Question

X-Country Bikes Inc. is developing a new all-terrain bike that includes a carbon-fiber frame, lightweight tensile steel gears, airless foam rubber tires, and air shocks on both the wheels and the seat. The companys cross-functional team believes the bike can be sold for $2,500, and the company desires a 20% profit.a. What is the target cost per bike?b.If the unit variable costs are $1,200 and the total fixed costs are $2,000,000, how many bikes must be produced and sold to achieve the target cost per bike?

Answer 1

The target cost per bike is $2,000. To achieve the target cost per bike, at least 1539 bikes must be produced and sold.

Step-by-step explanation:

To calculate the target cost per bike, we need to determine the desired profit and subtract it from the target selling price. Given that the company desires a 20% profit and wants to sell the bike for $2,500, the desired profit per bike would be 20% of $2,500, which is $500. So, the target cost per bike would be $2,500 - $500 = $2,000.

To determine the number of bikes that need to be produced and sold to achieve the target cost per bike, we first need to calculate the unit contribution margin. The unit contribution margin is the difference between the selling price and the unit variable cost. In this case, the unit variable cost is given as $1,200. So, the unit contribution margin would be $2,500 - $1,200 = $1,300.

Next, we can use the formula:

Break-even quantity = Total fixed costs / Unit contribution margin.

Given that the total fixed costs are $2,000,000, the break-even quantity would be $2,000,000 / $1,300 = 1538.46. Since you cannot produce and sell a fraction of a bike, you would need to produce and sell at least 1539 bikes to achieve the target cost per bike.