Suppose that you have $100 that you want to invest each month. In the first month, you buy stocks at $50/share. In the second month, you buy stocks at $25/share. On average, how much did you spend per share?
A. $37.50/share
B. $100/share
C. $33.33/share
D. $200/share
Answer (2)
Calculate shares bought in month 1: 50 100 = 2 .
Calculate shares bought in month 2: 25 100 = 4 .
Calculate total shares: 2 + 4 = 6 .
Calculate average cost per share: 6 200 = 33.33 . The average cost per share is 33.33 .
Explanation
Problem Analysis We are given that you invest $100 each month. In the first month, the stock price is $50/share, and in the second month, the stock price is $25/share. We want to find the average cost per share.
Shares Bought in Month 1 First, let's calculate how many shares were bought in the first month. Since you invested $100 and the price was 50/ s ha re , t h e n u mb ero f s ha res b o ug h t i s : 50 100 = 2 $
So, you bought 2 shares in the first month.
Shares Bought in Month 2 Next, let's calculate how many shares were bought in the second month. Since you invested $100 and the price was 25/ s ha re , t h e n u mb ero f s ha res b o ug h t i s : 25 100 = 4 $
So, you bought 4 shares in the second month.
Total Shares Bought Now, let's calculate the total number of shares bought. You bought 2 shares in the first month and 4 shares in the second month, so the total number of shares is: 2 + 4 = 6 You bought a total of 6 shares.
Total Amount Spent The total amount spent is the sum of the investments in both months, which is $100 in the first month and 100 in t h eseco n d m o n t h : 100 + 100 = 200 $
So, you spent a total of $200.
Average Cost Per Share Finally, let's calculate the average cost per share. The average cost is the total amount spent divided by the total number of shares bought: 6 200 = 33.333... So, the average cost per share is approximately $33.33.
Final Answer Therefore, the average cost per share is approximately $33.33.
Examples
Understanding average cost per share is crucial in finance. For example, if you're investing in a company's stock over time, the average cost per share helps you determine your overall investment efficiency. If you later sell those shares, comparing the selling price to your average cost per share tells you whether you made a profit or loss. This concept is also useful in inventory management, where businesses track the average cost of goods to make informed pricing and purchasing decisions.
The average cost per share when investing $100 each month is approximately $33.33. This is calculated by dividing the total amount spent ($200) by the total number of shares bought (6). Therefore, the answer is C. $33.33/share.
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