Reading 56: An Introduction to Security Valuation LOSc习题精 2010, par, interpret, discount, company

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LOS c, (Part 1): Calculate and interpret the value of a preferred stock using the dividend discount model (DDM).

The yield on a company’s 7.5%, $50 par preferred stock is 6%. The value of the preferred stock is closest to:

A) $62.50.

B) $12.50.

C) $50.00.

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The preferred dividend is 0.075($50) = $3.75. The value of the preferred = $3.75 / 0.06 = $62.50.

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A preferred stock’s dividend is $5 and the firm’s bonds currently yield 6.25%. The preferred shares are priced to yield 75 basis points below the bond yield. The price of the preferred is closest to:

A) $90.91.

B) $5.00.

C) $80.00.

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Preferred stock yield (K_p) = bond yield – 0.75% = 6.25% ? 0.75% = 5.5%

Value = dividend / K_p = $5 / 0.055 = $90.91.

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Assuming a discount rate of 15%, a preferred stock with a perpetual dividend of $10 is valued at approximately:

A) $1.50.

B) $66.67.

C) $8.70.

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The formula for the value of preferred stock with a perpetual dividend is: D / kp, or 10.0 / 0.15 = $66.67.

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Calculate the value of a preferred stock that pays an annual dividend of $5.50 if the current market yield on AAA rated preferred stock is 75 basis points above the current T-Bond rate of 7%.

A) $42.63.

B) $70.97.

C) $78.57.

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k_preferred = base yield + risk premium = 0.07 + 0.0075 = 0.00775

Value_Preferred = Dividend / k_preferred

Value = 5.50 / 0.0775 = $70.97

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A company has 8 percent preferred stock outstanding with a par value of $100. The required return on the preferred is 5 percent. What is the value of the preferred stock?

A) $160.00.

B) $152.81.

C) $100.00.

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The annual dividend on the preferred is $100(.08) = $8.00. The value of the preferred is $8.00/0.05 = $160.00.

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If a preferred stock that pays a $11.50 dividend is trading at $88.46, what is the market’s required rate of return for this security?

A) 11.76%.

B) 13.00%.

C) 7.69%.

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From the formula: Value_{Preferred Stock} = D / k_p, we derive k_p = D / Value_{Preferred Stock} = 11.50 / 88.46 = 0.1300, or 13.00%.

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A company has 6% preferred stock outstanding with a par value of $100. The required return on the preferred is 8%. What is the value of the preferred stock?

A) $75.00.

B) $92.59.

C) $100.00.

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The annual dividend on the preferred is $100(.06) = $6.00. The value of the preferred is $6.00/0.08 = $75.00.

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What is the value of a preferred stock that is expected to pay a $5.00 annual dividend per year forever if similar risk securities are now yielding 8%?

A) $40.00.

B) $62.50.

C) $60.00.

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$5.00/0.08 = $62.50.

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The preferred stock of the Delco Investments Company has a par value of $150 and a dividend of $11.50. A shareholder’s required return on this stock is 14%. What is the maximum price he would pay?

A) $150.00.

B) $82.14.

C) $54.76.

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Value of preferred = D / kp = $11.50 / 0.14 = $82.14

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

 

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) $19

B) $44

C) $104

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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.