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Reading 60: An Introduction to Security Valuation: Part II

11.A stock has the following elements: last year’s dividend = $1, next year’s dividend is 10 percent higher, the price will be $25 at year-end, the risk-free rate is 5 percent, the market premium is 5 percent, and the stock’s beta is 1.2.

What happens to the price of the stock if the beta of the stock increases to 1.5? It will:

A)   decrease.

B)   increase.

C)   be greater than $25.

D)   remain unchanged.


12.What will be the current price of the stock with a beta of 1.5?

A)   $23.51.

B)   $23.20.

C)   $20.23.

D)   $25.00.

13.Utilizing the infinite period dividend discount model, all else held equal, if the required rate of return (Ke) decreases, the model yields a price that is:

A)   increased, due to a smaller spread between required return and growth.

B)   reduced, due to the reduction in discount rate.

C)   increased, due to reduced growth in the numerator.

D)   reduced, due to increased spread between growth and required return.


14.A firm will not pay dividends until four years from now. Starting in year four dividends will be $2.20 per share, the retention ratio will be 40%, and ROE will be 15%. If k = 10%, what should be the value of the stock?

A)   $55.25.

B)   $41.32.

C)   $55.46.

D)   $58.89.


15.The following data pertains to a common stock:

It will pay no dividends for two years.

The dividend three years from now is expected to be $1.

Dividends are expected to grow at a 7% rate from that point onward.

If an investor requires a 17% return on this stock, what will they be willing to pay for this stock now?

A)   $ 6.24.

B)   $ 8.26.

C)   $10.00.

D)   $ 7.30.

答案和详解如下:

11.A stock has the following elements: last year’s dividend = $1, next year’s dividend is 10 percent higher, the price will be $25 at year-end, the risk-free rate is 5 percent, the market premium is 5 percent, and the stock’s beta is 1.2.

What happens to the price of the stock if the beta of the stock increases to 1.5? It will:

A)   decrease.

B)   increase.

C)   be greater than $25.

D)   remain unchanged.

The correct answer was A)

When the beta of a stock increases, its required return will increase. The increase in the discount rate leads to a decrease in the PV of the future cash flows.


12.What will be the current price of the stock with a beta of 1.5?

A)   $23.51.

B)   $23.20.

C)   $20.23.

D)   $25.00.

The correct answer was B)

k = 5 + 1.5(5) = 12.5% P0 = (1.1 / 1.125) + (25 / 1.125) = $23.20


13.Utilizing the infinite period dividend discount model, all else held equal, if the required rate of return (Ke) decreases, the model yields a price that is:

A)   increased, due to a smaller spread between required return and growth.

B)   reduced, due to the reduction in discount rate.

C)   increased, due to reduced growth in the numerator.

D)   reduced, due to increased spread between growth and required return.

The correct answer was A)

The denominator of the single-stage DDM is the spread between required return Ke, and expected growth rate, g. The smaller the denominator, all else held equal, the larger the computed value.


14.A firm will not pay dividends until four years from now. Starting in year four dividends will be $2.20 per share, the retention ratio will be 40%, and ROE will be 15%. If k = 10%, what should be the value of the stock?

A)   $55.25.

B)   $41.32.

C)   $55.46.

D)   $58.89.

The correct answer was B)

g = ROE × retention ratio = ROE × b = 15 × 0.4 = 6%

Based on the growth rate we can calculate the expected price in year 3:

P3 = D4 / (k-g) = 2.2 / (0.10 - 0.06) = $55

The stock value today is: P0 = PV (55) at 10% for 3 periods = $41.32


15.The following data pertains to a common stock:

It will pay no dividends for two years.

The dividend three years from now is expected to be $1.

Dividends are expected to grow at a 7% rate from that point onward.

If an investor requires a 17% return on this stock, what will they be willing to pay for this stock now?

A)   $ 6.24.

B)   $ 8.26.

C)   $10.00.

D)   $ 7.30.

The correct answer was D)

time line = $0 now; $0 in yr 1; $0 in yr 2; $1 in yr 3.
P2 = D3/(k - g) = 1/(.17 - .07) = $10
Note the math. The price is always one year before the dividend date.
Solve for the PV of $10 to be received in two years.
FV = 10; n = 2; i = 17; compute PV = $7.30

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