A share of DivCorp common stock does not pay a regular dividend, but

sometimes awards a special dividend of $$20$ per share at the end of each

year. The hypothetical $$marginal$$ investor has a subjective discount rate

of $\backslash$beta $=0\mathrm{.}975$ per year and power utility of consumption with risk aversion

coefficient $\backslash$gamma $=1.$ Assume that this investor$$s income is fixed at $$100,000$

per year in perpetuity. This investor believes that the probability that Di$-$

vCorp pays a dividend in a given year is always $\backslash$pi $=0\mathrm{.}35.$ The probability

that DivCorp pays a dividend in a given year is uncorrelated with the

probability that it pays a dividend in any other year. The next possible

special dividend date is one year from today.

What should be the market price of one share of DivCorp?