Problem 14 - Accounting

Question

Roadworthy Tire and Rubber Company has capacity to produce 170,000 tires. Roadworthy presently produces and sells 130,000 tires for the North American market at a price of \(\$ 90\) per tire. Roadworthy is evaluating a special order from a European automobile company, Euro Motors. Euro is offering to buy 25,000 tires for \(\$ 75\) per tire. Roadworthy's accounting system indicates that the total cost per tire is as follows: Direct materials \(32 Direct labor 8 Factory overhead (60% variable) 25 Selling and administrative expenses (35% variable) 20 ____ Total \)85 ____ ____ Roadworthy pays a selling commission equal to \(5 \%\) of the selling price on North American orders, which is included in the variable portion of the selling and administrative expenses. However, this special order would not have a sales commission. If the order was accepted, the tires would be shipped overseas for an additional shipping cost of \(\$ 6.00\) per tire. In addition, Euro has made the order conditional on receiving European safety certification. Roadworthy estimates that this certification would cost \(\$ 125,000\). a. Prepare a differential analysis report dated May 4, 2010, for the proposed sale to Euro Motors. b. What is the minimum price per unit that would be financially acceptable to Roadworthy?

Step-by-Step Solution

Answer

The special order yields a differential income of $50,000. The minimum price per tire is $73.

Step 1: Calculate the Incremental Revenue

Determine the additional revenue generated by selling 25,000 tires to Euro Motors at $75 each. The equation is: Incremental Revenue = 25,000 tires * $75/tire. Calculate this value to find $1,875,000.

Step 2: Calculate Incremental Costs

Calculate the total incremental costs associated with the special order. First, determine the variable costs: direct materials ($32), direct labor ($8), variable portion of factory overhead (60% of $25 = $15), and variable portion of selling and administrative expenses without commission (35% of $20 = $7). Add these to find a variable cost of $62 per tire. Additionally, add the shipping cost of $6 per tire. For 25,000 tires, the variable cost is $68 per tire, resulting in 25,000*($68) = $1,700,000. Also, include the European safety certification cost of $125,000. Total Incremental Costs = $1,700,000 + $125,000 = $1,825,000.

Step 3: Calculate Differential Net Income

Subtract the total incremental costs from the incremental revenue to find the differential net income. Differential Net Income = Incremental Revenue - Incremental Costs = $1,875,000 - $1,825,000 = $50,000.

Step 4: Calculate Minimum Acceptable Price

To find the minimum price per tire, cover all variable costs and the additional fixed costs per tire due to certification. The variable cost per tire is $62 + $6 = $68. Divide the certification cost by the number of tires to find the per-tire cost: $125,000/25,000 = $5. Thus, the minimum price per tire that covers all costs is $68 + $5 = $73 per tire.

Key Concepts

Incremental Revenue

Incremental revenue refers to the additional income a company generates from accepting a new business opportunity, such as a special order. It's calculated by multiplying the number of units in the order by the price per unit offered by the buyer. In this particular exercise, Roadworthy is considering a special order from Euro Motors. The order consists of 25,000 tires, with each tire priced at $75. Thus, the incremental revenue is calculated as follows:
\[ \text{Incremental Revenue} = 25,000 \times 75 = 1,875,000 \]
This figure represents the total additional revenue Roadworthy expects to earn if they fulfill Euro Motor's order at the offered price.

Incremental Costs

When evaluating a special order, it's crucial to calculate incremental costs, which are the additional costs incurred to produce the extra units. In this scenario, the incremental costs consist of several components:
- **Direct Materials:** \(32 per tire - **Direct Labor:** \)8 per tire - **Variable Factory Overhead:** This is 60% of the total overhead per tire, amounting to \(15 per tire - **Variable Selling and Administrative Expenses:** 35% of the total, without commission, amounts to \)7 per tire
- **Additional Shipping Costs:** \(6 per tire, because of overseas shipping requirements.
By summing these variable costs, we get a total variable cost of \)68 per tire. Since 25,000 tires are to be produced, the total variable cost is: \[ 25,000 \times 68 = 1,700,000 \]
One-time costs like the European safety certification fee, $125,000 in this case, add to the incremental costs. Therefore, the total incremental costs are:\[ 1,700,000 + 125,000 = 1,825,000 \].

Minimum Price Calculation

To ensure financial viability, it's important to determine the minimum price per unit that covers all additional costs incurred by fulfilling the special order. We start with the per-tire variable cost of \(68, which covers direct materials, labor, and all variable overheads.
Next, the European safety certification is a fixed cost of \)125,000 that must be distributed across all 25,000 tires, which computes to:\[ \frac{125,000}{25,000} = 5 \]\
Thus, the cost per tire due to the certification is \(5. Combining this with the \)68 variable cost gives us a minimum price per tire for Roadworthy to consider the order financially viable:\[ 68 + 5 = 73 \]
Therefore, Roadworthy should not sell below $73 per tire to ensure that the order covers all related costs.

European Safety Certification

For Roadworthy to supply tires to Euro Motors, attaining European safety certification is crucial. This certification ensures that the tires meet EU safety standards, which are stringent and essential for selling products in European markets. Achieving this certification, however, entails a significant one-time expense of $125,000. This cost is non-variable, as it doesn't change with the number of tires produced; hence it's considered a fixed cost. In a differential analysis, this cost impacts the total incremental costs associated with the special order. It means that for every tire sold, part of its price must cover this certification fee. Despite its high cost, European certification can open numerous market opportunities for Roadworthy, potentially leading to more orders or partnerships in the future.