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# Estimating the fair value of a stock

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Suppose a firm's common stock paid a dividend of \$2.50 yesterday. You expect the dividend to grow at the rate of 5% per year for the next 3 years, if you buy the stock, you plan to hold it for 3 years and then sell it.

a.Find the expected dividend for each of the next 3 years; in other words, calculate D1 , D2 and D3 . Note that D0 = \$2.50. Round your answers to the nearest cent.

1.D1 = \$

2.D2 = \$

3.D3 = \$

b.Given that the appropriate discount rate is 13% and that the first of these dividend payments will occur 1 year from now, find the present value of the dividend stream; that is, calculate the PV of D1, D2, and D3, and then sum these PVs. Round your answer to the nearest cent.
\$

c.You expect the price of the stock 3 years from now to be \$37.98 . Discounted at a 13% rate, what is the present value of this expected future stock price? In other words, calculate the PV of \$37.98. Round your answer to the nearest cent.
\$

d.If you plan to buy the stock, hold it for 3 years, and then sell it for \$37.98, what is the most you should pay for it? Round your answer to the nearest cent.
\$

e.Use Equation P Ë? ? 0 ???=???D ?0 ?(1???+???g) r ?s ???-???g ???=???D ?1 r ?s ???-???g to calculate the present value of this stock. Assume that g = 5%, and it is constant. Round your answer to the nearest cent.
\$

f.Is the value of this stock dependent on how long you plan to hold it? In other words, if your planned holding period were 2 years or 5 years rather than 3 years, would this affect the value of the stock today, P0? Explain your answer.

-Select-

I. Yes. The value of the stock is dependent upon the holding period. The value calculated in Parts a through d is the value for a 3-year holding period. It is not equal to the value calculated in Part e. Any other holding period would produce a different value of P0.
II. Yes. The value of the stock is dependent upon the holding period due to the fact that the value is determined as the present value of all future expected dividends.
III. No. The value of the stock is not dependent upon the holding period. The value calculated in Parts a through d is the value for a 3-year holding period. It is equal to the value calculated in Part e. Any other holding period would produce the same value of P0.
IV. No. The value of the stock is not dependent upon the holding period unless the growth rate remains constant for the foreseeable future.
V. Yes. The value of the stock is dependent upon the holding period as long as the growth rate remains constant for the foreseeable future.

#### Solution Preview

a. Find the expected dividend for each of the next 3 years; in other words, calculate D1 , D2 and D3 . Note that D0 = \$2.50.Round your answers to the nearest cent.

1. Growth rate=g=5%, Current dividend=Do=\$2.50
D1 =Do*(1+g)=2.50*(1+5%) =\$ 2.625 or say \$2.63

2. D2 =D1*(1+g)=2.625*(1+5%) =\$2.75625 or say \$2.76

3. D3 =D2*(1+g)=2.75625*(1+5%)=2.894063 or say \$2.89

b. Given that the appropriate discount rate is 13% and that the first of these dividend payments will occur 1 year from now, find the present value of the dividend stream; that is, ...

#### Solution Summary

Solution describes the steps to estimate the current price of the given stock.

\$2.19