To determine the cost of the product that remains in work-in-process (WIP), we need to calculate the cost of both materials and conversion for the unfinished product. Here's the step-by-step process:

Step 1: Define variables and important values

• Total production started: 105,000 liters
• Completed production: 90,000 liters
• Material costs: $46,820
• Conversion costs: $20,380
• Ending WIP completion percentage: 40%
• Beginning WIP: None (0 liters)

From this, the amount of work-in-process (WIP) is: $\text{WIP} = 105,000 - 90,000 = 15,000 \text{ liters}$

Step 2: Calculate costs per equivalent unit

We calculate the costs per equivalent unit separately for materials and conversion.

Materials:

All materials are added at the start of production, so the 15,000 liters of WIP are considered 100% complete for materials. The cost per liter for materials is:

$\text{Material cost per liter} = \frac{\text{Total material cost}}{\text{Total liters started}} = \frac{46,820}{105,000} = 0.44686 \, \text{\$ per liter}$

Conversion:

Since the ending WIP is 40% complete, we calculate the equivalent units for conversion. For the 15,000 liters of WIP, the equivalent units for conversion are:

$\text{Equivalent units for conversion} = 15,000 \times 40\% = 6,000 \, \text{equivalent units}$

The cost per liter for conversion is:

$\text{Conversion cost per equivalent unit} = \frac{\text{Total conversion cost}}{\text{Total completed and equivalent units}} = \frac{20,380}{90,000 + 6,000} = \frac{20,380}{96,000} = 0.21229 \, \text{\$ per liter}$

Step 3: Calculate the total cost of WIP

Now, we calculate the total cost of WIP by combining the materials and conversion costs:

Materials cost for WIP:

$\text{Materials cost of WIP} = 15,000 \times 0.44686 = 6,702.90 \, \text{\$}$

Conversion cost for WIP:

$\text{Conversion cost of WIP} = 6,000 \times 0.21229 = 1,273.74 \, \text{\$}$

Step 4: Total cost of WIP

The total cost of the product that remains in work-in-process is:

$\text{Total WIP cost} = 6,702.90 + 1,273.74 = 7,976.64 \, \text{\$}$

Conclusion:

The cost of the product that remains in work-in-process is $7,976.64.

Would you like more details on any part of this process or have any questions?

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Here are 5 related questions to extend your understanding:

1. How would the cost change if the ending WIP was 50% complete instead of 40%?
2. How are equivalent units used when calculating conversion costs?
3. What would happen to costs if the company had a beginning WIP?
4. How do material costs differ when they are added throughout production instead of at the start?
5. How would the total cost change if the company produced only 80,000 liters instead of 90,000?

Tip: Understanding the calculation of equivalent units is key in cost accounting for incomplete production, especially in scenarios involving partially completed inventory.