Question

Menlo Company distributes a single product. The company’s sales and expenses for last month follow: Total Per Unit Sales $ 450,000 $ 30 Variable expenses 180,000 12 Contribution margin 270,000 $ 18 Fixed expenses 216,000 Net operating income $ 54,000 Required: 1. What is the monthly break-even point in unit sales and in dollar sales? 2. Without resorting to computations, what is the total contribution margin at the break-even point? 3-a. How many units would have to be sold each month to attain a target profit of $90,000? 3-b. Verify your answer by preparing a contribution format income statement at the target sales level. 4. Refer to the original data. Compute the company's margin of safety in both dollar and percentage terms. 5. What is the company’s CM ratio? If sales increase by $50,000 per month and there is no change in fixed expenses, by how much would you expect monthly net operating income to increase?

Answer 1

The profit-maximizing quantity for Doggies Paradise Inc. is three units, which is determined by calculating total revenue, marginal revenue, total cost, and marginal cost for each output level and finding the point where marginal revenue equals or exceeds marginal cost.

Step-by-step explanation:

To determine the profit-maximizing quantity for Doggies Paradise Inc., we begin by calculating total revenue (TR), marginal revenue (MR), total cost (TC), and marginal cost (MC) for each output level from one to five units. We use the price per unit and the given variable costs along with the fixed costs to perform these calculations. The profit-maximizing quantity is the highest number of units for which marginal revenue equals or exceeds marginal cost prior to marginal cost exceeding marginal revenue.

Total Revenue (TR) is the total income from sales, calculated by multiplying the number of units sold by the price per unit.

Marginal Revenue (MR) in a perfectly competitive market is constant and equal to the price of the product ($72), as the firm can sell as many units as it wants at the market price.

Total Cost (TC) is the sum of fixed costs and total variable costs at each level of output.

Marginal Cost (MC) is the increase in total cost when an additional unit of output is produced, calculated by the change in total cost divided by the change in quantity.

The table of calculations is as follows:

Units Sold = 1: TR = $72, MR = $72, TC = $164 ($100 fixed + $64 variable), MC = $64

Units Sold = 2: TR = $144, MR = $72, TC = $184 ($100 fixed + $84 variable), MC = $20

Units Sold = 3: TR = $216, MR = $72, TC = $214 ($100 fixed + $114 variable), MC = $30

Units Sold = 4: TR = $288, MR = $72, TC = $284 ($100 fixed + $184 variable), MC = $70

Units Sold = 5: TR = $360, MR = $72, TC = $370 ($100 fixed + $270 variable), MC = $86

As we look at the marginal cost and revenue, we can observe that the profit-maximizing quantity occurs at the output level where marginal revenue is just equal to or greater than marginal cost before marginal cost exceeds marginal revenue, which in this case is at three units.