Hello, I am in an Investments class and this homework problem has me stumped as the book does a poor job of illustrating how to use the valuation methods described. The question is as follows:
Given the following information concerning a $2.00 convertible preferred stock:
One share of preferred is convertible into 0.50 shares of common stock; Price of common stock is $34; Price of convertible preferred stock is $25...
a) what is the value of the preferred stock in terms of common stock?
b) what is the premium over the preferred stock's value as common stock?
c) if the preferred stock is perpetual and comparable preferred stock offers a dividend yield of 10%, what would be the minimum price of this stock if it were not convertible?
d) if the price of the common stock rose to $60, what would be the minimum increase in the value of the preferred stock that you would expect?

Okay, so for part (a) I have $34/$2 = $17 as the value for the preferred stock in terms of the common stock.

For (b) Is the premium over the preferred stock's value as common stock $360? My computations are as follows:

$1,000 bond / $25 price of convertible preferred stock = 40 shares

40 shares x $34 price of common stock = $1,360 in terms of stock

$1,360 - $1,000 = $360 difference which is the premium... right?

OR is the premium over the preferred stock's value as common stock equal to $9, calculated as $35 - $24?

For (c) I have no idea... feeling really stupid at this point. :(

For (d) I'm sure this one is simple, but at this point I'm ready to call 'uncle!'

Help from anyone would be greatly appreciated at this point. :) Thanks, Courtney.

In (a) you're spot on.

For (b), where did the bond come from? No bond is mentioned in the question. Moving on, the question is really asking, "What is the convertible's value in terms of the common?" (You just answered this one in (a)). "And, what is the convertible actually selling for right now? And so, what is the premium---that is, the excess of its actual trading price over its conversion value?"

To answer (c), note that any perpetual instrument which pays an annual amount (dividend, interest, whatever) of $X, when the appropriate discount rate happens to be Y%, has a value of X / Y. (The "comparable preferred... " info in part (c) is just another way of saying that 10% is the appropriate discount rate.) For example, an instrument paying $5 a year, when 15% is an appropriate discount rate, is worth 5 / 0.15 = 33.33. This would be its value as a straight (i.e. nonconvertible) instrument, which is what (c) is asking about.

To tackle (d), keep in mind that a convertible instrument like this one will always trade for at least its value in terms of the common stock, and that's sufficient info for answering (d).

That ought to help you get around third, and I'll let you cross the plate and finish up.

ArcSine,

Thank you for taking the time to get me going around the bases! It is greatly appreciated. I think were I keep stumbling in this course is the fact that the text really does not go into any sort of detail about how to valuate investments. It talks all about them, but is seriously lacking in examples illustrating valuation methods. I will be really glad in two weeks when this class is over!

As for the answers this is what I managed to come up with... part (b) $25 - $17 = $8; part (c) $25 / 0.10 = $250; part (d) $60 / $2.00 = $30 - $17 = $13

I guess we will see if that is right when I get my graded assignment back, but I'm pretty sure I managed to make it in for a homerun thanks to your assistance! Thanks, Courtney.



In (a) you're spot on.

For (b), where did the bond come from? No bond is mentioned in the question. Moving on, the question is really asking, "What is the convertible's value in terms of the common?" (You just answered this one in (a)). "And, what is the convertible actually selling for right now? And so, what is the premium---that is, the excess of its actual trading price over its conversion value?"

To answer (c), note that any perpetual instrument which pays an annual amount (dividend, interest, whatever) of $X, when the appropriate discount rate happens to be Y%, has a value of X / Y. (The "comparable preferred ... " info in part (c) is just another way of saying that 10% is the appropriate discount rate.) For example, an instrument paying $5 a year, when 15% is an appropriate discount rate, is worth 5 / 0.15 = 33.33. This would be its value as a straight (i.e., nonconvertible) instrument, which is what (c) is asking about.

To tackle (d), keep in mind that a convertible instrument like this one will always trade for at least its value in terms of the common stock, and that's sufficient info for answering (d).

That ought to help you get around third, and I'll let you cross the plate and finish up.

Hmmm.. . With (a) and (b) you're safely on second.

To stretch it out into a three-bagger, for (c) go back and review the example I gave earlier. In particular, note that the numerator is the annual payment the instrument makes, not the current price. In the case of your preferred stock, its annual dividend payment is given in the description of the preferred stock itself, near the beginning of the question.

For (d) you're correct that in the event the common goes to $60 per share, the convertible pfd would have to go to at least $30. But to successfully steal home for the score, note where the convertible pfd is currently trading, and re-read (d)'s question carefully.