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A share of DivCorp common stock does not pay a regular dividend, but sometimes awards a special dividend of $ 2 0 per share at
A share of DivCorp common stock does not pay a regular dividend, but
sometimes awards a special dividend of $ per share at the end of each
year. The hypothetical marginal investor has a subjective discount rate
of beta per year and power utility of consumption with risk aversion
coefficient gamma Assume that this investors income is fixed at $
per year in perpetuity. This investor believes that the probability that Di
vCorp pays a dividend in a given year is always pi 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? points
Hint : Start by writing out the FPE and see if you can plug in each cash
flow and the appropriate discount factor. In terms of discounting for im
patience, payoffs one period away are multiplied by beta payoffs two periods
away are multiplied by beta and so on Remember that an expectation is
also just a summation over outcomes, which can be probabilistic outcomes
that are realized simultaneously ie the result of coin flip outcomes that
are realized sequentially in time ie payments on a riskfree bond or a
combination of both ie a stream of risky cash flows that default with
some probability
Hint : You can translate the subjective discount rate beta to a net
return r using the relationship:
beta
r
Hint : The value p of a perpetuity or a contract that provides a fixed
sum of cash X at regular intervals forever, is given by:
p X
r X
r X
r
Where r is the discount rate expressed as a net return ie interest
rate per interval.
Hint : Remember that a constant can move inside and outside the expec
tation operator: EaX aEX for a constant a and a random variable
X Any value that is known at time t when the expectation is evaluated
can be treated as a constant.
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