91Ó°ÊÓ

\((\mathrm{CPA}, \text { adapted })\). The vertical axes of the graphs below represent total cost, and the horizontal axes represent units produced during a calendar year. In each case, the zero point of dollars and production is at the intersection of the two axes. Select the graph that matches the numbered manufacturing cost data (requirements 1-9). Indicate by letter which graph best fits the situation or item described. The graphs may be used more than once. 1\. Annual depreciation of equipment, where the amount of depreciation charged is computed by the machine-hours method. 2\. Electricity bill-a flat fixed charge, plus a variable cost after a certain number of kilowatt-hours are used, in which the quantity of kilowatt-hours used varies proportionately with quantity of units produced. 3\. City water bill, which is computed as follows: The gallons of water used vary proportionately with the quantity of production outputt 4\. cost of direct materials, where direct material cost per unit produced decreases with each pound of material used (for example, if 1 pound is used, the costis S10; if 2 pounds are used, the costis \$19.98 3 pounds are used, the cost is \(\$ 29.94\), with a minimum cost per unit of \(\$ 9.20\) 5\. Annual depreciation of equipment, where the amount is computed by the straight-line method. When the depreciation schedule was prepared, it was anticipated that the obsolescence factor would be greater than the wear-and- tear factor. 6\. Rent on a manufacturing plant donated by the city, where the agreement calls for a fixed-fee payment unless 200,000 labor-hours are worked, in which case no rent tis paid. 7\. Salaries of repair personnel, where one person is needed for every 1,000 machine-hours o o less (that is, 0 to 1,000 hours requires one person, 1,001 to 2,000 hours requires two people, and so on 8\. cost of direct materials used (assume no quantity discounts).) 9\. Rent on a manufacturing plant donated by the county, where the agreement calls for rent of \(\$ 100,000\) to be reduced by s1 for each direct manufacturing labor-hour worked in excess of 200,000 hours, but a minimum rental fee of \(\$ 20,000\) must be paid.

Step by step solution

01

1. Machine-Hours Depreciation Method

For the machine-hours depreciation method, depreciation expense increases linearly with the number of hours a machine is used. So, the graph should show a straight line with a positive slope.

02

2. Electricity Bill

For the electricity bill, there is a flat fixed charge plus a variable cost proportional to the number of kilowatt-hours used, which varies with the units produced. In this case, the graph should show a fixed cost followed by a linear increase proportional to the unit production.

03

3. City Water Bill

The gallons of water used varies proportionately with the quantity of production output. This means that the cost should increase linearly as the units produced increases. The graph should show a straight line with a positive slope.

04

4. Direct Materials Cost

The direct material cost per unit produced decreases with each pound of material used, and there's a minimum cost per unit. The graph should show a concave curve, starting at a higher cost per unit and eventually reaching a minimum cost and then remaining constant.

05

5. Straight-Line Depreciation Method

For the straight-line depreciation method, the annual depreciation is the same regardless of the units produced. Hence, the graph should be a horizontal line representing the fixed depreciation cost.

06

6. Rent on Donated Plant

For this cost data, rent is a fixed fee unless 200,000 labor-hours are worked, in which case no rent is paid. The graph should show a constant value until 200,000 hours, after which the cost drops to zero.

07

7. Salaries of Repair Personnel

For salaries of repair personnel, one person is needed for every 1,000 machine-hours or less. So, the cost of salaries increases in a stepwise manner as the number of machine-hours increases. The graph should be a staircase-like shape.

08

8. Direct Materials Cost (No Quantity Discounts)

In this case, since there are no quantity discounts, the direct materials cost should increase linearly with the number of units produced. The graph should show a straight line with a positive slope.

09

9. Rent on Donated Plant (County)

For this rent agreement, the rent of \(\$100,000\) is reduced by \(1 for each direct manufacturing labor-hour worked in excess of 200,000 hours, but a minimum rental fee of \)\$20,000\( must be paid. This means that the rent will be a constant \)\$100,000\( up to 200,000 hours, then it will decrease linearly with an increase in labor-hours worked until it reaches the minimum rent of \)\$20,000$. The graph should show a straight line followed by a downward diagonal line followed by a horizontal line at the minimum rent value. Now that we've described the cost behavior for each numbered item, refer to your graphs and select the graph which best matches each description. Note that graphs may be used more than once.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Machine-Hours Depreciation Method

When a manufacturing company utilizes equipment, it's essential to spread the cost of this equipment over its useful life. One such method is the machine-hours depreciation method. Simply put, this approach allocates the cost of an asset to expense based on the actual usage of the machine. The logic here is straightforward: the more you use the equipment, the more it wears out, and consequently, the higher the depreciation expense for that period.

Depreciation calculated through this method is directly proportional to the machine's operation. Therefore, if a machine is used for more hours during a particular month or year, the depreciation expense will be higher for that time, reflecting increased use. This contrasts with methods like straight-line depreciation, where the expense is the same each period, regardless of how much the machine is used.

From the accounting point of view, businesses that have fluctuating usage rates of their machinery across different periods might find the machine-hours method more reflective of the 'wear and tear' on their equipment. An educator may emphasize the importance of selecting an appropriate depreciation method that best represents the asset's usage patterns to accurately match expenses with the revenue earned in a financial period.

Variable Costing in Action

When delving into variable costing, we distinguish between costs with a direct relationship to production volume and those that remain fixed regardless of how much is produced. Variable costs increase with each additional unit produced because they include expenses like raw materials and certain utilities that vary with production output.

For example, consider electricity in a factory: part of the bill might be a flat rate, common in residential billing, but beyond a certain threshold, the cost scales with consumption. In an educational setting, variable costing is used to demonstrate how a company's profitability can be affected by the efficiency of production.

Moreover, variable costing provides crucial insights for decision-making. It helps in setting pricing strategies, as well as in budgeting and forecasting. When preparing variable costing analyses, it's key to include only variable production costs, excluding fixed costs like salaried labor and rent, providing a clearer view of the incremental costs attributable to each product.

Step Costing: Understanding the Staircase Effect

Certain costs within a business operation have a unique behavior that is best described by step costing. Step costs are those that remain constant over a range of activity, but jump to a higher level when a threshold is exceeded. These costs are fixed within certain activity levels but become variable across different levels. An analogy often used is a staircase: flat at each level (representing the fixed cost within an activity level), but the overall cost 'steps up' when production increases beyond a certain point.

In our textbook problem, this is perfectly illustrated by the salaries of repair personnel, which remain constant up until a new repair person is required to handle additional machine-hours. Educators highlight the importance of understanding step costing for budget planning, as companies need to anticipate when such thresholds will be crossed and additional resources will be necessary.

Understanding step costing is also essential for accurately predicting cost behavior and managing resources efficiently. It can have a significant impact on both short-term operational decisions and long-term strategic planning, particularly when scaling up production in a manufacturing environment.