Try to avoid using the Dividend Discount Model to compute a stocks price, given the presence of a strictly positive probability of bankruptcy. Much academic work has been done to try to incorporate this information into the model, but much has not been successful.
Instead, if you're interested, check out a paper released in the Financial Analyst Journal, Vol. 50, No. 4, 1994. This paper is entitled "A Realistic Dividend Valuation Model" by William Hurley and Lewis Johnson.
In this paper, the authors propose two methods in computing the price of a stock using divdends and probability of bankruptcy. I'm not going to go into too much detail here, but they basically propose two methods: the additive model and the geometric model. Use the additive approach with firms that display erratic dividend payments. Use the geometric approach for stocks that display more stable dividend income over their lifetime.
The Additive Model
The additive model computes and expected value (V) of the stocks price and a lower bound of this expected value (L). The two equations are:
V = D/k
L = (D*(1-prob(bankruptcy))/(k+prob(bankruptcy)) + [(1/(k + prob(bankruptcy)) + (1/(k + prob(bankruptcy)^2))]*delta*p
D = next dividend payment expected
prob(bankruptcy) = Probability of bankruptcy
k = discount rate (estimate this using simple CAPM)
p = probability of raising the dividend (compute this using historical dividend data. If for 16 years of dividend payment, 14 years were increasing, then p = 0.875).
delta = the amount of dividend increase, on average. (Once again, compute this using historical data. It is enough to compute a simple arithmetic average of the increase in dividend payments over the past).
Compute the numbers and plug the values into the equation. V will give you a better value for the firms stock price given you probability of bankruptcy. L will give you a lower bound on the value of V, which can be used to measure dispersion of your calculation of L.
I am not going to put the geometric approach as the math is slightly more involved and typing it here would be cumbersome. Let me know if you are interested in further reading and I can direct you to some articles.
Hope this has been of some help,
Amit
