Colin was a professional classical guitar player until his motorcycle accident that left him disabled. After long months of therapy, he hired an experienced luthier (maker of stringed instruments) and started a small shop to make and sell Spanish guitars. The guitars sell for $700 and the fixed monthly operating costs are as follows: $$\begin{array} { | l | r | }
\hline \text { Rent and utilities } & \$ 800 \
\hline \text { Wages and benefits to luthier } & 2,500 \
\hline \text { Other expenses } & 480 \
\hline
\end{array}$$ Colin's accountant told him about contribution margin ratios and he understood clearly that for every dollar of sales, $0.60 went to cover his fixed costs, and that anything past that point was pure profit.
Colin is planning to increase the selling price to $750. What impact will the increase in selling price have on the contribution margin ratio?

Question

Colin was a professional classical guitar player until his motorcycle accident that left him disabled. After long months of therapy, he hired an experienced luthier (maker of stringed instruments) and started a small shop to make and sell Spanish guitars. The guitars sell for $700 and the fixed monthly operating costs are as follows: $$\begin{array} { | l | r | } 
\hline \text { Rent and utilities } & \$ 800 \
\hline \text { Wages and benefits to luthier } & 2,500 \
\hline \text { Other expenses } & 480 \
\hline
\end{array}$$ Colin's accountant told him about contribution margin ratios and he understood clearly that for every dollar of sales, $0.60 went to cover his fixed costs, and that anything past that point was pure profit.
Colin is planning to increase the selling price to $750. What impact will the increase in selling price have on the contribution margin ratio?

Quizplus · Accepted Answer

Contribution margin per unit can be calculated as the selling price per unit minus the variable cost per unit. Since the only cost given is the selling price, we must assume that it includes all the variable costs. Therefore, the contribution margin per unit is $750 - $0 = $750.

The contribution margin ratio is the contribution margin per unit divided by the selling price per unit, expressed as a percentage. So the contribution margin ratio is ($750 - $0) / $750 = 1 or 100%.

Since the increase in selling price does not affect the variable costs, the contribution margin ratio will remain the same at 100%.

However, the information given in the question about the $0.60 of each dollar going towards fixed costs is relevant. If we assume that this $0.60 is based on the current selling price of $700, then increasing the selling price to $750 will increase the contribution margin per unit to $750 - $0 = $750, while the fixed costs remain the same. This means that the portion of each dollar that goes towards fixed costs will decrease, and the portion that contributes to profit will increase.

To calculate the new contribution margin ratio, we need to divide the new contribution margin per unit by the new selling price per unit, expressed as a percentage. So the new contribution margin ratio is ($750 - $0) / $750 = 100%. However, the portion of each dollar that goes towards fixed costs will decrease from $0.60 to $0.53, which means that the new contribution margin ratio as a percentage of sales revenue will increase from (1 - $0.60) = 40% to (1 - $0.53) = 47%, or an increase from 60% to approximately 63%. Therefore, the answer is C.

Colin Was a Professional Classical Guitar Player Until His Motorcycle