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Q: Finance ( Answered 5 out of 5 stars,   0 Comments )
Subject: Finance
Category: Business and Money > Finance
Asked by: baseball2-ga
List Price: $5.00
Posted: 30 Jul 2005 12:49 PDT
Expires: 29 Aug 2005 12:49 PDT
Question ID: 549836
Need to check if I am doing my calculation right.

Background information is: A company has issued preferred stock witn
an annual 8.00 divident that will be paid inperpetutity. The discount
rate is 12 percent.

Would the calucalion to state what price the preferred sell be 8/.12=$66.66?

Would the calculation to determine what the price should the stock
seell in 1 year from now be  8.00 + 66.66 / 12 = 67.52

Would the expected rate of return be 8 + 67.52 - 66.66 / 66.66 = 13%

What would the calculation be to determen divedent yeild and capital gain yeild?

Any help would be greatful. Thanks
Subject: Re: Finance
Answered By: omnivorous-ga on 31 Jul 2005 03:25 PDT
Rated:5 out of 5 stars
Baseball2 ?

The general case for figuring a stock value (it also figures a bond or
loan value too) is:

P0 = D1 / (r-g)

P0 = today's price
D1 = dividends in period 1
r = required rate of return (in decimals)
g = dividend growth rate

You?ve simplified this greatly by saying that there?s an annual
dividend and that it never changes.  So, g (growth rate) = 0 and
today?s price is:

P0 = D1 / r

As a result you?ve figured the price correctly at $66.67.


Essentially the $8 paid on the preferred is the ?interest? on holding
1 share of the $66.67 stock.  In fact, securities analysts would move
this preferred stock into ?debt? rather than equity when doing a
discounted cash flow.

The dividends won?t change a year from now ? they?ll still be $8 and
still be paid in perpetuity.  This stock price will change only if the
discount rate changes.  So it will still be $66.67.

The dividend yield will match the discount rate ? by definition.  But
you can calculate it too:

Yield = Dividend / Stock Price = $8 / $66.67 = .12 or 12%

With no change in stock price, there?s no capital gain.

A final note: if there were some constant growth in the dividend, of
say 4% you?d recalculate the stock price every year and would be able
to determine capital gains.  But in the case of a constant perpetuity,
it changes price only with a change in discount rate or if the company
should default on the dividends.

Best regards,


Request for Answer Clarification by baseball2-ga on 31 Jul 2005 15:20 PDT
Thanks Livioflores! I am still a bit confused with the final portion
of your answer.  Actually, I gave you one wrong bit of information. I
neglected to tell you the discount rate would rise to 12% therfore
that is why I asked if 67.52 is the correct amount for the stock in
one year. I am not sure that I followed your last part of your answer.
However, this is how I figured the following (if you tell me if I am
going in the right direction that would be grteat)

Divendend yeild 67.53-66.67 / 66.67 = 1.29

Capital gain 67.52+ 66.67/ 66.67 =  2.01

Expected rate of return = 67.52 - 66.67/ 66.67 = 13%

Request for Answer Clarification by baseball2-ga on 31 Jul 2005 18:16 PDT
Sorry I meant thank you ominivorous!

Clarification of Answer by omnivorous-ga on 31 Jul 2005 18:23 PDT
Baseball2 --

I think that you meant that the discount rate rises to 13% (not 12%). 
And just to be clear: this happens at the end of year 1, correct? 
Note that this causes the stock to DECLINE.

However, if the discount rate starts at 13% (stock price $61.54), then
the stock will rise with a new discount rate of 12% ($66.67).

As a side note: the stock drops by $8 on the day after the dividend is
paid -- then slowly rises by $8 until the end of the dividend-year. 
So we do have to be careful about choosing comparable dates each year.

Best regards,

baseball2-ga rated this answer:5 out of 5 stars

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