Belmont Records produces DVD records. The fixed costs for producing a record are $160,000, and unit cost amount to 85 cents per record. The revenue is $5 per DVD.
(a) How many DVDs must be sold in order to break even?
(b) Find the profit or loss if 20,000 DVDs are sold.
(c) Find the profit or loss if 50,000 DVDs are sold.
for x DVDs, break-even is when
160000+.85x = 5x
p(x) = 5x - (160000+.85x)
that should help
To answer these questions, we need to understand the concept of break-even point and profit/loss calculation. Let me explain the necessary steps to get the answers.
(a) To find the break-even point, we need to determine the number of DVDs that need to be sold in order to cover the total cost.
1. Start by calculating the variable cost per unit. The unit cost is given as $0.85.
Variable Cost per Unit = Unit Cost = $0.85
2. Next, calculate the contribution margin per unit, which is the difference between the selling price and the variable cost per unit. The selling price is given as $5.
Contribution Margin per Unit = Selling Price - Variable Cost per Unit = $5 - $0.85 = $4.15
3. Now, determine the break-even point in terms of units sold using the following formula:
Break-even Point (in units) = Fixed Costs / Contribution Margin per Unit
Break-even Point (in units) = $160,000 / $4.15
Calculate the result to find the number of DVDs that must be sold to break even.
(b) To find the profit or loss when 20,000 DVDs are sold, we need to compare the total revenue with the total cost.
1. Calculate the total cost by adding the fixed costs to the variable costs.
Fixed Costs = $160,000
Variable Costs = Unit Cost × Number of DVDs Sold
Variable Costs = $0.85 × 20,000 DVDs
Calculate the total cost by adding the fixed costs and variable costs.
2. Calculate the total revenue by multiplying the selling price by the number of DVDs sold.
Total Revenue = Selling Price × Number of DVDs Sold
Total Revenue = $5 × 20,000 DVDs
Calculate the profit or loss by subtracting the total cost from the total revenue.
(c) To find the profit or loss when 50,000 DVDs are sold, follow the same steps as in part (b) but substitute the number of DVDs sold as 50,000.