Math in Our World Section 8.6 Stocks and Bonds

Learning Objectives Find information from a stock listing. Compute the P/E ratio for a stock. Compute the total cost of a stock purchase. Compute the profit or loss from a stock sale.

Stocks and Bonds In order to get information about a certain stock, you can refer to a stock table. In this case, a stock listing for a company called Computer Programming and Systems, Inc. will be used as an example.

Stocks and Bonds The first two columns give the highest and lowest selling prices for one share of stock in this company during the past 52 weeks. Sales volume in 1000s for yesterday. Dividends paid per share last year. Percent Yield. Symbol company uses.

Stocks and Bonds The annual percentage yield is the dividend per share divided by the current price. This percent can be compared to other stocks as a measure of performance. Percent Yield.

Stocks and Bonds The P/E column is the price-to-earnings ratio. It is the ratio of yesterday’s closing price of the stock (found in the CLOSE column) to its annual earnings per share. Closing Price – last price traded yesterday. The NET CHG is the change in the price of the stock between the day before yesterday and yesterday at closing time. Net Change in Closing Price.

EXAMPLE 1 Reading a Stock Listing The following is a stock listing for the Terex Corporation. Use the listing to answer the questions. (d) If you owned 250 shares of stock, how much did you make in dividends last year? SOLUTION 250 x $0.24 = $60

EXAMPLE 1 Reading a Stock Listing The following is a stock listing for the Terex Corporation. Use the listing to answer the questions. (e) How many shares were traded yesterday? (f ) What was the closing price per share the day before yesterday? SOLUTION (e) 7,143 x 1,000 = 7,143,000 (f ) $24.51 + 0.06 = $24.57

P/E Ratio The P/E ratio of a stock is a comparison of the current selling price to the company’s earnings per share.

EXAMPLE 2 Computing a P/E Ratio If the annual earnings per share for Terex is $0.98, find the P/E ratio. SOLUTION This means that the price of a share of stock is 25 times the company’s annual earnings per share. In general, the lower the P/E ratio is, the better the investment.

Annual Earnings Per Share Knowing the price per share of stock and the P/E ratio, you can find the annual earnings per share for the last 12 months by using the following formula:

EXAMPLE 3 Computing Annual Earnings per Share If the closing price for Kellogg’s stock was $44.23 and the P/E ratio is 15, find the annual earnings per share for last year. SOLUTION

Current Yield for Stock The current yield for a stock can be calculated by using the following formula:

EXAMPLE 4 Computing Yield for a Stock For the CPSI stock, the annual percent yield is 6.5%. Verify the current yield by using the preceding formula. SOLUTION The dividend per share is $1.44 and the closing price is $22.25:

EXAMPLE 5 Finding the Total Cost of Buying Stock Shares of Apple Computer (AAPL) closed at $12.89 on April 1, 2004. Suppose that an investor bought 600 shares at that price using a broker that charged a 2% commission. Find the amount of commission and the total cost to the investor. SOLUTION Step 1 Find the purchase price. 600 shares x $12.89 = $7,734.00

EXAMPLE 5 Finding the Total Cost of Buying Stock SOLUTION Step 2 Find the broker’s commission. 2% of purchase price = 0.02 x $7,734.00 = $154.68 Step 3 Add the commission to the purchase price. $7,734.00 + $154.68 = $7,888.68 The investor paid a total of $7,888.68 for the transaction.

EXAMPLE 6 Finding the Amount Made from Selling Stock On May 1, 2008, shares of Apple stock reached $192.24. If the investor in Example 5 sold all of his Apple stock at that point, and the broker also charges a 2% commission on sales, find the commission, proceeds, and the amount of profit made by the investor. SOLUTION Step 1 Find the total amount of the sale. 600 shares x $192.24 = $115,344.00

EXAMPLE 6 Finding the Amount Made from Selling Stock SOLUTION Step 2 Find the broker’s commission. 2% of purchase price = 0.02 x $115,344.00 = $2,306.88 Step 3 Subtract the commission amount from the total amount of the sale to get the proceeds. $115,344.00 – $2,306.88 = $113,037.12 Step 4 The profit is the proceeds minus the total cost from Example 5. $113,037.12 – $7,888.68 = $105,148.44