CFA论坛 - Powered by Discuz! Board

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?

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%.

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)?

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%

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?

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%

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?

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

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?

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

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?

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

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?

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

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?

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.

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?

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%

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?

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.

An investor buys shares of a firm at $10.00. A year later she receives a dividend of $0.96 and sells the shares at $9.00. What is her holding period return on this investment?

The holding period return = ($0.96 + $9.00 / $10.00) – 1 = –0.004 or –0.4%