For a non-callable, non-convertible perpetual preferred share paying a level dividend and assuming a constant required rate of return, the value is given by the equation below:
where: V0 = present value of the perpetuity; D0 = dividend and r = rate of return
A $100 par value, non-callable, non-convertible perpetual preferred stock pays a 5% dividend. The discount rate is 8%. Calculate the intrinsic value of the preferred share.
Expected annual dividend = 0.05 x 100 = 5
Value of the preferred share = 5.00/0.08 = 62.50
Other types of preferred shares to consider are:
One of the disadvantages of the dividend discount model is that it is difficult to accurately estimate the amount of dividends for a long period of time. The Gordon growth model simplifies this by assuming that dividends grow indefinitely at a constant rate; it is also called the constant-growth dividend discount model. According to this model, the intrinsic value of a security can be calculated as:
g = dividend growth rate = b * ROE
b = earnings retention rate = (1- dividend payout ratio)
ROE = return on equity
In the equation above, if the growth rate is zero, then the equation reduces to the present value of a perpetuity.
Assumptions of the Gordon Growth model:
When is it not appropriate to use the Gordon Growth Model?
What happens to the value if dividend value is increased?
Let us look at the formula again.
When dividend increases, numerator increases. If the payout ratio increases, retention rate decreases and value of g decreases. If g decreases, the denominator increases. As a result, the impact on value, if dividend is increased cannot be determined with certainty.
Estimate the intrinsic value of a stock given the following data:
Beta =1.5; RFR = 3%; market risk premium = 5%; dividend just paid = $1.00; dividend payout ratio = 0.4; return on equity = 15%.
Note: the values of r, g and expected dividend are not given. So, first calculate these values.
r = RFR + Beta x market risk premium = 3+ 1.5 x 5 = 10.5%
g = b x ROE = (1 – 0.4) x 0.15 = 0.09
Applying the Gordon growth model, V0= = 72.67
A company does not currently pay dividend but is expected to begin to do so in 4 years. The first dividend is expected to be $2.00 and to be received at the end of year 4. The dividend is expected to grow at 5% into perpetuity. The required return is 10%. What is the estimated current intrinsic value?
To calculate the intrinsic value, first calculate the value of dividend at the end of period 3 and then discount it to t=0 using the Gordon growth model.
Instructor’s Note: Do not forget to discount 40 to the present value. The undiscounted value is commonly presented as one of the answer options as a trap.
It is an ideal situation to assume that all companies grow at a constant rate indefinitely and pay a constant dividend; the assumption is true to an extent only for stable companies. In reality, companies go through a finite rapid growth phase followed by an infinite period of sustainable growth.
A two-stage DDM can be used to calculate the value of such companies transitioning from growth to mature stage. The Gordon growth model may be used to calculate the terminal value at the beginning of the second stage which represents the present value of dividends during the sustainable growth phase.
The first term is discounting the dividends during the high growth period. The second term is calculating the terminal value for the second sustainable growth period and then discounting it to the present value where Vn = terminal value at time n estimated using the Gordon growth model.
Let us understand the concept better with the help of an example. The current dividend for a company is $4.00. The dividends are expected to grow at 20% a year for 4 years and then at 10% after that. The required rate of return is 18%. Estimate the intrinsic value.
First draw a timeline.
We will use this formula:
where n = 4 (high growth period)
Solve for the second term:
Using the financial calculator, we can calculate the present value of dividends and terminal value by entering the following values: CF0 = 0; CF1 = 4.8; CF2 = 5.76; CF3 = 6.91; CF4 = 8.29 + 114; I = 18; NPV = 75.48
Note: while calculating V4, you need to use 10% as growth rate since it is the long term growth rate.
Three Stage Models
The concept of a two-stage model can be extended to as many stages as a company goes through. Often, companies go through three stages beyond the startup phase: growth, transition and maturity.