Act like a helpful tutor and exlain me :
Give step-by-step solution with explanation and final answer:Netincome $411.78
The company has the following summarized statement of changes in equity:
Cont

Question

Act like a helpful tutor and exlain me :
Give step-by-step solution with explanation and final answer:Netincome $411.78
The company has the following summarized statement of changes in equity:
Contributed
Convertible Contributed Surplus—
Preferred Preferred Surplus— Convertible Common Retained
Shares, Shares Options Bond Shares Earnings
pe $1,200,000 0 $44,000 $5,055 $600,000 $600,000
Shares issued [J $800,000 0 o 280,000 0
Shores o 0 o o (80000) o
reacquired
Netincome 0 o 0 0 o au
Dividends [J 0 0 0 [J (120,000)
Ending value $1,200,000 $800,000 $44,000 $5,055 $800,000 $891,778
Notes:
9 Convertible preferred shares were issued on January 1.
2. ‘Additional common shares were issued on September 1.
3. Common shares were reacauired on April 1
4, Dividends were paid to cumulative preferred shareholders.
5 ‘Average price of the common shares was $28 per share.
(a)
Calculate the basic earnings per share. (Round answer to 2 decimal places, eg. 5.75)
Basic EPS $
Sevafor Later Attempts: 0 of 3used

VIPSolutions · Accepted Answer

Let's break down step-by-step how to **calculate the basic earnings per share (EPS)**.

---

## **Step 1: Find Net Income Available to Common Shareholders**

**Net income (from above):**  
$$
\$411,778
$$

**Less: Preferred Dividends**  
- Dividends were paid to cumulative preferred shareholders:  
  $$
  \$120,000
  $$
- These must be subtracted from net income to get the earnings available to common shareholders.

$$
\text{Net income available to common} = \$411,778 - \$120,000 = \$291,778
$$

---

## **Step 2: Calculate Weighted Average Number of Common Shares Outstanding**

We need to account for shares issued and repurchased during the year.

### **Beginning of Year**
- **Beginning common shares:**  $600,000

### **April 1: Shares Repurchased**
- **Shares repurchased:** 80,000
- **Months outstanding before repurchase:** Jan, Feb, Mar = 3 months (out of 12)
- **Months after repurchase:** 9 months (Apr-Dec)

### **September 1: Shares Issued**
- **Shares issued:** 280,000
- **Months outstanding after issue:** 4 months (Sep-Dec)

Let's calculate the weighted average:

1. **Shares outstanding Jan 1 – Mar 31:**  
   $600,000$ shares for $3/12$ of the year

2. **Shares outstanding Apr 1 – Aug 31:**  
   $600,000 - 80,000 = 520,000$ shares for $5/12$ of the year

3. **Shares outstanding Sep 1 – Dec 31:**  
   $520,000 + 280,000 = 800,000$ shares for $4/12$ of the year

Weighted average formula:
$$
\begin{align*}
\text{Weighted average} = 
& (600,000 \times \frac{3}{12}) \
+ & (520,000 \times \frac{5}{12}) \
+ & (800,000 \times \frac{4}{12}) \
\end{align*}
$$

Calculate each part:
- $600,000 \times \frac{3}{12} = 150,000$
- $520,000 \times \frac{5}{12} = 216,667$
- $800,000 \times \frac{4}{12} = 266,667$

Sum it up:
$$
150,000 + 216,667 + 266,667 = 633,334
$$

---

## **Step 3: Calculate Basic EPS**

$$
\text{Basic EPS} = \frac{\text{Net income available to common}}{\text{Weighted average common shares}}
$$

$$
\text{Basic EPS} = \frac{291,778}{633,334} \approx .46
$$

---

## **Final Answer**

**Basic EPS = $.46** (rounded to two decimal places)

---

### **Summary Table**

| Step | Value               |
|------|---------------------|
| Net income                | $411,778            |
| Less: Preferred dividends | $120,000            |
| Net income to common      | $291,778            |
| Weighted avg shares       | 633,334             |
| Basic EPS                 | **$.46**           |

---

Let me know if you have any questions or want to see the diluted EPS calculation!

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