Name: Ngoc Lam Pham
Student ID: 110183330
Special Order – Peterson's Ice Cream Shop
• Each coupon book has 25 coupons and sells for $20.
• 600 coupon books sold → 600 × 25 = 15,000 coupons
• Total revenue = 600 × $20 = $12,000
• Variable cost per coupon redeemed = $1.50
• Total variable cost = 15,000 × $1.50 = $22,500
• Printing cost (Fixed cost) = $75
• Total cost = Total variable cost + Fixed cost = $22,500 + $75 = $22,575
a. Determine the loss if all coupons are redeemed without any other effect on sales.
• Loss = Total revenue – Total cost = $12,000 – $22,575 = –$10,575
Peterson’s will incur a loss of $10,575 if all coupons are redeemed and there are no additional
sales
b. Determine the coupon redemption rate at which Peterson’s will break even (no additional effect
on sales).
• Let x = number of coupons redeemed
• Total cost = Variable cost ($1.50 × x) + Fixed cost ($75)
• Break-even condition: Total revenue = Total cost
$12,000 = ($1.50 × x) + $75 => x = 7,950 coupons
• Total coupons available: 15,000
• Redemption rate = 7,950 / 15,000 = 53%
=> Peterson’s will break even if only 53% of the coupons are redeemed.
c. Determine the break-even coupon redemption rate if one additional regular cone is sold at $2.00
for each coupon redeemed.
• One regular cone is sold at full price ($2.00)
• Each redeemed coupon triggers a regular cone sale:
• Profit from each cone = $2.00 – $1.50 = $0.50
• Let x = number of coupons redeemed
• Cost from coupon redemptions (variable cost) = $1.50x
• Profit from additional cones = $0.50x
• Printing cost (Fixed cost) = $75
• Break-even condition:
Total revenue and extra profits = Total costs (Variable cost + Fixed cost)
$12,000 + $0.50x = $1.50x + $75 ⇒ $12,000 – $75 = $1.00x ⇒ x = 11,925 coupons
• Redemption rate = 11,925 / 15,000 = 79.5%
=> Peterson’s breaks even at a 79.5% redemption rate if one regular cone is sold per coupon redeemed.
d. Determine the profit or loss if the coupon redemption rate is 60% and:
• Total coupon books sold = 600 books × 25 coupons = 15,000 coupons
• Redemption rate = 60% × 15,000 = 9,000 coupons redeemed
• Cost for each redeemed coupon = $1.50
• Total revenue = $12,000
• Printing cost = $75
• Variable cost from 9,000 redemptions = 9,000 × $1.50 = $13,500
• So total costs = $13,500 (variable cost) + $75 (fixed cost) = $13,575
• Loss before considering other effects = $12,000 – $13,575 = –$1,575
1. One-fourth of redeemed coupons have no effect on sales.
• No extra income from 25% of 9,000 = 2,250
• The other 75% also don’t change anything, so there's no additional income at all
• Loss = Total revenue – Total cost = $12,000 – $13,575 = –$1,575
=> Loss = $1,575
2. One-fourth result in 2 extra cones sold at $2 each (profit = $0.50 each)
• 2,250 coupons lead to 2 × 2,250 = 4,500 extra cone sales
• Profit per cone = $0.50 => 4,500 × $0.50 = $2,250 profit
=> Net profit = $2,250 - $1,575 = $675
3. One-fourth result in 3 extra cones sold
• 2,250 coupons lead to 3 × 2,250 = 6,750 extra cone sales
• Profit = 6,750 × $0.50 = $3,375
=> Net profit = $3,375 – $1,575 = $1,800
4. One-fourth replace regular sales (lost profit = $0.50 each)
• 2,250 coupons are redeemed instead of people buying at full price
• Lost profit = 2,250 × $0.50 = $1,125
• Add this loss to the original $1,575 loss:
=> Total loss = $1,575 + $1,125 = $2,700
