Reading 60: An Introduction to Security Valuation: Part II

答案和详解如下：

6.The last dividend paid on a common stock was $2.00, the growth rate is 5% and investors require a 10% return. Using the infinite period dividend discount model, calculate the value of the stock.

A)   $42.00.

B)   $40.00.

C)   $13.33.

D)   $14.33.

The correct answer was A)

2(1.05) / (0.10 - 0.05) = $42.00

7.An analyst gathered the following information about a company:

 The stock is currently trading at $31.00 per share.

 Estimated growth rate for the next three years is 25%.

 Beginning in the year 4, the growth rate is expected to decline and stabilize at 8%.

 The required return for this type of company is estimated at 15%.

 The dividend in year 1 is estimated at $2.00.

The stock is undervalued by approximately:

A)   $0.00.

B)   $6.40.

C)   $15.70.

D)   $2.30.

The correct answer was B)

The high “supernormal” growth in the first three years and the decrease in growth thereafter signals that we should use a combination of the multi-period and finite dividend growth models (DDM) to value the stock.

Step 1: Determine the dividend stream through year 4

  D₁ = $2.00 (given)

  D₂ = D₁ * (1 + g) = 2.00 * (1.25) = $2.50

  D₃ = D₂ * (1 + g) = $2.50 * (1.25) = $3.13

  D₄ = D₃ * (1 + g) = $3.13 * (1.08) = $3.38

Step 2: Calculate the value of the stock at the end of year 3 (using D₄)

  P₃ = D₄ / (k_e – g) = $3.38 / (0.15 – 0.08) = $48.29

Step 3: Calculate the PV of each cash flow stream at k_e = 15%, and sum the cash flows. Note: We suggest you clear the financial calculator memory registers before calculating the value. The present value of:

  D₁ = 1.74 = 2.00 / (1.15)¹, or FV = -2.00, N=1, I/Y = 15, PV = 1.74

  D₂ = 1.89 = 2.50 / (1.15)², or FV = -2.50, N=2, I/Y = 15, PV = 1.89

  D₃ = 2.06 = 3.13 / (1.15)³, or FV = -3.13, N=3, I/Y = 15, PV = 2.06

  P₃ = 31.75 = 48.29 / (1.15)³, or FV = -48.29, N=3, I/Y = 15, PV = 31.75

  Sum of cash flows = 37.44.

  Thus, the stock is undervalued by 37.44 – 31.00 = approximately 6.40.

Note: Future values are entered in a financial calculator as negatives to ensure that the PV result is positive. It does not mean that the cash flows are negative. Also, your calculations may differ slightly due to rounding. Remember that the question asks you to select the closest answer.

8.Use the following information and the multi-period dividend discount model to find the value of Computech’s common stock.

 Last year’s dividend was $1.62.

 The dividend is expected to grow at 12 percent for three years.

 The growth rate of dividends after three years is expected to stabilize at 4 percent.

 The required return for Computech’s common stock is 15 percent.

Which of the following statements about Computech's stock is FALSE?

A)   At the end of two years, Computech's stock will sell for $20.64.

B)   The dividend at the end of year three is expected to be $2.27.

C)   The dividend at the end of year four is expected to be $2.36.

D)   Computech's stock is currently worth $17.46.

The correct answer was D)

The dividends for years 1, 2, 3, and 4 are expected to be ($1.62)(1.12) = $1.81; ($1.81)(1.12) = $2.03; ($2.03)(1.12) = 2.27; and ($2.27)(1.04) = $2.36, respectively. At the end of year 3, the stock should sell for ($2.36)/(0.15 – 0.04) = $21.46. At the end of year 2, the stock should sell for ($21.46 + 2.27)/1.15 = $20.64. The stock should sell currently for ($20.64 + $2.03)/(1.15)² + ($1.81)/(1.15) = $17.14 + $1.57 = $18.71.

9.Assume a company has earnings per share of $5 and this year paid out 40% in dividends. The earnings and dividend growth rate for the next 3 years will be 20%. At the end of the third year the company will start paying out 100% of earnings in dividends and earnings will increase at an annual rate of 5% thereafter. If a 12% rate of return is required, the value of the company is approximately:

A)   $92.92.

B)   $102.80.

C)   $55.69.

D)   $104.80.

The correct answer was B)

First, calculate the dividends in years 0 through 4: (We need D₄ to calculate the value in Year 3)

D₀ = (0.4)(5) = 2
D₁ = (2)(1.2) = 2.40
D₂ = (2.4)(1.2) = 2.88
D₃ = E₃ = 5(1.2)³ = 8.64

g after year 3 will be 5%, so

D₄ = 8.64 * 1.05 = 9.07

Then, solve for the terminal value at the end of period 3 = D₄/(k - g) = 9.07/(0.12 – 0.05) = $129.57

Present value of the cash flows = value of stock = 2.4 / (1.12)¹ + 2.88 / (1.12)² + 8.64 / (1.12)³ + 129.57 / (1.12)³ = 2.14 + 2.29 + 6.15 + 92.22 = 102.80

10.What value would be placed on a stock that currently pays no dividend but is expected to start paying a $1 dividend five years from now? Once the stock starts paying dividends, the dividend is expected to grow at a 5 percent annual rate. The appropriate discount rate is 12 percent.

A)   $8.11.

B)   $14.29.

C)   $16.00.

D)   $9.08.

The correct answer was D)

P₄ = D5/(k-g) = 1/(.12-.05) = 14.29

P₀ = [FV = 14.29; n = 4; i = 12] = $9.08.