Question

Consider the following production and cost data for two products, X and Y:



The company has 15,000 machine hours available each period, and there is unlimited demand for each product. What is the largest possible total contribution margin that can be realized each period?



a. $120,000

b. $125,000

c. $135,000

d. $150,000

Answer 1

Concepts and reason

CVP analysis: CVP is one of the techniques of decision accounting to achieve the targeted profits by changing different variables. The relationship between cost, profit and sales volume provides the basis for the manager to take effective steps about the future profits.

Selling price: Selling price is the price at which products is sold in the market. It includes the total cost incurred to the product and profit.

Variable Cost: Variable cost is a cost that varies according to the output produced or any service rendered. It is the cost paid by the company that depends on the activities concerned with the business. Variable cost for a single unit is known as unit variable cost.

Fundamentals

Contribution margin: The difference between the sales revenue and the variable costs is called contribution margin. The management uses contribution margin to develop the weight of sales mix for multiple products. The contribution margin signifies the profit earned after deducting the fixed costs. Contribution margin for an individual product is unit contribution margin.

Contribution margin: Contribution margin shows the amount of sales remained after the variable expenses paid off. It is calculated by subtracting the variable costs from sales.

Calculate contribution per hour of Product X and Product Y.

Therefore, the contribution per hour for Product X is $8 and Product Y is $9.

Working note:

Calculate contribution per hour for Product X.

$\begin{array}{c}\\\left. \begin{array}{l}\\{\rm{Contribution per hour}}\\\\{\rm{ for Product X}}\\\end{array} \right\}{\rm{ = }}\frac{{{\rm{Contribution margin per unit of Product X}}}}{{{\rm{Machine hours needed per unit}}}}{\rm{ }}\\\\{\rm{ = }}\frac{{{\rm{\$ 24}}}}{{{\rm{3 hours}}}}{\rm{ }}\\\\{\rm{ = \$ 8 per hour}}\\\end{array}$

Calculate contribution per hour for Product Y.

$\begin{array}{c}\\\left. \begin{array}{l}\\{\rm{Contribution per hour}}\\\\{\rm{ for Product Y}}\\\end{array} \right\}{\rm{ = }}\frac{{{\rm{Contribution margin per unit of Product Y}}}}{{{\rm{Machine hours needed per unit}}}}{\rm{ }}\\\\{\rm{ = }}\frac{{{\rm{\$ 18}}}}{{{\rm{2 hours}}}}{\rm{ }}\\\\{\rm{ = \$ 9 hours}}\\\end{array}$

Calculate largest possible total contribution margin.

$\begin{array}{c}\\\left. \begin{array}{l}\\{\rm{Largest possible total}}\\\\{\rm{ contribution margin}}\\\end{array} \right\}{\rm{ = }}\left( \begin{array}{l}\\{\rm{Highest contribution margin per hour }}\\\\ \times {\rm{ Available machine hours}}\\\end{array} \right){\rm{ }}\\\\{\rm{ = \$ 9 per hour}}\, \times \;{\rm{15,000 machine hours }}\\\\{\rm{ = \$ 135,000}}\\\end{array}$

Therefore, the largest possible total contribution margin is $135,000.

Ans:

Largest possible total contribution margin is $135,000.