Reading 40: Discounted Dividend Valuation-LOS n, (Part 2) 习 class, expected, div, required, return

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Session 11: Equity Valuation: Industry and Company Analysis in a Global Context
Reading 40: Discounted Dividend Valuation

LOS n, (Part 2): Calculate a required return using the Gordon growth model and the H-model.

 

 

 

If the expected return on the equity market is 10%, the risk-free rate is 3%, and an asset’s beta is 0.6, what is the appropriate equity risk premium for the asset in applying the Gordon growth model?

A) 4.20%.

B) 6.40%.

C) 9.00%.

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The asset’s equity risk premium is equal to it’s beta times the difference between the expected return on the equity market and the risk-free rate. Equity Risk Premium = 0.6(0.10 ? 0.03) = 0.042 or 4.2%.

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A firm pays a current dividend of $1.00 which is expected to grow at a rate of 5% indefinitely. If current value of the firm’s shares is $35.00, what is the required return applicable to the investment based on the Gordon dividend discount model (DDM)?

A) 8.00%.

B) 8.25%.

C) 7.86%.

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The Gordon DDM uses the dividend for the period (t + 1) which would be $1.05.
$35 = $1.05 / (required return – 0.05)
Required return = 0.08 or 8.00%

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Given an equity risk premium of 3.5%, a forecasted dividend yield of 2.5% on the market index and a U.S. government bond yield of 4.5%, what is the consensus long-term earnings growth estimate?

A) 8.0%.

B) 10.5%.

C) 5.5%.

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Equity risk premium = forecasted dividend yield + consensus long term earnings growth rate – long-term government bond yield.

Therefore,
Consensus long term earnings growth rate =
Equity risk premium - forecasted dividend yield + long-term government bond yield
Consensus long term earnings growth rate = 3.5% - 2.5% + 4.5% = 5.5%

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An investor projects the price of a stock to be $16.00 in one year and expected the stock to pay a dividend at that time of $2.00. If the required rate of return on the shares is 11%, what is the current value of the shares?

A) $14.11.

B) $16.22.

C) $15.28.

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The value of the shares = ($16.00 + $2.00) / (1 + 0.11) = $16.22

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An investor computes the current value of a firm’s shares to be $34.34, based on an expected dividend of $2.80 in one year and an expected price of the share in one year to be $36.00. What is the investor’s required rate of return on this investment?

A) 10%.

B) 13%.

C) 11%.

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The required return = [($36.00 + $2.80) / $34.34 ] – 1 = 0.13 or 13%.

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Currently the market index stands at 1,190.45. Firms in the index are expected to pay cumulative dividends of 35.71 over the coming year. The consensus 5-year earnings growth forecast for these firms is expected to increase to 6.2% up from last year’s forecast of 4.5%. The long-term government bond is yielding 5.0%. According to the Gordon growth model, what is the equity risk premium?

A) 4.2%.

B) 2.5%.

C) 1.2%.

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Equity risk premium = (35.71 / 1,190.45) + (6.2%) – 5.0% = 4.2%

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Recent surveys of analysts report long-term earnings growth estimates as 5.5% and a forecasted dividend yield of 2.0% on the market index. At the time of the survey, the 20-year U.S. government bond yielded 4.8%. According to the Gordon growth model, what is the equity risk premium?

A) 7.5%.

B) 2.7%.

C) 0.4%.

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Equity risk premium = 2.0% + 5.5% – 4.8% = 2.7%

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CAB Inc. just paid a current dividend of $3.00, the forecasted growth is 9%, declining over four years to a stable 6% thereafter, and the current value of the firm’s shares is $50, what is the required rate of return?

A) 9.8%.

B) 10.5%.

C) 12.7%.

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The required rate of return is 12.7%.

r = ($3 / $50)[(1 + 0.06) + (4 / 2)(0.09 ? 0.06)] + 0.06 = 12.7%

Since the H-model is an approximation model, it is possible to solve for r directly without iteration.

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Given that a firm’s current dividend is $2.00, the forecasted growth is 7% for the next two years and 5% thereafter, and the current value of the firm’s shares is $54.50, what is the required rate of return?

A) Can’t be determined.

B) 9%.

C) 10%.

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The equation to determine the required rate of return is solved through iteration.

$54.50 = $2(1.07) / (1 + r) + $2(1.07)² / (1 + r)² + {[$2(1.07)²(1.05)] / (r - 0.05)} / [(1 + r)²

Through iteration, r = 9%

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Given that a firm’s current dividend is $2.00, the forecasted growth is 7%, declining over three years to a stable 5% thereafter, and the current value of the firm’s shares is $45, what is the required rate of return?

A) 7.8%.

B) 9.8%.

C) 10.5%.

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The required rate of return is 9.8%.

r = ($2/$45) [(1 + 0.05) + (3/2)(0.07 – 0.05)] + 0.05 = 0.0980

Since the H-model is an approximation model, it is possible to solve for r directly without iteration.