Question

Pepe, the owner of Pepe’s Pizza in New Haven, CT, is considering a new oven in which to bake the restaurants signature pizza. Oven type A can handle up to 20 pizzas per hour. The oven costs $20,000, including purchase price, insurance, and other fixed costs. The oven’s operating costs are $40 per hour for electricity and fuel. Oven B is larger and can handle up to 40 pizzas per hour. The fixed costs are $30,000 and the operating costs are $50 per hour. The pizza sells for $14 each. The cost of ingredients and labor is $5 per pizza. a. For each oven, how many pizzas does Pepe have to sell per hour to avoid losing money on oven operating costs? b. At max operating capacity, what are the breakeven sales quantities? c. At max operating capacity, how many pizzas must Pepe sell for Oven B to be preferred to Oven A? d. At what operating capacity (in pizzas per hour) would Oven B have to be used at to be more profitable per unit sold (ignoring fixed costs)?

Answer 1

a. For each oven, how many pizzas does Pepe have to sell per hour to avoid losing money on oven operating costs?

• for type A oven, Pepe must sell $40 / $9 = 4.44 ≈ 5 pizzas per hour
• for type B oven, Pepe must sell $50 / $9 = 5.56 ≈ 6 pizzas per hour

b. At max operating capacity, what are the break even sales quantities?

• break even point for type A oven = $20,000 / $7 = 2,857.14 ≈ 2,858 pizzas
• break even point for type A oven = $30,000 / $7.75 = 3,870.97 ≈ 3,871 pizzas

c. At max operating capacity, how many pizzas must Pepe sell for Oven B to be preferred to Oven A?

• 13,334 pizzas

d. At what operating capacity (in pizzas per hour) would Oven B have to be used at to be more profitable per unit sold (ignoring fixed costs)?

• 26 pizzas per hour

Step-by-step explanation:

Cost analysis for oven type A:

ingredients and labor per pizza = $5 per pizza

price of pizza - ingredients and labor = $14 - $5 = $9

variable overhead = $40 / 20 = $2 per pizza

total contribution margin = $7 per pizza

fixed costs = $20,000

Cost analysis for oven type B:

ingredients and labor per pizza = $5 per pizza

ingredients and labor per pizza = $9 per pizza

variable overhead = $50 / 40 = $1.25 per pizza

total contribution margin = $7.75 per pizza

fixed costs = $30,000

7x - 20,000 = 7.75x - 30,000

10,000 = 0.75x

x = 10,000 / 0.75 = 13,333.33 ≈ 13,334 pizzas

(13,334 x $7) - $20,000 = $73,338

(13,334 x $7.75) - $30,000 = $73,338.50

50/x = 40/20

50/x = 2

x = 50 / 2 = 25

operating costs at 25 pizzas per hour = $50 + ($5 x 25) = $175

average operating cost per unit = $175 / 25 = $7

since oven B must be more profitable, then you must sell at least 26 pizzas:

operating costs at 26 pizzas per hour = $50 + ($5 x 26) = $180

average operating cost per unit = $180 / 26 = $6.92