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LOS c, (Part 2): Calculate and interpret the value of a common stock using the dividend discount model (DDM).fficeffice" />

Q1. Which of the following statements about the constant growth dividend discount model (DDM) in its application to investment analysis is FALSE? The model:

A)   is best applied to young, rapidly growing firms.

B)   can’t be applied when g>K.

C)   can’t handle firms with variable dividend growth.

Correct answer is A)        

The model is most appropriately used when the firm is mature, with a moderate growth rate, paying a constant stream of dividends. In order for the model to produce a finite result, the company’s growth rate must not exceed the required rate of return.

 

Q2. A firm pays an annual dividend of $1.15. The risk-free rate (RF) is 2.5 percent, and the total risk premium (RP) for the stock is 7 percent. What is the value of the stock, if the dividend is expected to remain constant?

A)   $25.00.

B)   $16.03.

C)   $12.10.

Correct answer is C)

If the dividend remains constant, g = 0.

P = D₁ / (k-g) = 1.15 / (0.095 - 0) = $12.10

 

Q3. Given the following estimated financial results, value the stock of FishnChips, Inc., using the infinite period dividend discount model (DDM).

• Sales of $1,000,000
• Earnings of $150,000
• Total assets of $800,000
• Equity of $400,000
• Dividend payout ratio of 60.0%
• Average shares outstanding of 75,000
• Real risk free interest rate of 4.0%
• Expected inflation rate of 3.0%
• Expected market return of 13.0%
• Stock Beta at 2.1

The per share value of FishnChips stock is approximately: (Note: Carry calculations out to at least 3 decimal places.)

A)   Unable to calculate stock value because k_e < g.

B)   $17.91.

C)   $26.86.

Correct answer is C)

Here, we are given all the inputs we need. Use the following steps to calculate the value of the stock:

First, expand the infinite period DDM:
DDM formula: P₀ = D₁ / (k_e – g)

D1	= (Earnings × Payout ratio) / average number of shares outstanding
	= ($150,000 × 0.60) / 75,000 = $1.20
ke	= nominal risk free rate + [beta × (expected market return – nominal risk free rate)]
	Note: Nominal risk-free rate		= (1 + real risk free rate) × (1 + expected inflation) – 1
			= (1.04)×(1.03) – 1 = 0.0712, or 7.12%.
ke	= 7.12% + [2.1 × (13.0% ? 7.12%)] = 0.19468
g	= (retention rate × ROE)
	Retention	= (1 – Payout) = 1 – 0.60 = 0.40.
	ROE	= (net income / sales)(sales / total assets)(total assets / equity)
		= (150,000 / 1,000,000)(1,000,000 / 800,000)(800,000 / 400,000)
		= 0.375
g	= 0.375 × 0.40 = 0.15

Then, calculate: P₀ = D₁ / (k_e – g) = $1.20 / (0.19468 ? 0.15) = 26.86.

 

Q4. Which of the following statements concerning security valuation is least accurate?

A)   A stock to be held for two years with a year-end dividend of $2.20 per share, an estimated value of $20.00 at the end of two years, and a required return of 15% is estimated to be worth $18.70 currently.

B)   A stock with an expected dividend payout ratio of 30%, a required return of 8%, an expected dividend growth rate of 4%, and expected earnings of $4.15 per share is estimated to be worth $31.13 currently.

C)   A stock with a dividend last year of $3.25 per share, an expected dividend growth rate of 3.5%, and a required return of 12.5% is estimated to be worth $36.11.

Correct answer is C)

A stock with a dividend last year of $3.25 per share, an expected dividend growth rate of 3.5%, and a required return of 12.5% is estimated to be worth $37.33 using the DDM where P_o = D₁ / (k ? g). We are given D_o = $3.25, g = 3.5%, and k = 12.5%. What we need to find is D₁ which equals D_o × (1 + g) therefore D₁ = $3.25 × 1.035 = $3.36 thus ffice:smarttags" />P_o = 3.36 / (0.125 ? 0.035) = $37.33.

In the answer choice where the stock value is $18.70, discounting the future cash flows back to the present gives the present value of the stock. the future cash flows are the dividend in year 1 plus the dividend and value of the stock in year 2 thus the equation becomes: V_o = 2.2 / 1.15 + (2.2 + 20) / 1.15² = $18.70

For preferred stock with a perpetual dividend V_o = 3.00 / 0.115 = $26.09

For the answer choice where the stock value is $31.13 use the DDM which is P_o = D₁ / (k ? g). We are given k = 0.08, g = 0.04, and what we need to find is next year’s dividend or D₁. D₁ = Expected earnings × payout ratio = $4.15 × 0.3 = $1.245 thus P_o = $1.245 / (0.08 ? 0.04) = $31.13

 

Q5. Use the following information and the dividend discount model to find the value of GoFlower, Inc.’s, common stock?

• Last year’s dividend was $3.10 per share.
• The growth rate in dividends is estimated to be 10% forever.
• The return on the market is expected to be 12%.
• The risk-free rate is 4%.
• GoFlower’s beta is 1.1.

A)   $121.79.

B)   $34.95.

C)   $26.64.

Correct answer is A)

The required return for GoFlower is 0.04 + 1.1(0.12 – 0.04) = 0.128 or 12.8%. The expect dividend is ($3.10)(1.10) = $3.41. GoFlower’s common stock is then valued using the infinite period dividend discount model (DDM) as ($3.41) / (0.128 – 0.10) = $121.79.

 

Q6. Which of the following is a shortcoming(s) of the constant growth dividend discount model?

A)   Small differences in key assumptions can produce widely varying values.

B)   All these choices are correct.

C)   Firms with temporary high-growth expectations have characteristics that are inconsistent with model.

Correct answer is B)

The constant growth dividend discount model cannot be used to value firms that don’t pay dividends or are experiencing supernormal growth and are very dependent on the assumed values of k and g.

 

Q7. What is the value of a stock that paid a $0.25 dividend last year, if dividends are expected to grow at a rate of 6% forever? Assume that the risk-free rate is 5%, the expected return on the market is 10%, and the stock's beta is 0.5.

A)   $16.67.

B)   $3.53.

C)   $17.67.

Correct answer is C)

The discount rate is k_e = 0.05 + 0.5(0.10 ? 0.05) = 0.075. Use the infinite period dividend discount model to value the stock. The stock value = D₁ / (k_e – g) = (0.25 × 1.06) / (0.075 – 0.06) = $17.67.

 

Q8. Assuming the risk-free rate is 5% and the expected return on the market is 12%, what is the value of a stock with a beta of 1.5 that paid a $2 dividend last year if dividends are expected to grow at a 5% rate forever?

A)   $12.50.

B)   $17.50.

C)   $20.00.

Correct answer is C)

P₀ = D₁ / (k ? g)

R_s = R_f + β(R_M ? R_f) = 0.05 + 1.5(0.12 ? 0.05) = 0.155

D₁ = D₀(1 + g) = 2 × (1.05) = 2.10

P₀ = 2.10 / (0.155 ? 0.05) = $20.00