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# Stock price

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1) Equilibrium stock price: The risk free rate return rRF, is 6 percent: the required rate of return on the market is rM, is 10 percent; and Upron Company's stock has a beta coefficient of 1.5.

a. IF the dividend expected during the coming year, D1, is \$2.25, and if g=a constant 5 percent and at what price should Upton's stock sell?
b. Now, suppose the Federal Reserve Board increases the money supply, casing the risk-free rate to drop to 5 percent and rm to fall to 9 %. What would happen to Upton's price?
c. In addition to the change in part b, suppose investors' risk aversion declines, and this, combined with the decline in rRF, causes rM to fall to 8%, Now what is the Upton's price?
d. Now suppose Upton had a change in management, The new group institutes policies that increase the expected constant growth rate form 5 to 6 %. Also, the new management smooths out fluctuations in sales and profits, causing beta to decline form 1.5 to 1.3. Assuming that rRF and rM are equal to the values in part c. After all these changes, what is its new equilibrium price? (Note: D1 is now \$2.27)

2) Constant Growth - Your broker offers to sell you some shares of Bahnsen & Co. common stock that paid a divident of \$2 yesterday. Bahnsen's dividend is expected to gorw at 5% per yr for the next 3 yrs , and if you buy the stock, you plan to hold it for 3 yrs and then sell it. The appropriate discount rate is 12%.

a. Find the expected dividend for each of the next 3 yrs; that is, calculate D1, D2, and D3 Note that D0 =\$2.00

b. Given that the first dividend payment will occur 1 yr from now, find the present value of the dividend stream; that is, calculate the PV of D1, D2, and D3, and sum these PVs.

c: You expect the price of stock 3yrs from now to be \$34.73; that is, you expect P3 to equal \$34.73. Discounted at a 12% rate, what is the present value of this expected future stock price? In other words, calculate the PV of \$34.73

d) If you plan to buy the stock, hold it for 3 yrs, and then sell it for \$34.73, what is the most you should pay for it today?

e. use the horizon value equation to calculate the present value of this stock. Assuming that g=5% and it is constant

f) Is the value for this stock dependent upon how long you plan to hold it? In other words, if you planned holding period were 2 yrs or h yrs rather than 3y rs, would this affect the value of the stock today P0? Explain.

See attached file for full problem description.

#### Solution Preview

1) Equilibrium stock price: The risk free rate return rRF, is 6 percent: the required rate of return on the market is rM, is 10 percent; and Upron Company's stock has a beta coefficient of 1.5.

a. IF the dividend expected during the coming year, D1, is \$2.25, and if g=a constant 5 percent and at what price should Upton's stock sell?

First calculate the required rate of return

CAPM (Capital Asset Pricing Model equation is:
r = r f + beta (r m - r f)

risk free rate= r f = 6.0%
beta of stock= beta = 1.50
return on market portfolio= r m = 10.0%
required return on security r = to be determined
Plugging in the values
r = 12. % =6.%+1.5 x ( 10.% - 6.% )

Now use the dividend discount model to calculate the price of stock:

Po= Div1/ (r-g)

Dividend for next year= Div1 = \$2.25
Cost of equity= r= 12. %
growth rate of dividends/earnings= g= 5.00%
Current stock price= Po=
Plugging in the values:
Po= \$32.14 =\$2.25/ (12.% - 5.%)

Answer: Price of Upton's stock: \$32.14

b. Now, suppose the Federal Reserve Board increases the money supply, casing the risk-free rate to drop to 5 percent and rm to fall to 9 %. What would happen to Upton's price?

First calculate the required rate of return

CAPM (Capital Asset Pricing Model equation is:
r = r f + beta (r m - r f)

risk free rate= r f = 5.0%
beta of stock= beta = 1.50
return on market portfolio= r m = 9.0%
required return on security r = to be determined
Plugging in the values
r = 11. % =5.%+1.5 x ( 9.% - 5.% )

Now use the dividend discount model to calculate the price of stock:

Po= Div1/ (r-g)

Dividend for next year= Div1 = \$2.25
Cost of equity= r= 11. %
growth rate of ...

#### Solution Summary

The stock prices have been calculated using CAPM and Dividend Discount (Constant Growth) model.

\$2.19