Steven 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 $800 and the fixed monthly operating costs are as follows: $$\begin{array} { | l | r | }
\hline \text { Rent and utilities } & \$ 1,250 \
\hline \text { Wages and benefits to luthier } & 2,500 \
\hline \text { Other expenses } & 490 \
\hline
\end{array}$$ Steven's accountant told him about contribution margin ratios and he understood clearly that for every dollar of sales,$0.65 went to cover his fixed costs,and that anything past that point was pure profit.
Steven wishes to earn $6,000 of operating profit each month.Calculate the number of guitars Steven will have to sell to achieve the target profit.
A) 19 guitars
B) 37 guitars
C) 9 guitars
D) 20 guitars

Question

Steven 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 $800 and the fixed monthly operating costs are as follows: $$\begin{array} { | l | r | } 
\hline \text { Rent and utilities } & \$ 1,250 \
\hline \text { Wages and benefits to luthier } & 2,500 \
\hline \text { Other expenses } & 490 \
\hline
\end{array}$$ Steven's accountant told him about contribution margin ratios and he understood clearly that for every dollar of sales,$0.65 went to cover his fixed costs,and that anything past that point was pure profit.
Steven wishes to earn $6,000 of operating profit each month.Calculate the number of guitars Steven will have to sell to achieve the target profit.
A) 19 guitars
B) 37 guitars
C) 9 guitars
D) 20 guitars

Quizplus · Accepted Answer

To calculate the number of guitars Steven needs to sell to achieve his target profit, we first determine the total fixed costs and then use the contribution margin ratio to find out how much sales revenue is needed to cover both the fixed costs and the desired profit. The fixed costs are $1,250 (rent and utilities) + $2,500 (wages and benefits) + $490 (other expenses) = $4,240. Steven wants to earn $6,000 in profit, so the total amount needed from sales is $4,240 (fixed costs) + $6,000 (desired profit) = $10,240. Since the contribution margin ratio is 0.65, this means $0.65 of every sales dollar goes towards covering fixed costs and profit. Therefore, the required sales revenue is $10,240 / 0.65 = $15,754.62. Since each guitar sells for $800, the number of guitars needed to be sold is $15,754.62 / $800 ≈ 19.69. Since Steven cannot sell a fraction of a guitar, he needs to sell 20 guitars to meet his target.

Steven Was a Professional Classical Guitar Player Until His Motorcycle