Problem 3 - Accounting

Question

Pocket 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 4,500 units at \(\$ 325\) per unit. The equipment has a cost of \(\$ 870,000\), residual value of \(\$ 30,000\), and a 10 -year life. The equipment can only be used to manufacture the PDA. The cost to manufacture the PDA is shown below. \(\begin{array}{lr}\text { Cost per unit: } & \$ 42.00 \\ \text { Direct labor } & 195.00 \\ \text { Direct materials } & 58.00 \\ \text { Factory overhead (including depreciation) } & \$ 295.00 \\ \text { Total cost per unit }\end{array}\) Determine the average rate of return on the equipment.

Step-by-Step Solution

Answer

The average rate of return on the equipment is approximately 32.14%.

Step 1: Calculate Total Annual Revenue

First, calculate the total annual revenue generated from the sales of PDAs. The number of units sold annually is 4,500, and each unit sells for $325. Thus, the total annual revenue is calculated as follows: \[ ext{Total Annual Revenue} = 4,500 imes 325 = 1,462,500 \, \text{USD} \]

Step 2: Calculate Total Annual Cost

Next, determine the total annual cost of manufacturing the PDAs. Sum up the cost per unit: direct labor (2), direct materials (5), and factory overhead (8). This equals \( \ ext{Total Cost Per Unit} = 42 + 195 + 58 = 295 \ ext{USD} \). Multiply this by the number of units produced (4,500): \[ \text{Total Annual Cost} = 4,500 imes 295 = 1,327,500 \, \text{USD} \]

Step 3: Calculate Net Annual Cash Flow

The net annual cash flow is the difference between the total annual revenue and the total annual cost. \( \text{Net Annual Cash Flow} = 1,462,500 - 1,327,500 = 135,000 \, \text{USD} \)

Step 4: Calculate Average Investment

Calculate the average investment by taking the initial cost of the equipment and subtracting the residual value, then dividing by 2, to average it over its life. \[ \text{Average Investment} = \frac{{870,000 - 30,000}}{2} = 420,000 \, \text{USD} \]

Step 5: Calculate Average Rate of Return

Finally, the average rate of return is calculated by dividing the net annual cash flow by the average investment, then multiplying by 100 to convert it to a percentage. \[ \text{Average Rate of Return} = \left(\frac{135,000}{420,000}\right) \times 100 \approx 32.14\,\% \]

Key Concepts

Investment Analysis

Investment analysis is the process of evaluating the financial potential of an asset or project, like purchasing new equipment. The main goal is to determine whether the investment will yield a beneficial return. In the context of Pocket Communications Inc., investment analysis involves examining the potential gains from new equipment used to manufacture PDAs.

To perform this analysis, key factors to consider include:

• Initial cost of the equipment
• Estimated revenue from the sales of PDAs
• Operating expenses, such as manufacturing and maintenance costs
• Residual value (the estimated value of the equipment at the end of its useful life)
• Expected lifespan of the equipment

These elements help determine if the investment is financially viable and how it compares to other possible investments. A thorough investment analysis ensures that the resources are efficiently allocated towards projects with the best potential returns.

Net Annual Cash Flow

Net annual cash flow is a critical measurement that shows the net amount of cash generated by an investment each year. It is found by subtracting the total annual costs from the total annual revenues.

For Pocket Communications Inc., this involves calculating the difference between the revenue from PDA sales and the cost of manufacturing them.

The significance of net annual cash flow includes:

• Providing insights into the expected liquidity from the investment
• Helping assess the project's profitability and sustainability
• Assisting in comparing different investment opportunities

This value is indispensable for determining whether the equipment purchase will provide sufficient financial returns to justify the investment.

Manufacturing Cost Calculation

Manufacturing cost calculation is the process of determining the total cost required to produce a product. For Pocket Communications Inc., this includes the cost associated with labor, materials, and overhead.

Understanding the manufacturing cost per unit is essential to:

• Evaluate the production efficiency
• Optimize pricing strategies to ensure competitiveness and profitability
• Identify potential areas for cost reduction

In the case study, the total cost to manufacture a PDA was calculated by adding all individual cost components, resulting in a per-unit cost that was crucial for further financial analysis.

Depreciation Calculation

Depreciation calculation is a method to spread the cost of a tangible asset over its useful life. It reflects how the asset loses value over time due to use and obsolescence.

In evaluating the equipment purchase for Pocket Communications Inc., depreciation is vital for:

• Accounting for wear and tear on the asset
• Providing a tax shield since depreciation expenses can reduce taxable income
• Offering a realistic view of the equipment's actual value over its lifecycle

The exercise uses straight-line depreciation, which is calculated as: \[ \text{Depreciation per year} = \frac{\text{Initial Cost} - \text{Residual Value}}{\text{Useful Life}} \]This consistent annual depreciation figure ensures that the financial analysis remains straightforward and transparent.