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system
how to determine duration of a common stock whose dividends grow in perpetuity?
user
the dividend discount model is based on the concept that the present value of a stock is the sum of all future dividends, discounted back to the present. since you said: dividends are expected to grow at a constant rate in perpetuity ... the gordon growth model is a simple variant of the ddm, tailored for a firm in "steady state" mode, with dividends growing at a rate that can be sustained forever. consider mccormick (mkc), who's last dividend was 31 cents, or $1.24 annualized. the dividend has been growing just a little over 7% annually. let's use a discount, or hurdle rate of 10%. mkc closed today at $50.32, for what it's worth. the model is extremely sensitive to inputs. as g approaches r, the stock price rises to infinity. if g > r, stock goes negative. be conservative with 'g' -- it must be sustainable forever.  the next step up in complexity is the two-stage ddm, where the company is expected to grow at a higher, unsustainable rate in the early years (stage 1), and then settling down to the terminal rate for stage 2. stage 1 is the present value of dividends during the high growth period. stage 2 is the gordon model, starting at the end of stage 1, and discounting back to the present. consider abbott labs (abt). the current annual dividend is $1.92, the current dividend growth rate is 12%, and let's say that continues for ten years (n), after which point the growth rate is 5% in perpetuity. again, the discount rate is 10%. stage 1 is calculated as follows: stage 2 is ggm, using not today's dividend, but the 11th year's dividend, since stage 1 covered the first ten years. 'gn' is the terminal growth, 5% in our case. then... the value of the stock today is 21.22 + 51.50 = 72.72 abt closed today at $56.72, for what it's worth.
assistant