Give step-by-step solution with explanation and final answer:

Logan Products has two production departments: assembly and finishing. These are supported by two service departments: sourcing
(
purch

Question

Give step-by-step solution with explanation and final answer:

Logan Products has two production departments: assembly and finishing. These are supported by two service departments: sourcing 
(
purchasing and handling of materials and human resources
)
 ﻿and operations 
(
work scheduling, supervision, and inspection
)
.
 ﻿Logan has the following labor hours devoted by each of the service departments to the other departments.
 
Total Labor Hours Used by DepartmentsSourcingOperationsAssemblyFinishingSourcing
-
2
0
,
0
0
0
4
0
,
0
0
0
6
0
,
0
0
0
Operations
1
0
,
0
0
0
-
6
0
,
0
0
0
5
0
,
0
0
0
The costs incurred in the plant are as follows:
DepartmentsDepartmental CostsSourcing$ 
1
7
7
,
0
0
0
Operations
2
2
5
,
0
0
0
Assembly
4
1
8
,
0
0
0
Finishing
2
6
3
,
0
0
0
Total$ 
1
,
0
8
3
,
0
0
0
Required:
What are the costs allocated to the two production departments using
(
a
)
 ﻿the direct method,
(
b
)
 ﻿the step method, when the sourcing department that provides the greatest percentage of services to other service departments goes first, and
(
c
)
 ﻿the reciprocal method?
What are the total costs in the production departments after allocation?

Give Chegg like answer so that I can cop

VIPSolutions · Accepted Answer

**Let's break down the solution step by step:**

---

## **Step 1: Organize the Data**

### **Labor Hours Matrix (Service Provided TO):**

| **From \ To** | Sourcing | Operations | Assembly | Finishing | **Total** |
|:-------------:|:--------:|:----------:|:--------:|:---------:|:---------:|
| **Sourcing**  |   —      | 20,000     | 40,000   | 60,000    | 120,000   |
| **Operations**| 10,000   |    —       | 60,000   | 50,000    | 120,000   |

### **Departmental Costs:**
- Sourcing: **$177,000**
- Operations: **$225,000**
- Assembly: **$418,000**
- Finishing: **$263,000**
- **Total:** $1,083,000

---

# **(a) Direct Method**

**Service department costs are allocated only to production departments, ignoring services between service departments.**

## **Step 1: Calculate Allocation Percentages (from service to production depts only)**

### **Sourcing:**
- To Assembly: 40,000 / (40,000 + 60,000) = 40%
- To Finishing: 60,000 / (40,000 + 60,000) = 60%

### **Operations:**
- To Assembly: 60,000 / (60,000 + 50,000) = 54.545%
- To Finishing: 50,000 / (60,000 + 50,000) = 45.455%

## **Step 2: Allocate Costs**

### **Allocate Sourcing ($177,000):**
- To Assembly: $177,000 × 40% = **$70,800**
- To Finishing: $177,000 × 60% = **$106,200**

### **Allocate Operations ($225,000):**
- To Assembly: $225,000 × 54.545% = **$122,726**
- To Finishing: $225,000 × 45.455% = **$102,274**

## **Step 3: Compute Total Costs in Production Departments**

- **Assembly:** $418,000 + $70,800 + $122,726 = **$611,526**
- **Finishing:** $263,000 + $106,200 + $102,274 = **$471,474**

---

## **(b) Step Method**  
*"The service department that provides the greatest percentage of services to other service departments goes first."*

### **Step 1: Find Which Service Department Goes First**

- **Sourcing provides 20,000 hrs to Operations (service dept) out of 120,000 total = 16.67%**
- **Operations provides 10,000 hrs to Sourcing out of 120,000 total = 8.33%**
- **Sourcing goes first.**

### **Step 2: Allocate Sourcing Costs (including to Operations)**

- **To Operations:** 20,000 / 120,000 = 16.67%
- **To Assembly:** 40,000 / 120,000 = 33.33%
- **To Finishing:** 60,000 / 120,000 = 50%

- To Operations: $177,000 × 16.67% = **$29,559**
- To Assembly: $177,000 × 33.33% = **$58,410**
- To Finishing: $177,000 × 50% = **$88,500**

### **Step 3: Add Allocated Sourcing Cost to Operations**

- **Operations new cost:** $225,000 + $29,559 = **$254,559**

### **Step 4: Allocate Operations (now $254,559) to Assembly and Finishing**

- **To Assembly:** 60,000 / (60,000 + 50,000) = **54.545%**
- **To Finishing:** 50,000 / (60,000 + 50,000) = **45.455%**

- To Assembly: $254,559 × 54.545% = **$138,145**
- To Finishing: $254,559 × 45.455% = **$116,414**

### **Step 5: Compute Total Costs in Production Departments**

- **Assembly:** $418,000 + $58,410 (from Sourcing) + $138,145 (from Operations) = **$614,555**
- **Finishing:** $263,000 + $88,500 (from Sourcing) + $116,414 (from Operations) = **$467,914**

---

## **(c) Reciprocal Method**

*Solve for total cost of each service dept including what they provide to each other.*

Let:
- **S = total cost of Sourcing (includes costs allocated from Operations)**
- **O = total cost of Operations (includes costs allocated from Sourcing)**

### **Step 1: Set Up Equations**

From usage percentages based on labor hours:
- **Sourcing provides:** 16.67% to Operations, 33.33% to Assembly, 50% to Finishing
- **Operations provides:** 8.33% to Sourcing, 50% to Finishing, 41.67% to Assembly

#### **Percentages to other service department:**
- **From Sourcing to Operations:** 16.67%
- **From Operations to Sourcing:** 8.33%

#### **Equations:**
$$
\begin{align*}
S &= 177,000 + 0.0833O \
O &= 225,000 + 0.1667S \
\end{align*}
$$

### **Step 2: Solve Simultaneously**

Substitute S into O:

$$
O = 225,000 + 0.1667S \
O = 225,000 + 0.1667(177,000 + 0.0833O) \
O = 225,000 + 0.1667 \times 177,000 + 0.1667 \times 0.0833O \
O = 225,000 + 29,559 + 0.01389O \
O - 0.01389O = 254,559 \
0.98611O = 254,559 \
O = \frac{254,559}{0.98611} \
O = 258,269 \
$$

Now substitute O into S:

$$
S = 177,000 + 0.0833 \times 258,269 \
S = 177,000 + 21,517 \
S = 198,517 \
$$

### **Step 3: Allocate Service Costs to Production Departments**

#### **Sourcing total cost: $198,517**
- To Assembly: 33.33% = $198,517 × 33.33% = **$66,171**
- To Finishing: 50% = $198,517 × 50% = **$99,259**

#### **Operations total cost: $258,269**
- To Assembly: 50% = $258,269 × 50% = **$129,135**
- To Finishing: 41.67% = $258,269 × 41.67% = **$107,612**

### **Step 4: Compute Total Costs in Production Departments**

- **Assembly:** $418,000 + $66,171 + $129,135 = **$613,306**
- **Finishing:** $263,000 + $99,259 + $107,612 = **$469,871**

---

## **Summary Table**

| Method      | Assembly | Finishing |
|-------------|----------|-----------|
| Direct      | $611,526 | $471,474  |
| Step        | $614,555 | $467,914  |
| Reciprocal  | $613,306 | $469,871  |

---

## **Final

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