Exotic Roses, owned by Margarita Rameriz, provides a variety of rare rose bushes to local nurseries that sell Rameriz's roses to the end consumer (landscapers and retail customers). Rameriz grows the roses from cuttings that she has specifically cultivated for their unusual characteristics (color, size, heartiness, and resistance to disease). Margarita's roses are in great demand as evidenced by the wholesale price she charges nurseries, $15 per potted plant. Exotic Roses has the following cost structure (variable costs are per potted plant):

Question

a. How many potted rose plants must Exotic Roses sell each year to break even?

b. If Rameriz wants to make profits of $10,000 before taxes per year, how many potted rose plants must be sold?

c. If Rameriz wants to make profits of $10,000 after taxes per year, how many potted rose plants must be sold assuming a 35 percent income tax rate?

Answer 1

a. Fixed costs total $27,000 per year and variable costs are $1.50 per plant. The break-even number of potted roses is found by solving the following equation for Q:
Profits = $15 Q - $1.50 Q - $27,000 = 0
Or Q = $27,000/($15 - $1.50) = $27,000/$13.50 = 2,000 plants

b. To make $10,000 of profits before taxes per year, solve the following equation for Q:
Profits = $15 Q - $1.50 Q - $27,000 = $10,000
Or Q = $37,000/($15 - $1.50) = $37,000/$13.50 = 2,740.74 plants

c. To make $10,000 of profits AFTER taxes per year, solve the following equation for Q:
Profits = [$15 Q - $1.50 Q - $27,000] × (1 - 0.35) = $10,000
= [$15 Q - $1.50 Q - $27,000] = $10,000/0.65 = $15,384.62
Or, Q = $42,384.62/$13.50 = 3,139.60 plants