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Dividend Growth Model - How to Value Common Stock with a Constant Dividend and Steady Growth

If the dividend grows at a steady rate, we do not need to forecast an infinite number of future dividends; however we just need to come up with a single growth rate which is a lot simpler. Taking D0 to be the dividend just paid and g to be the constant growth rate, the value of one share of stock can be simply written as:

 P0 = [(D1 / (1 + r)1)] + [(D2 / (1 + r)2)] + [(D3 / (1 + r)3)]

This can be cut down to the following:

 P0 = [D0 x (1 + g)] / (r – g) = (D1) / (r – g)

We have therefore just derived the dividend growth model which is a model that determines the current price or value of a share of stock as its dividend next period divided by the discount rate minus the dividend growth rate.

Example

Consider a case where the current dividend payout is \$1.80 and the rate of return required is 15% while the constant growth rate is 5%. What will the current price of the stock be?

 P0 = [D0 x (1 + g)] / (r – g) P0 = [\$1.80 x (1 + 0.05) / (0.15 – 0.05) P0 = [\$1.80 x (1.05) / (0.1) P0 = \$1.89 / 0.1 P0 = \$18.90

Bank of America Dividend Growth Model Application - Example Bank of America announces its next dividend will be \$2 a share and from research we know that investors typically require a 14% annual rate of return from American banks, thus this will be the required rate of return. The bank increases its dividend at a steady rate of 8% a year. Based on the dividend growth model, what is the value of the Bank of America stock today? What is the value in 4 years?

a) Since we are already given the next dividend as \$2 per share, we will not multiply D1 with (1 + g) as it is given as \$2. Having said this, the dividend growth formula we will use is:

 P0 = D1 / (r – g) P0 = 2 / (0.14 – 0.08) P0 = 2 / 0.06 P0 = \$33.33

b) Since we already know the dividend in one year, the dividend in four years is equal to:

 P0 = D1 / (r – g) P0 = 2 / (0.14 – 0.08) P0 = 2 / 0.06 P0 = \$33.33

Therefore, the price of the stock in four years will be:

 P4 = [(D4 x (1 + g)] / (r – g) P4 = (\$2.52 x (1 + 0.08) / (0.14 – 0.08) P4 = (\$2.52 x (1.08) / 0.06 P4 = 2.7216 / 0.06 P4 = \$45.36

Dividend Growth Sample Problems – Example 1

ABC Company has just paid a \$1.5 dividend and dividends are expected to grow at 5% per year. Return on shareholder’s equity is 12%. What is the stock price?

 P0 = [(D0 (1 + g) / (re – g)] P0 = 1.5 (1.05) / (0.12 – 0.05) P0 = 1.575 / 0.07 P0 = \$22.50 (Current stock price)

Dividend Growth Sample Problems – Example 2

ABC Company is a declining company and dividends are expected to decrease by 4% a year. Next year’s dividends are expected to come in at \$2 per share and the required shareholder return is 8%.

a) What is the current price of the stock?

 P0 = D1 / (Re – g) P0 = \$2 / (0.08 - - (0.04)) P0 = \$2 / 0.12 P0 = \$16.67