Problem 3 - Accounting

Question

Airwave Communications Inc. is considering an investment in new equipment that will be used to manufacture a PDA (personal data assistant). The PDA is expected to generate additional annual sales of 4,800 units at \(\$ 350\) per unit. The equipment has a cost of \(\$ 910,000\), residual value of \(\$ 50,000\), and a 10 -year life. The equipment can only be used to manufacture the PDA. The cost to manufacture the PDA is shown below. \(\begin{array}{lr}\text { Cost per unit: } & \$ 52.00 \\ \text { Direct labor } & 195.00 \\ \text { Direct materials } & 58.00 \\ \text { Factory overhead (including depreciation) } & \$ 305.00 \\ \text { Total cost per unit }\end{array}\) Determine the average rate of return on the equipment.

Step-by-Step Solution

Answer

The average rate of return on the equipment is approximately 14.29%.

Step 1: Calculate Annual Revenues

First, determine the revenue generated by the sale of the PDAs. This is calculated by multiplying the number of units sold annually by the selling price per unit. \[\text{Annual Revenue} = 4800 \text{ units} \times \\(350 = \\)1,680,000\]

Step 2: Calculate Annual Manufacturing Costs

Next, calculate the total annual manufacturing cost by multiplying the number of units produced by the total cost per unit.\[\text{Annual Manufacturing Cost} = 4800 \text{ units} \times \\(305 = \\)1,464,000\]

Step 3: Determine Annual Income Before Depreciation

Find the annual income generated before accounting for depreciation by subtracting the annual manufacturing cost from the annual revenue.\[\text{Income Before Depreciation} = \\(1,680,000 - \\)1,464,000 = \$216,000\]

Step 4: Calculate Annual Depreciation Expense

The depreciation expense is found by subtracting the residual value from the equipment cost and dividing by its useful life.\[\text{Depreciation Expense} = \frac{\\(910,000 - \\)50,000}{10} = \$86,000 \]

Step 5: Find Annual Income After Depreciation

Subtract the annual depreciation expense from the income before depreciation to get the annual income after depreciation.\[\text{Income After Depreciation} = \\(216,000 - \\)86,000 = \$130,000\]

Step 6: Calculate Average Rate of Return

The average rate of return is calculated by dividing the annual income after depreciation by the initial cost of the equipment, then multiplying by 100 to convert to a percentage.\[\text{Average Rate of Return} = \left(\frac{\\(130,000}{\\)910,000}\right) \times 100 \approx 14.29\%\]

Key Concepts

Understanding Average Rate of Return

The average rate of return (ARR) is a fundamental financial metric used in capital budgeting decisions. It helps companies evaluate the profitability of an investment by comparing the net income it generates against the cost of the investment.
To compute ARR, you take the annual income after accounting for non-operating expenses (like depreciation). In this context, depreciation represents the loss of value of an asset over time due to wear and tear or obsolescence.
Once the annual income after depreciation is calculated, the ARR is determined by dividing that income by the initial investment cost, and then converted to a percentage. This percentage represents how much return an equipment is generating annually compared to its initial cost, providing insight into whether an investment is worth pursuing.

• An ARR above the target rate suggests that an investment is likely profitable.
• An ARR below the target rate may indicate that the investment is not generating sufficient returns.

The Role of Depreciation

Depreciation is an accounting method used to allocate the cost of a tangible asset over its useful life. In financial accounting, depreciation affects a company's financial statements and tax liabilities.
For the equipment used by Airwave Communications Inc., depreciation is calculated using the straight-line method. This method distributes the expense evenly across each year of the asset’s life. The formula for this is: \[ \text{Depreciation Expense} = \frac{\text{Cost of Asset} - \text{Residual Value}}{\text{Useful Life}}\]
This expense is a crucial factor in determining the net profitability of an investment.

• Reduces taxable income, thereby affecting net income.
• Influences the average rate of return calculation by affecting annual net income.

Evaluating Capital Investment

Capital investments involve significant expenditure of funds to acquire or upgrade physical assets. These investments are essential for a company's growth and operational efficiency.
In this example, Airwave Communications Inc. is considering significant capital investment in new manufacturing equipment.

• Such investments usually require detailed analysis to ensure they will generate sufficient returns.
• Key metrics like the average rate of return help determine if the initial outlay will lead to adequate profit.

Capital investments, like purchasing new equipment, typically have long-term implications for a company. Therefore, it's important to carefully analyze potential returns, payback periods, and the equipment's residual value at the end of its useful life.

Calculating Manufacturing Costs

Manufacturing costs are expenses directly incurred from the production of goods. These include direct materials, direct labor, and overhead costs. For Airwave Communications Inc., these costs greatly impact the overall profitability.
To calculate these costs for the PDA:

• Direct Materials: Costs of components and raw materials that are directly attributable to the production of the product.
• Direct Labor: Wages paid to workers who are directly involved in manufacturing.
• Overhead Costs: Includes indirect costs associated with manufacturing, such as factory utilities, maintenance, and depreciation.

Understanding these components helps a company manage its finances more efficiently and optimize production processes. Cost management ensures that production remains profitable and pricing strategies are competitive.