Reading 60: Equity Valuation: Concepts and Basic Tools-LOS e security, discount, interpret, following, 2011

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Session 14: Equity Analysis and Valuation
Reading 60: Equity Valuation: Concepts and Basic Tools

LOS e: Calculate and interpret the intrinsic value of an equity security based on the Gordon (constant) growth dividend discount model or a two-stage dividend discount model, as appropriate.

 

 

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 ke < g.

B) $17.91.

C) $26.86.

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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.

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A stock is expected to pay a dividend of $1.50 at the end of each of the next three years. At the end of three years the stock price is expected to be $25. The equity discount rate is 16 percent. What is the current stock price?

A) $19.39.

B) $24.92.

C) $17.18.

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The value of the stock today is the present value of the dividends and the expected stock price, discounted at the equity discount rate:

$1.50/1.16 + $1.50/1.16² + $1.50/1.16³ + $25.00/1.16³ = $19.39

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Use the following information on Brown Partners, Inc. to compute the current stock price.

• Dividend just paid = $6.10

• Expected dividend growth rate = 4%

• Expected stock price in one year = $60

• Risk-free rate = 3%

• Equity risk premium = 12%

A) $59.55.

B) $57.70.

C) $57.48.

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The current stock price is equal to (D₁ + P₁) / (1 + k_e). D₁ equals $6.10(1.04) = $6.34. The equity discount rate is 3% + 12% = 15%. Therefore the current stock price is ($6.34 + $60)/(1.15) = $57.70

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An investor is considering acquiring a common stock that he would like to hold for one year. He expects to receive both $1.50 in dividends and $26 from the sale of the stock at the end of the year. What is the maximum price he should pay for the stock today to earn a 15 percent return?

A) $27.30.

B) $23.91.

C) $24.11.

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By discounting the cash flows for one period at the required return of 15% we get: x = (26 + 1.50) / (1+.15)¹

(x)(1.15) = 26 + 1.50

x = 27.50 / 1.15

x = $23.91

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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) $10.00.

B) $ 6.24.

C) $ 7.30.

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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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An analyst projects the following pro forma financial results for Magic Holdings, Inc., in the next year:

• Sales of $1,000,000
• Earnings of $200,000
• Total assets of $750,000
• Equity of $500,000
• Dividend payout ratio of 62.5%
• Shares outstanding of 50,000
• Risk free interest rate of 7.5%
• Expected market return of 13.0%
• Stock Beta at 1.8

If the analyst assumes Magic Holdings, Inc. will produce a constant rate of dividend growth, the value of the stock is closest to:

A) $104

B) $19

C) $44

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Infinite period DDM: P₀ = D₁ / (k_e – g)

D1	= (Earnings × Payout ratio) / average number of shares outstanding
	= ($200,000 × 0.625) / 50,000 = $2.50.
ke	=  risk free rate + [beta × (expected market return – risk free rate)]
ke	=  7.5% + [1.8 × (13.0% - 7.5%)] = 17.4%.
g	=    (retention rate × ROE)
		Retention = (1 – Payout) = 1 – 0.625 = 0.375.
		ROE  = net income/equity
				= 200,000/500,000 = 0.4
g	= 0.375 × 0.4 = 0.15.

P₀ = D₁ / (k_e – g) = $2.50 / (0.174 - 0.15) = 104.17.

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

A) $25.00.

B) $16.03.

C) $12.10.

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If the dividend remains constant, g = 0.

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

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If a stock sells for $50 that has an expected annual dividend of $2 and has a sustainable growth rate of 5%, what is the market discount rate for this stock?

A) 7.5%.

B) 9.0%.

C) 10.0%.

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k = [(D₁ / P) + g] = [(2/50) + 0.05] = 0.09, or 9.00%.

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All else equal, if there is an increase in the required rate of return, a stock’s value as estimated by the constant growth dividend discount model (DDM) will:

A) decrease.

B) increase or decrease, depending upon the relationship between ke and ROE.

C) increase.

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If k_e increases, the spread between k_e and g widens (increasing the denominator), resulting in a lower valuation.

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Which of the following statements about the constant growth dividend discount model (DDM) is least accurate?

A) For the constant growth DDM to work, the growth rate must exceed the required return on equity.

B) The constant growth DDM is used primarily for stable mature stocks.

C) In the constant growth DDM dividends are assumed to grow at a constant rate forever.

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Dividends grow at constant rate forever.

Constant growth DDM is used for mature firms.

k must be greater than g.