Question

You run a business out of your dorm room selling ACC2020 textbooks in both paper and digital versions. The paper version costs you $190 and you can sell it for $380. The digital version costs you $80 and you can sell it for $125. Last semester you sold 20 paper versions for $7.600 and 80 digital versions for $10,000. You expect that sales mix will continue this semester. If your semester fixed costs are $5,000 for a publisher's license, what dollar amount of sales will you need to breakeven? How many paper and digital books will you have to sell to breakeven (round up to whole books)? Round all percentages to the nearest 100th (i.e., 45.6666% would be 45.67%) and round dollars to the nearest whole dollar.
if you could post your work with the answers, it would be very appreciated. thank you!

Answer 1

Answer:

Paper Versions Sales = $7,600
Digital Version Sales = $10,000
Total Sales = $7,600 + $10,000 = $17,600

Proportion of Paper Version Sales in Total Sales = $7,600 / $17,600 * 100
Proportion of Paper Version Sales in Total Sales = 43.18%

Proportion of Digital Version Sales in Total Sales = $10,000 / $17,600 * 100
Proportion of Digital Version Sales in Total Sales = 56.82%

Contribution Margin = Unit Selling Price – Unit Variable Cost
Contribution Margin Ratio = Contribution Margin / Sales * 100

Paper Version’s Contribution Margin = $380 - $190 = $190
Paper Version’s Contribution Margin Ratio = $190 / $380 * 100
Paper Version’s Contribution Margin Ratio = 50%

Digital Version’s Contribution Margin = $125 - $80 = $45
Digital Version’s Contribution Margin Ratio = $45 / $125 * 100
Digital Version’s Contribution Margin Ratio = 36%

Combined Contribution Margin Ratio = (0.4318 * 50%) + (0.5682 * 36%)
Combined Contribution Margin Ratio = 42.05%

Break Even Point (Dollar Sales) = Fixed Cost / Combined Contribution Margin Ratio
Break Even Point (Dollar Sales) = $5,000 / 0.4205
Break Even Point (Dollar Sales) = $11,891

Proportion of Paper Version Sales in Break Even Sales = $11,891 * 43.18%
Proportion of Paper Version Sales in Break Even Sales = $5,315
Units of Paper Versions to be sold for Break Even Point = $5,135 / $380
Units of Paper Versions to be sold for Break Even Point = 14 versions

Proportion of Digital Version Sales in Break Even Sales = $11,891 * 56.82%
Proportion of Digital Version Sales in Break Even Sales = $6,756
Units of Digital Versions to be sold for Break Even Point = $6,756 / $125
Units of Digital Versions to be sold for Break Even Point = 54 versions