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?Solution s

Question

Now give this answer completely without skipping even a small step of calculation and try not to give answer in long paragraphs and answer the questions by following these instructions:

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VIPSolutions · Accepted Answer

# Problem Objective

**Objective:**  
Find the **opening price** for the stock of AK Enterprises given the following data:

- **Annual dividend:** $.79  
- **Dividend yield:** 1.40%  
- **PE ratio:** 22  
- **Shares outstanding:** 90 million  
- **Change in price for the day:** $.26  
- **% Change for the day:** .46%  
- **Closing price:** (To be calculated)  
- **Volume:** 18,649,130 shares

---

## Step 1: Understand the Relationship

The **dividend yield** is given by:
$$
\text{Dividend Yield} = \frac{\text{Annual Dividend}}{\text{Closing Price}}
$$

---

## Step 2: Calculate the Closing Price

Given:
- Dividend Yield = 1.40% = .014
- Annual Dividend = $.79

$$
\text{Closing Price} = \frac{\text{Annual Dividend}}{\text{Dividend Yield}}
$$
$$
\text{Closing Price} = \frac{.79}{.014}
$$
$$
\text{Closing Price} = 56.42857143
$$

---

## Step 3: Calculate the Opening Price

Given:
- Change in Price = $.26 (positive, so Closing Price > Opening Price)
- \% Change = .46% = .0046

The % change formula:
$$
\% \text{Change} = \frac{\text{Change}}{\text{Opening Price}}
$$

$$
.0046 = \frac{.26}{\text{Opening Price}}
$$

$$
\text{Opening Price} = \frac{.26}{.0046}
$$

$$
\text{Opening Price} = 56.52173913
$$

---

## Step 4: Round the Answer

Round to **2 decimal places**:

$$
\text{Opening Price} = 56.52
$$

---

## Final

**The opening price for AK Enterprises' stock was $\boxed{56.52}$.**

VIPSolutions · Answer

# Explanation of Each Step

## Step 1: Understanding the Relationship
The dividend yield relates the annual dividend to the stock's closing price. To find the closing price, we rearranged the dividend yield formula, making it clear how the annual dividend affects the price of the stock.

## Step 2: Calculating the Closing Price
By substituting the known values into the rearranged formula for closing price, we calculated how much the stock was worth based on the given annual dividend and dividend yield. This step provided us with the closing price necessary for the next calculation.

## Step 3: Calculating the Opening Price
Using the change in price and the percentage change, we set up an equation to find the opening price. This calculation showed how the closing price and the change in price related to determine the opening price of the stock.

## Step 4: Rounding the Answer
After calculating the opening price, we rounded it to two decimal places to present it in a standard financial format. This final adjustment ensures clarity and precision for reporting the price.

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