of unit sales and dollar sales will be necessary to maintain
the level of total contribution dollars if the price of each product is
reduced by 10 percent?
Current Contribution $s
Rash-Away:
$0.60 × 1,000,000 =
$600,000
Red-Away:
$0.75 × 1,500,000 =
$1,125,000
Required Quantity at New Contribution Margin
Rash-Away:
Red-Away:
Rash-Away:
Red-Away:
$600,000
$0.40 × Q =
$0.65 × Q = $1,125,000
Unit Sales
1,500,000
1,730,769
$1.80 × 1,500,000
Dollar Sales
2,700,000
1,557,692
$0.90 × 1,730,769
3. For the two proposed changes, you estimate that demand elasticity
with respect to advertising is .5 and that demand elasticity with respect to
price is -2.0. What would total unit and dollar sales be for each option?
E = %DQ / %DPromo E = .5
E = %DQ / %DPrice
E = -2
.5 = %DQ / (150,000/200,000)
-2.0 = %DQ / -.10
.75 × .5 = %DQ = .375
-.10 × -2.0 = %DQ = .20
DQ = .375 × 1,000,000 = 375,000
DQ = .20 × 1,000,000 = 200,000
Q = 1,000,000 + 375,000
Q = 1,000,000 + 200,000
-2.0 = %DQ / -.10
.5 = %DQ / (150,000/150,000)
-.10 × -2.0 = %DQ
1 × .5 = %DQ
DQ = .20 × 1,500,000 = 300,000
DQ = .5 × 1,500,000 = 750,000
Q = 1,500,000 + 300,000
Q = 1,500,000 + 750,000
$150,000 Increase in Ad Spend
Unit Sales
Dollar Sales
Rash-Away:
1,375,000
$2,750,000
Red-Away:
2,250,000
$2,250,000
10% Price Reduction
Unit Sales
Dollar Sales
Rash-Away:
1,200,000 × $1.80 $2,160,000
Red-Away:
1,800,000 × $.90 $1,620,000
What Do You Recommend?
$150,000 Increase in Ad Spend Breakeven
Unit Sales
Dollar Sales
Rash-Away:
1,250,000
$2,500,000
Red-Away:
1,700,000
$1,700,000
10% Price Reduction Breakeven
Unit Sales
Dollar Sales
1,500,000
Rash-Away:
2,700,000
1,730,769
Red-Away:
1,557,692
$150,000 Increase in Ad Spend Forecast
Unit Sales
Dollar Sales
Rash-Away:
1,375,000
$2,750,000
Red-Away:
2,250,000
$2,250,000
10% Price Reduction Forecast
Unit Sales
Dollar Sales
Rash-Away:
1,200,000
$2,160,000
Red-Away:
1,800,000
$1,620,000
$.75 × 550,000 = $412,500
1,800,000 × $.65 – 1,500,000 × $.75 = $45,000
Rash-Away: Yes to increased ad spend because forecasted sales are
greater than breakeven; no to price reduction…
Red-Away: Might depend on the objective, but increased ad spend appears
to dominate – unit sales, dollar sales, and contribution.
Channel Margin Arithmetic
After spending $300,000 for research and development, chemists at Diversified
Citrus Industries have developed a new breakfast drink, called Zap, which provides the
consumer with twice the amount of vitamin C currently available in breakfast drinks
using all natural ingredients. Zap will be packaged in an 8-ounce container and will be
introduced to the breakfast drink market, which is estimated to be equivalent to 21
million 8-ounce servings nationally.
A major concern is the lack of funds available for marketing so management has
decided to use newspapers to promote Zap and distribute Zap in major metropolitan
areas that account for 65 percent of U.S. breakfast drink volume. Newspaper
advertising will carry a coupon for $0.20 off the price of the first can purchased. The
retailer will receive the regular margin and be reimbursed for redeemed coupons by
Diversified Citrus Industries. Past experience indicates that for every five cans sold
during the introductory year, one coupon will be returned. The cost of the newspaper
advertising campaign (excluding coupon returns) will be $250,000. Other fixed
overhead costs are expected to be $90,000 per year.
Management has decided that the suggested retail price to the consumer for the 8ounce can should be $0.50. The only unit variable costs for the product are $0.18 for
materials and $0.06 for labor. Retailers demand a margin of 20 percent of the
suggested retail price and distributors a margin of 10 percent of the retailers’ cost.
Channel Margin Arithmetic
1. Wholesale Cost = Manufacturer Price =
$.50 – 20% × $.50 – 10% × ($.50 – 20% × $.50) =
$.50 –
$.10
– 10% × ($.40) = $.36
2. Contribution per unit
$.36 - $.18 - $.06 - $.20/5 = $.08
3. B/E Volume =
$340,000/$.08 = 4,250,000
4. B/E Share =
4,250,000/13,650,000 = 31%
Questions?