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Estimating the current value of a stock

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Problem 1
Suppose a dividend of $1.25 was paid. The stock has a required rate of return of 11.2% and investors expect the dividend to grow at a constant rate of 10%. Complete parts (a) through (e) below.
a) Compute D0, D1, D2, D3 and D7.
b) Compute the present value of the dividends for t = 3 years.
c) Compute the current market price.
d) Assume that the constant growth rate is actually 0%. What is the current market price?
e) Describe the behavior of the present value of each future dividend (i.e. the behavior as t increases).

Problem 2
Suppose a dividend that pays at $1.07 has a growth rate of 20% for the first 3 years. After the 3 years, there is a long-run growth rate of 8%. The stock has a required rate of return of 12.4%. Find the current market price of a share of common stock.

Problem 3
Assume the beta coefficient for a company's stock is B = 0.2, the risk-free rate of return, rRF, is 8% and the required rate of return on the market, rM, is 14%. Assume the dividend expected during the coming year is D1 = $2.50 and the growth rate is a constant 7%. Complete parts (a) through (c) below.
a) Compute the price at which the company's stock should sell.
b) Find the new price of the stock assuming the risk-free rate of return is 5% and the required rate of return on the market is 11%.
c) What would be needed for a stock to be in equilibrium?

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Solution Preview

Problem 1
a) Compute D0, D1, D2, D3 and D7.

Current dividend=Do=$1.25
Growth Rate=g=10%
Expected dividend to be paid at the end of year 1=D1=Do*(1+g)=1.25*(1+10%)=$1.375
Expected dividend to be paid at the end of year 2=D2=Do*(1+g)^2=1.25*(1+10%)^2=$1.5125
Expected dividend to be paid at the end of year 3=D3=Do*(1+g)^3=1.25*(1+10%)^3=$1.66375
Expected dividend to be paid at the end of year 7=D7=Do*(1+g)^7=1.25*(1+10%)^7=$2.435896

b) Compute the present value of the dividends for t = 3 years.
PV of dividend to received at the end of Year 3=PV3=D3/(1+r)^3=1.66375/(1+11.2%)^3=$1.209968

c) Compute the current market ...

Solution Summary

Solution depicts the steps to estimate the current value of stock in the given cases. Calculations are carried out with the help of suitable formulas.

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Financial Management

Use both the CAPM (capital asset pricing model) and the constant growth model (CGM) to arrive at XYZ's stock price.

Find an estimate of the risk-free rate of interest (krf). To obtain this value, go to Bloomberg.com: Market Data and use the "U.S. 10-year Treasury" bond rate (middle column) as the risk-free rate. In addition, you also need a value for the market risk premium. Use an assumed market risk premium of 7.5%.
Download the XYZ Stock Information by clicking the link.
Using the information from the XYZ Stock Information document, record the following values:
XYZ's beta (Ã?)
XYZ's current annual dividend
XYZ's 3-year dividend growth rate (g)
Industry P/E
XYZ's EPS
With the information you recorded, use the CAPM to calculate XYZ's required rate of return (ks).
Use the CGM to find the current stock price for XYZ. We will call this the theoretical price (Po).
Now use appropriate Web resources to find XYZ's current stock quote (P). Compare Po and P and answer the following questions:
Are there any differences?
What factors may be at work for such a difference in the two prices?
Now assume the market risk premium has increased from 7.5% to 10% and this increase is due only to the increased risk in the market. In other words, assume the krf and the stock's beta remain the same for this exercise.
What will the new price be? Explain.
Recalculate XYZ's stock price using the P/E ratio model and the needed info found in the XYZ Stock Information file.
Why is the present stock price different from the price arrived at using CGM (Constant Growth Model)?
Use Microsoft Word to arrive at your answers and provide an explanation of the formulas and calculations.

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