# Explain the relationship observed between ratings and yield to maturity.

Unit 3 IP Assignment: Deliverable Length 700 words in a Word file. Submit an Excel Spreadsheet showing calculations (submit separately). Fill out the 4 Tables completely.

A.

1.Bond Table 1: To fill out the first table, you will need to select 3 bonds with maturities between 10 and 20 years with bond ratings of “A to AAA,” “B to BBB” and “C to CC” (you may want to use bond screener at the http://finance.yahoo.com/). All of these bonds will have these values (future values) of \$1,000. You will need to use a coupon rate of the bond times the face value to calculate the annual coupon payment. You should subtract the maturity date from the current year to determine the time to maturity. The Web site should provide you with the yield to maturity and the current quote for the bond. (Be sure to multiply the bond quote by 10 to get the current market value.) You will then need to indicate whether the bond is currently trading at a discount, premium, or par.

2. Analysis of Bond Table 1:

•Explain the relationship observed between ratings and yield to maturity.

•Explain why the coupon rate and the yield to maturity determine why the bonds would trade at a discount, premium, or par.

•Based on the material you learn in this Phase, what would you expect to happen to the yield to maturity and market value of the bonds if the time to maturity was increased or decreased by 5 years?

B.

Select a stock that has at least a 5-year history of paying dividends and 2 of its closest competitors.

1. Stock Table 1: You will calculate the required rate of return for each of the 3 stocks. You will need to determine the risk-free rate (see Note below). You will need the market return that was calculated in Phase 2, and the beta that you find on the Web site.

2. Stock Table 2: You will determine whether the model suggests your stocks are over-priced or underpriced. You will need the most recent dividends paid over the past year for each stock, expected growth rate for the stocks, and the required rate of return you calculated in the previous table. Compare your results with the current value of each stock to determine whether the model suggests that they are over-priced or underpriced.

3. Stock Table 3: You will determine whether the model suggests your stocks are over-priced or underpriced again in a different model. You will need to find the price to earnings ratio (P/E) and the average expected earnings per share. (This should be available on the Web, though P/E can be calculated.) Compare your results with the current value of each stock to determine whether or not the model suggests that the stocks are over-priced or underpriced.

4. Analysis of Stock Tables:

•Explain the relationship observed between the required rate of return, growth rate and the dividend paid, and the estimated value of the stock using the Gordon Model.

•Explain the value and weaknesses of the Gordon model.

•Explain the how the price-to-earnings model is used to estimate the value of the stocks.

•Explain which of the 2 models seemed to be the most accurate in estimating the value of the stocks.

•Based on the material that you learn in this Phase, what would you expect to happen to the value of the stock if the growth rate, dividends, required rate of return, or the estimated earnings per share were to increase or decrease

You can find information about the top 500 stocks at:

http://finance.yahoo.com/echarts?s=%5egspc+interactive#symbol=^gspc;range=1y;compare=;indicator=volume;charttype=area;crosshair=on;ohlcvalues=0;logscale=off;source=;”

NOTE: You are not asked to find stocks that have a risk free rate of return. You are only asked to list the risk free rate of return, that is the 5 year treasury rate. It is not necessary to actually calculate it. What you have to calculate is the REQUIRED RATE OF RETURN.

The risk free rate will be the same for all stocks and the 5-year Return on the S&P 500 will be the same for all stocks. The beta will be different (you should look this up for the stocks you selected) and with this information you can use the CAPM to calculate the Required rate of return.

The Current dividend, growth rate, current stock price, estimated earnings, p/e ratio, are all given.

For the required rate of return you should use the CAPM model Required rate of return = Risk free rate + Beta x (Market Return – Risk Free rate). The market return is the return on the S&P.

To estimate the stock price you should use the Gordon Model = The Gordon Model as defined by Ozyasar, is a model that an investor can use to determine a “fair stock price” and is easily calculated by the equation Stock Price = Dividend divided by the next years expected dividend – growth rate of dividend. This model is also know as the Dividend Discount Model.

To estimate the stock price based on the P/E:

Stock price = Earning per share * P/E Ratio.

CAPM

The capital asset pricing model (CAPM) is used to calculate the required rate of return for any risky asset. Your required rate of return is the increase in value you should expect to see based on the inherent risk level of the asset.

