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Q26. 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: ffice ffice" />
A) $102.80.
B) $92.92.
C) $55.69.
Correct answer is A)
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
Q27. 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% for three years.
- The growth rate of dividends after three years is expected to stabilize at 4%.
- The required return for Computech’s common stock is 15%.
Which of the following statements about Computech's stock is least accurate?
A) Computech's stock is currently worth $17.46.
B) At the end of two years, Computech's stock will sell for $20.64.
C) The dividend at the end of year three is expected to be $2.27.
Correct answer is A)
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.
Q28. 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) $15.70.
B) $6.40.
C) $0.00.
Correct answer is 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 / (ke – g) = $3.38 / (0.15 – 0.08) = $48.29
Step 3: Calculate the PV of each cash flow stream at ke = 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.
Q29. 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) $40.00.
B) $13.33.
C) $42.00.
Correct answer is C)
2(1.05) / (0.10 - 0.05) = $42.00
Q30. Day and Associates is experiencing a period of abnormal growth. The last dividend paid by Day was $0.75. Next year, they anticipate growth in dividends and earnings of 25% followed by negative 5% growth in the second year. The company will level off to a normal growth rate of 8% in year three and is expected to maintain an 8% growth rate for the foreseeable future. Investors require a 12% rate of return on Day.
What is the approximate amount that an investor would be willing to pay today for the two years of abnormal dividends?
A) $1.62.
B) $1.83.
C) $1.55.
Correct answer is C)
First find the abnormal dividends and then discount them back to the present.
$0.75 × 1.25 = $0.9375 × 0.95 = $0.89.
D1 = $0.9375; D2 = $0.89.
At this point you can use the cash flow keys with CF0 = 0, CF1 = $0.9375 and CF2 = $0.89.
Compute for NPV with I/Y = 12. NPV = $1.547.
Alternatively, you can put the dividends in as future values, solve for present values and add the two together.
Q31. What would an investor pay for Day and Associates today?
A) $24.03.
B) $18.65.
C) $20.71.
Correct answer is C)
Here we find P2 using the constant growth dividend discount model.
P2 = $0.89 × 1.08 / (0.12 – 0.08) = $24.03.
Discount that back to the present at 12% for 2 periods and add it to the answer in the previous question.
N = 2; I/Y = 12; PMT = 0; FV = $24.03; CPT &rarr PV = $19.16.
Add $1.55 (the present value of the abnormal dividends) to $19.16 and you get $20.71.
Q32. Calculate the value of a common stock that last paid a $2.00 dividend if the required rate of return on the stock is 14 percent and the expected growth rate of dividends and earnings is 6 percent. What growth model is an example of this calculation?
Value of stock Growth model
A) $26.50 Supernormal growth
B) $25.00 Gordon growth
C) $26.50 Gordon growth
Correct answer is C)
$2(1.06)/0.14 - 0.06 = $26.50.
This calculation is an example of the Gordon Growth Model also known as the constant growth model.
Q33. A company last paid a $1.00 dividend, the current market price of the stock is $20 per share and the dividends are expected to grow at 5 percent forever. What is the required rate of return on the stock?
A) 10.00%.
B) 10.25%.
C) 9.78%. B)
Correct answer is
D0 (1 + g) / P0 + g = k
1.00 (1.05) / 20 + 0.05 = 10.25%.
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发表于 2009-3-2 13:55
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