## Allocating Overhead Using a Single, Plant-wide Rate

### Learning Outcomes

• Allocate manufacturing overhead to cost objects using a single, plant-wide rate

Once we have determined our allocation rate, we apply that rate to each product or product line in order to assign costs to individual items or batches.

## Allocating Based on Direct Machine Hours

In our example, Yore Company’s automated process turns out a basic purse every nine hours, but the more complicated deluxe purse takes 32.5 hours of machine time. Our machines will run for 28,800 hours to produce 3,200 basic purses (9 * 3,200) and another 18,200 hours to produce 560 deluxe purses (32.5 * 560) for a total of 47,000 hours. Imagine 65 machines running 24 hours a day. Forty of them are producing nothing but basic purses and the other 25 are producing deluxe purses.

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The standard overhead rate based on direct machine hours (DMH) would be $4.00 per machine-hour ($188,000/47,000 machine-hours). Based on that rate, we would allocate $36.00 to each basic purse ($4/DMH * 9 hours) and $130.00 to each deluxe purse ($4/DMH * 32.5 hours).

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The full cost of each purse would be:

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* basic = 4.125 hours * $20/hour, deluxe = 10 hours *$20/hour

This would result in a gross profit per unit of:

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To check our work, let’s multiply the gross profit per purse by unit sales to compute total gross profit by product line and by total:

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Notice that under this allocation method, using direct machine hours instead of units, we have a dramatically different outcome. Under this allocation method, it looks like the deluxe purse is actually losing money.

## Allocating Based on Direct Labor

Let’s say we consider our operation to be labor-intensive rather than capital-intensive (automated). In that case, we might choose to allocate fixed overhead based on direct labor hours (DLH) or direct labor dollars (DL$). If our standard direct labor cost is the same for both purses, these two calculations will produce the same results, so in this lesson, we’ll use DL$. However, if workers producing deluxe purses are more highly paid than workers producing basic purses, the outcome between the two direct labor methods would be different.

Let’s review our standard costs again:

Basic Deluxe
Planned production 3,200 560
Standard/Budget to make one purse
Direct Machine Hours             9.000           32.500
Direct Labor Hours             4.125           10.000
Direct Labor Cost per Hour $20.00$          20.00
Direct Materials $100.00$        210.00

Workers turn out a basic purse every 4.125 hours, but the more complicated deluxe purse takes 10 hours of labor. Our line workers put in 13,200 hours to produce 3,200 basic purses (4.125 * 3,200) and another 5,600 hours to produce 560 deluxe purses (10 * 560) for a total of 18,800 hours. This would be 78 laborers working in three shifts, running the machines and finishing the products by hand, 24 hours a day (26 direct labor workers each shift). Eighteen of those laborers are working on basic purses, and 8 are working on deluxe.

At a standard rate of $20 for wages and benefits, the Direct Labor Dollars for basic and deluxe purses will be$264,000 and $112,000, respectively (13,200 hours *$20/hour = $264,000, and 5,600 hours *$20/hour = $112,000) for a total DL$ base of $376,000. A standard overhead rate based on direct labor dollars (DL$) would be $0.50 per DL$ ($188,000/376,000). Based on that rate, we would allocate$41.25 to each basic purse ($0.50/DL$ * $82.50/purse) and$100.00 to each deluxe purse ($0.50/DL$ * \$200.00/purse).

The full cost of each purse would be:

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This would result in a gross profit per unit of:

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To check our work, let’s multiply the gross profit per purse by unit sales to compute total gross profit by product line and by total:

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Notice that the total gross profit remains the same no matter how we allocated fixed manufacturing overhead to product lines. What is changing is the gross profit for each type of product.

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Here is a recap of our results so far:

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Again, notice that dividing fixed manufacturing overhead by number of units makes the gross profit for the deluxe purse significantly higher than if fixed manufacturing overhead is allocated according to direct labor. By allocating fixed manufacturing overhead by machine hours, the deluxe purse is actually costing more to produce than it is selling for.

Allocating based on a single rate for the entire organization has pros and cons:

Dividing by number of total units of all products:

• Simple.
• May not accurately reflect the use of resources because it allocates fixed manufacturing overhead evenly over all products.

Allocating based on direct machine hours:

• May be more accurate for automated processes (e.g. where fixed manufacturing overhead includes depreciation on machines, repairs and maintenance, etc.).
• Slightly more complicated than simply dividing fixed manufacturing overhead by number of units of everything produced.

Allocating based on direct labor hours:

• May be more accurate for labor-intensive processes (e.g. where people are doing most of the work by hand).
• Slightly more complicated than simply dividing fixed manufacturing overhead by number of units of everything produced.
• May or may not give desired results if hourly labor costs are higher for certain product lines.

Allocating based on direct labor dollars:

• May be more accurate for labor-intensive processes (e.g. where people are doing most of the work by hand).
• Slightly more complicated than simply dividing fixed manufacturing overhead by number of units of everything produced.
• May or may not give desired results if hourly labor costs are higher for certain product lines.

We used a single rate to allocate all of the factory overhead to each product line, but we can also use a single rate for each department:

We’ll study how this works in the next section, but first check your understanding of using a single rate to allocate fixed manufacturing overhead to products.