Example:

As an analyst, you could use CAPM to decide what price you should pay for a particular stock. If Stock A is riskier than Stock B, the price of Stock A should be lower to compensate investors for taking on the increased risk.

The CAPM formula is:

ra = rrf + Ba (rm-rrf)

where:

rrf = the rate of return for a risk-free security

rm = the broad market’s expected rate of return

Ba = beta of the asset

CAPM can be best explained by looking at an example.

Assume the following for Asset XYZ:

rrf = 3%

rm = 10%

Ba = 0.75

By using CAPM, we calculate that you should demand the following rate of return to invest in Asset XYZ: ra = 0.03 + [0.75 * (0.10 – 0.03)] = 0.0825 = 8.25%

The inputs for rrf , rm and Ba are determined by the analyst and are open to interpretation.

Beta (Ba) — Most investors use a beta calculated by a third party, whether it’s an analyst, broker or Yahoo! Finance.

Market return (rm) – Your input of market rate of return, rm, can be based on past returns or projected future returns.

Risk-free return (rrf): U.S. Treasury bills and bonds are most often used as the proxy for the risk-free rate.

Why it Matters:

CAPM is most often used to determine what the fair price of an investment should be. When you calculate the risky asset’s rate of return using CAPM, that rate can then be used to discount the investment’s future cash flows to their present value and thus arrive at the investment’s fair value.

By extension, once you’ve calculated the investment’s fair value, you can then compare it to its market price. If your price estimate is higher than the market’s, you could consider the stock a bargain. If your price estimate is lower, you could consider the stock to be overvalued.

GORDON MODEL OR DIVIDEND DISCOUNT MODEL

The Gordon Growth Model, also known as the dividend discount model (DDM), is a method for calculating the intrinsic value of a stock, exclusive of current market conditions. The model equates this value to the present value of a stock’s future dividends.

We will assume that dividend grow at a constant rate. This is the stable model.

Stable Model

Value of stock = D1/ (k – g)

where:

D1 = next year’s expected annual dividend per share

k = the investor’s discount rate or required rate of return, which can be estimated using the Capital Asset Pricing Model or the Dividend Growth Model.

g = the expected dividend growth rate (note that this is assumed to be constant)

How it works/Example:

Stable Model

Let’s assume XYZ Company intends to pay a \$1 dividend per share next year and you expect this to increase by 5% per year thereafter. Let’s further assume your required rate of return on XYZ Company stock is 10%. Currently, XYZ Company stock is trading at \$10 per share. Using the formula above, we can calculate that the intrinsic value of one share of XYZ Company stock is:

\$1.00/(.10-.05) = \$20

According to the model, XYZ Company stock is worth \$20 per share but is trading at \$10; the Gordon Growth Model suggests the stock is undervalued.

The Gordon Growth Model allows investors to calculate the value of a share of stock exclusive of current market conditions. This exclusion allows investors to make apples-to-apples comparisons among companies in different industries, and for this reason Gordon Growth Model is one of the most widely used equity analysis and valuation tools.

The Gordon Growth Model’s exclusion of nondividend factors tends to undervalue stocks in companies with exceptional brand names, customer loyalty, unique intellectual property, or other nondividend, value-enhancing characteristics.

STOCK PRICE BASED ON P/E:

To estimate the stock price based on the P/E:

Stock price = Earning per share * P/E Ratio.

Step 1

Obtain a company’s long-term EPS growth rate from a financial portal such as Yahoo! Finance or MSN Money for the past three or five years.

Step 2

Calculate the current EPS growth rate by comparing the EPS for the last two or three quarters to the same quarters last year.

Step 3

Compare the EPS growth with the current P/E. The current P/E can be obtained from an extended quote provided by Yahoo! Finance or a similar portal. The rule of thumb is that a fully valued stock should have a P/E that equals its earnings growth rate. If the P/E is below the EPS growth rate, the stock is undervalued; if the P/E is above the EPS rate, the stock is overvalued.

Step 4

Assume that the stock you are researching is fully valued — that is, its EPS growth rate equals its P/E. Substitute the EPS growth rate for the current P/E and multiply it by the current earnings per share (which can also be obtained from a financial portal) to arrive at the stock’s potential value. If the figure is higher than the current stock price, the stock is undervalued; if the figure is lower than the current stock price, the stock is overvalued

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