You own 500 shares of stock at a particular company. The company will
pay a $2-per-share dividend one year from today. Two years from now,
the company will close its doors. Stockholders will receive
liquidating dividends of $17.5375 per share. The required rate of
return on the company stock is 15 percent. What is the current price
of the stock? You prefer to receive equal amounts of money in each of
the next two years, how can this be accomplished?

Hi cop189!
The current market value of a stock should be the present value of its
flow of dividends, discounted at its required rate of return. We know
that this stock will pay $2 in one year, $17.5375 in two years and
then it will be worthless. Therefore, the price of the stock should
be:

P = 2/(1.15) + 17.5375/(1.15)^2 = 15

The current value of the stock is then $15.

Receving equal amounts of money in each of the next two years will
involve selling some shares immediately after receiving the dividend
payment. In order to find how much money you'll receive from the sale
of these stocks, we must find the price of the stock one year from
now, after the first dividend payment.

Basically, immediately after the first dividend payment, the stock
will only make one more payment one year after that. Therefore, the
value of the stock in one year, after the $2 dividend payment will be:

P1 = 17.5375/1.15 = $15.25

Now we can find out how many shares should you sell after the $2
dividend payment in order to receive equal amounts of money at the end
of the next two years. Let's call 'x' to the amount of shares you'll
sell next year. Then we have that:

Income year 1 = 1000 + x*15.25
Income year 2 = 17.5375*(500-x)

Notice that the 1000 in the year 1 income come from the $2 dividend
payment multiplied by 500 shares. Finally, in order to find x, we
simply equalize the income of both years and solve the equation:

1000 + x*(15.25) = 17.5375*(500-x)
x*(15.25+17.5375) = 7768.75
x*32.7875 = 7768.75
x = 236.94

So now we have the solution. In order to receive equal amounts of
money in each of the next 2 years, you should, in year 1, collect the
first dividend, and immediately then sell 237 shares at market value
(15.25). This will give you $1000+$15.25*237=$4614.25 and leave you
with 263 shares. So at the end of year 2, you'll receive the
liquidating dividend for these shares, for an amount of $17.5375*263 =
$4612.36 (the small difference is due to the fact that we rounded the
number of shares to 237).


I hope this helps! If you have any doubts regarding my answer, please
don't hesitate to request clarification before rating it; otherwise I
await your rating and final comments.

Best wishes!
elmarto