Problem 13 - Basic Statistics for Business and Economics with Student

Question

In June an investor purchased 300 shares of Oracle (an information technology company) stock at \(\$ 20\) per share. In August she purchased an additional 400 shares at \(\$ 25\) per share. In November she purchased an additional 400 shares, but the stock declined to \(\$ 23\) per share. What is the weighted mean price per share?

Step-by-Step Solution

Answer

The weighted mean price per share is approximately $22.91.

Step 1: Calculate Total Shares

First, determine the total number of shares purchased. The investor bought 300 shares in June, 400 shares in August, and another 400 shares in November. Add these together:\[300 + 400 + 400 = 1100\text{ shares}\]

Step 2: Calculate Total Investment Per Month

Compute the total expenditure on shares for each purchase. Multiply the number of shares by the price per share for each month:- June: \(300 \times 20 = \\(6000\)- August: \(400 \times 25 = \\)10000\)- November: \(400 \times 23 = \$9200\)

Step 3: Calculate Total Investment

Add together the total investments made in June, August, and November to find the overall amount spent:\[6000 + 10000 + 9200 = \$25200\]

Step 4: Calculate the Weighted Mean Price

To find the weighted mean price per share, divide the total investment by the total number of shares:\[\text{Weighted Mean Price} = \frac{25200}{1100} \approx 22.91\]

Key Concepts

Total Shares

Understanding the concept of "total shares" is crucial for any investor or student studying investments. Essentially, total shares refer to the sum of all shares acquired by the investor over a period of time. In our example, the investor purchased shares on three separate occasions: 300 shares in June, 400 shares in August, and 400 shares in November. To calculate the total shares, you simply add these quantities together:

• June: 300 shares
• August: 400 shares
• November: 400 shares

Adding these together gives us:\[300 + 400 + 400 = 1100 \text{ shares}\]The total of 1100 shares represents the full extent of the investor's stake in the company as of November. Calculating total shares accurately is important because this figure is used in further calculations, like determining the weighted mean price per share.

Total Investment

The "total investment" in a stock scenario represents the total amount of money an investor spends to purchase shares at different points in time. It is calculated by multiplying the number of shares bought with the price per share at each purchase date. In this example, the investor bought shares in three transactions:

• June: 300 shares * \(\\( 20\) per share = \(\\) 6000\)
• August: 400 shares * \(\\( 25\) per share = \(\\) 10000\)
• November: 400 shares * \(\\( 23\) per share = \(\\) 9200\)

To find the total investment, one would add all these expenditures together:\[6000 + 10000 + 9200 = \\( 25200\]This sum, \(\\) 25200\), represents the overall amount spent on the shares. Knowing the total investment is key when calculating the weighted mean price, as it provides the total cost of owning the shares.

Price Per Share

When discussing stocks, "price per share" refers to the cost for each individual share at the time of purchase. Prices per share can fluctuate over time due to a variety of factors including market conditions, company performance, and investor sentiment. In this case study, our investor purchased shares at three different price points:

• June: \(\\( 20\) per share
• August: \(\\) 25\) per share
• November: \(\\( 23\) per share

The weighted mean price per share provides a more nuanced understanding of the average price paid over multiple transactions. It is calculated by dividing the total investment by the total number of shares:\[\text{Weighted Mean Price} = \frac{\\) 25200}{1100} \approx \\( 22.91\]This calculation shows that although individual prices varied, the average price paid for each share over all purchases was approximately \(\\) 22.91\). Understanding the weighted mean price per share is critical as it reflects the investor's average cost and can influence future investment decisions.