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VIPSolutions · Accepted Answer

Let's solve **ALL THREE QUESTIONS** step by step by extracting all necessary data and formulae for each.  
We will use the **same dataset** for all three parts.

---

## **Available Data:**

- Sales = \$10,000
- Gross Profit Margin = 40%
- Inventory Turnover Ratio = 4 times
- Net Profit Margin = 8%
- Average Collection Period = 45 days
- Return on Equity (ROE) = 50%
- Return on Assets (ROA) = 20%
- Cash = \$250
- Current Ratio = 2.5
- Accounts Payable Days = 30 days

---

# **Step 1: Calculate All Missing Balances**

### **A. Calculate Net Income**

**Formula:**  
$$
\text{Net Profit Margin} = \frac{\text{Net Income}}{\text{Sales}}
$$
$$
.08 = \frac{\text{Net Income}}{10,000}
\implies \text{Net Income} = .08 \times 10,000 = 800
$$

---

### **B. Calculate Gross Profit and COGS**

$$
\text{Gross Profit Margin} = \frac{\text{Gross Profit}}{\text{Sales}}
$$
$$
.4 = \frac{\text{Gross Profit}}{10,000}
\implies \text{Gross Profit} = .4 \times 10,000 = 4,000
$$
$$
\text{COGS} = \text{Sales} - \text{Gross Profit} = 10,000 - 4,000 = 6,000
$$

---

### **C. Calculate Average Inventory**

**Formula:**  
$$
\text{Inventory Turnover Ratio} = \frac{\text{COGS}}{\text{Average Inventory}}
$$
$$
4 = \frac{6,000}{\text{Average Inventory}}
\implies \text{Average Inventory} = \frac{6,000}{4} = 1,500
$$

---

### **D. Calculate Average Receivables**

**Formula:**  
$$
\text{Average Collection Period} = \frac{365}{\text{Receivables Turnover}}
$$
$$
\text{Receivables Turnover} = \frac{365}{45} = 8.111
$$
$$
\text{Receivables Turnover} = \frac{\text{Sales}}{\text{Average Receivables}}
\implies 8.111 = \frac{10,000}{\text{Average Receivables}}
\implies \text{Average Receivables} = \frac{10,000}{8.111} = 1,233
$$

---

### **E. Calculate Average Accounts Payable**

**Formula:**  
$$
\text{Accounts Payable Days} = \frac{365}{\text{Payables Turnover}}
$$
$$
\text{Payables Turnover} = \frac{365}{30} = 12.167
$$
$$
\text{Payables Turnover} = \frac{\text{COGS}}{\text{Average Payables}}
\implies 12.167 = \frac{6,000}{\text{Average Payables}}
\implies \text{Average Payables} = \frac{6,000}{12.167} = 493
$$

---

### **F. Calculate Total Assets**

**Formula:**  
$$
\text{ROA} = \frac{\text{Net Income}}{\text{Total Assets}}
$$
$$
.20 = \frac{800}{\text{Total Assets}}
\implies \text{Total Assets} = \frac{800}{.20} = 4,000
$$

---

### **G. Calculate Equity**

**Formula:**  
$$
\text{ROE} = \frac{\text{Net Income}}{\text{Equity}}
$$
$$
.50 = \frac{800}{\text{Equity}}
\implies \text{Equity} = \frac{800}{.50} = 1,600
$$

---

### **H. Calculate Current Liabilities**

**Formula:**  
$$
\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}}
$$
Let’s first find **Current Assets**.

We know:
- Cash = \$250
- Receivables = \$1,233
- Inventory = \$1,500

$$
\text{Current Assets} = 250 + 1,233 + 1,500 = 2,983
$$
$$
2.5 = \frac{2,983}{\text{Current Liabilities}}
\implies \text{Current Liabilities} = \frac{2,983}{2.5} = 1,193
$$

---

### **I. Calculate Total Liabilities**

$$
\text{Total Assets} = \text{Total Liabilities} + \text{Equity}
$$
$$
4,000 = \text{Total Liabilities} + 1,600
\implies \text{Total Liabilities} = 4,000 - 1,600 = 2,400
$$

---

### **J. Calculate Long Term Debt**

$$
\text{Total Liabilities} = \text{Current Liabilities} + \text{Long Term Debt}
$$
$$
2,400 = 1,193 + \text{Long Term Debt}
\implies \text{Long Term Debt} = 2,400 - 1,193 = 1,207
$$

---

### **K. Calculate Net Fixed Assets**

$$
\text{Total Assets} = \text{Current Assets} + \text{Net Fixed Assets}
$$
$$
4,000 = 2,983 + \text{Net Fixed Assets}
\implies \text{Net Fixed Assets} = 4,000 - 2,983 = 1,017
$$

---

## **Step 2: Answer Each Question**

---

## **Question 29: Notes Payable**

Notes payable is usually part of **current liabilities**. But, in this case:
- **Current Liabilities = 1,193**
- **Accounts Payable = 493** (from average accounts payable)

$$
\text{Notes Payable} = \text{Current Liabilities} - \text{Accounts Payable}
$$
$$
\text{Notes Payable} = 1,193 - 493 = 700
$$

---

## **Question 30: Long Term Debt**

$$
\text{Long Term Debt} = 1,207
$$

---

## **Question 31: Net Fixed Assets**

$$
\text{Net Fixed Assets} = 1,017
$$

---

# **Final Answers Summary**

---

### **Question 29: Notes Payable**
$$
\boxed{700}
$$

### **Question 30: Long Term Debt**
$$
\boxed{1207}
$$

### **Question 31: Net Fixed Assets**
$$
\boxed{1017}
$$

---
**Final Answer:**  
The Atlanta Company's 2012 balance sheet shows Notes Payable of **700**, Long Term Debt of **1207**, and Net Fixed Assets of **1017**.

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