Question

The inventory of Royal Decking consisted of five products. Information about December 31, 2018, inventory is as follows:

Per Unit
Product Cost Replacement Cost Selling Price
A $ 42 $37 $62
B 82 72 102
C 42 57 82
D 102 72 132
E 22 30 32

Selling costs consist of a sales commission equal to 10% of selling price and shipping costs equal to 5% of the cost. The normal gross profit percentage is 20% of the selling price.

Required:
What unit value should Royal Decking use for each of its products when applying the lower of cost or market (LCM) rule to units of ending inventory? (Do not round intermediate calculations. Round final answers to 2 decimal places)

Product Cost Replacement cost NRV NRV - NP Market Per Unit Inventory Value
A
B
C
D
E

Answer 1

To find the profit-maximizing quantity for Doggies Paradise Inc., we calculate total revenue, marginal revenue, total cost, and marginal cost for output levels one to five units. The firm should produce at the level where marginal revenue equals marginal cost, which is at 3 units in this case.

Step-by-step explanation:

Profit Maximization in a Perfectly Competitive Market

In order to determine the profit maximizing quantity for Doggies Paradise Inc., we need to calculate the total revenue, marginal revenue, total cost, and marginal cost for each level of output. Since it is a perfectly competitive market, the marginal revenue is equal to the selling price of $72 for every unit sold.

The fixed costs are $100 regardless of the quantity produced. We calculate total cost by adding fixed costs to variable costs at each output level. Total revenue is the selling price multiplied by the number of units sold. Marginal cost is calculated as the change in total cost divided by the change in quantity.

Using the provided variable costs, we can fill out a table:

• 
  
• For 1 unit: Total Revenue = $72, Marginal Revenue = $72, Total Cost = $100 + $64 = $164, Marginal Cost = —
• 
  
• For 2 units: Total Revenue = $144, Marginal Revenue = $72, Total Cost = $100 + $84 = $184, Marginal Cost = $20
• 
  
• For 3 units: Total Revenue = $216, Marginal Revenue = $72, Total Cost = $100 + $114 = $214, Marginal Cost = $30
• 
  
• For 4 units: Total Revenue = $288, Marginal Revenue = $72, Total Cost = $100 + $184 = $284, Marginal Cost = $70
• 
  
• For 5 units: Total Revenue = $360, Marginal Revenue = $72, Total Cost = $100 + $270 = $370, Marginal Cost = $86

To maximize profits, the firm should produce up to the point where marginal revenue equals marginal cost, as producing additional units beyond that point would lower profits. Looking at the marginal costs, we see that the marginal cost for the third unit is lower than the marginal revenue, but the marginal cost for the fourth unit is higher. Therefore, the profit-maximizing quantity is 3 units.