kim226

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) $26.86.

B) Unable to calculate stock value because ke < g.

C) $17.91.

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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 / (ke – 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 / (ke – g) = $1.20 / (0.19468 − 0.15) = 26.86.

kim226

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 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.

C) 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.

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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 Po = D1 / (k − g). We are given Do = $3.25, g = 3.5%, and k = 12.5%. What we need to find is D1 which equals Do × (1 + g) therefore D1 = $3.25 × 1.035 = $3.36 thus Po = 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: Vo = 2.2 / 1.15 + (2.2 + 20) / 1.152 = $18.70
For the answer choice where the stock value is $31.13 use the DDM which is Po = 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 Po = $1.245 / (0.08 − 0.04) = $31.13

kim226

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) $34.95.

B) $121.79.

C) $26.64.

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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.

kim226

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.

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The discount rate is ke = 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 / (ke – g) = (0.25 × 1.06) / (0.075 – 0.06) = $17.67.

kim226

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) $20.00.

B) $12.50.

C) $17.50.

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P0 = D1 / (k − g)
Rs = Rf + β(RM − Rf) = 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

kim226

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) 10.0%.

C) 9.0%.

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

kim226

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

B) decrease.

C) increase.

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