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. Flashcards
SchweserNotes: Book 4 p.299 CFA Program Curriculum: Vol.5 p.258
The Gordon growth model assumes the growth rate in dividends is constant:
A firm with high growth over some number of periods followed by a constant growth rate of dividends forever can be valued using a multistage model
A firm with high growth over some number of periods followed by a constant growth rate of dividends forever can be valued using a multistage model:
Pn =
gc = constant growth rate of dividends
n = number of periods of supernormal growth
The sustainable growth rate is the rate at which earnings and dividends can continue to grow indefinitely:
g = b × ROE
where:
b = earnings
retention (retained earnings) = 1 − dividend payout rate
ROE = return on equity
A company with a return on equity (ROE) of 27%, required return on equity (ke) of 20%, and a dividend payout ratio of 40% has an implied sustainable growth rate closest to:
g = (RR)(ROE)
= (.60)(.27)
= 0.162 or 16.2%
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?
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
A company’s payout ratio is 0.45 and its expected return on equity (ROE) is 23%. What is the company’s implied growth rate in dividends?
Growth Rate = (ROE)(1 – Payout Ratio) = (0.23)(0.55) = 12.65%
The capital asset pricing model can be used to estimate which of the following inputs to the dividend discount model?
The required return on equity.
The capital asset pricing model is a rate of return model that can be used to estimate a stock’s required rate of return, given the nominal risk-free rate, the market risk premium, and the stock’s beta:
k = Rnominal risk free rate + (beta)(Rmarket - Rnominal risk free rate).
When calculating a sustainable growth rate for a company an analyst most likely assumes: the dividend payout ratio is constant.
The sustainable growth rate is the rate at which equity, earnings, and dividends can continue to grow indefinitely assuming that ROE is constant, the dividend payout ratio is constant, and no new equity is sold.
Company B paid a $1.00 dividend per share last year and is expected to continue to pay out 40% of its earnings as dividends for the foreseeable future. If the firm is expected to earn a 10% return on equity in the future, and if an investor requires a 12% return on the stock, the stock’s value is closest to:
P0 = Value of the stock = D1 / (k − g)
g = (RR)(ROE)
RR = 1 − dividend payout = 1 − 0.4 = 0.6
ROE = 0.1
g = (0.6)(0.1) = 0.06
D1 = (D0)(1 + g) = (1)(1 + 0.06) = $1.06
P0 = 1.06 / (0.12 − 0.06) = 1.06 / 0.06 = $17.67
A stock has the following elements: last year’s dividend = $1, next year’s dividend is 10% higher, the price will be $25 at year-end, the risk-free rate is 5%, the market risk premium is 5%, and the stock’s beta is 1.5. The stock’s price is closest to:
Cost of equity capital = 5% + 1.5(5%) = 12.5%
P0 = (1.1 / 1.125) + (25 / 1.125) = $23.20.
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.
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
A company’s growth rate in dividends and earnings can be estimated as the:
product of the retention ratio and the return on equity.
Assuming past investments are stable and earnings are calculated to allow for maintenance of past earnings power, then the firm’s expected dividend growth rate (g) can be defined as the firm’s earnings plowback or retention rate (RR) times the return on the equity (ROE) portion of new investments. This growth rate is also called the sustainable growth rate.
Using an infinite period dividend discount model, find the value of a stock that last paid a dividend of $1.50. Dividends are expected to grow at 6 percent forever, the expected return on the market is 12 percent and the stock’s beta is 0.8. The risk-free rate of return is 5 percent.
First find the required rate of return using the CAPM equation.
k = 0.05 + 0.8(0.12 - 0.05) = 10.6%
$1.50(1.06) /(0.106 - 0.06) = $34.57
