Question

The cost of purple dye has been increasing over the last few months, and Robyn uses this dye as part of her tie dye scarf business. She’s worried that it will continue to rise to the point where she no longer makes a profit on her scarf sales. She currently has a 20% profit margin ([price - unit costs]/price) and dye is currently 60% of unit costs. What is the lowest percentage increase in the cost of dye that would make Robyn’s scarves unprofitable?

Answer 1

The lowest percentage increase in the cost of dye that would make the scarves unprofitable is 42%

How to calculate the percentage?

(Price- Unit Cost)/Price= 20% or 0.2

Price- Unit Cost= 0.2 Price

0.8 Price = Unit Cost

Let Unit Cost be x

Price = x/0.8= 1.25x

Dye is 60% of unit costs= 0.6x

Cost of remaining material= 1 - 0.6x = 0.4x

Unit Cost= Cost of Dye+ Cost of remaining material

So, in order to become unprofitable, Unit Cost must be 1.25x

Therefore

1.25x= Maximum cost of dye+ 0.4x

Maximum Cost of Dye = (1.25-0.4)x = 0.85x

Percentage change in cost of dye= {(0.85x-0.6x)/0.6x}*100= 41.66 or 42%

Therefore, theowest percentage increase in the cost of dye that would make the scarves unprofitable is 42%.

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