Mohnish Pabrai Boston College Presentation

[hyten1]

good discussion, bmichaud i too took a while to understand this stuff, ever since eric first wrote about it in the bac leverage thread

 

i have been contemplating what to do with the GM B warrant since it seems likely that GM will initiated a dividend in the future. i am still trying to figure it out. modifying your example (good example) to use numbers closer to real thing.

 

GM stock price $40.7

GM divy $1.08

GM B warrant price $22.88

Strike $18.33

 

40.7 stock price -  22.88 B warrant price = 17.82 leverage

 

Assuming no dividend:

17.82 leverage x (1+x) = 18.33 strike. X = 2.85%.

 

With dividend, the $1.08 gets added to the strike:

17.82 leverage x (1+x) = (18.33 + 1.08) = 19.41 adj strike. X =8.45%.

 

its good that we solve for X but what is really X? for me it took my dense brain a while to come around to the idea of "leverage" not sure why that word confused me a great deal. instead if i use "hurdle rate to breakeven" it makes more sense to me.

 

EDIT: however the above example is for 1 year. since B warrant doesn't expire until 2019 which is approx 6 year away. here is my attempt to do that calculation

 

Assuming no dividend:

17.82 leverage  (1+x)^6 = 18.33 strike. X = 0.5%.

 

With dividend, the $1.08 gets added to the strike each year (making it simple):

17.82 leverage x (1+x)^6 = (18.33 + 1.08 + 1.08 + 1.08 + 1.08+1.08+1.08) = 24.81 adj strike. X = 5.7%.

 

 

hmmm, thinking outload here, did i do this right? why is X lower when its for 6 year vs the 1 year?  5.7% doesn't seem like such a large cost.

 

hyy

[bmichaud]

I was wondering about that exact thing. My guess is Eric would say, assuming the dividend remains flat, that you just compound the no dividend leverage cost with the dividend yield on the strike price. So....

 

No dividend leverage cost is .5% in your example. The 1.08 dividend on the 18.33 strike is 5.9%. Adding 1 to each, multiplying together, then subtracting 1 gets you to 6.4% leverage.

 

It's lower than the 1 year b/c the 1-year 2.85% no div leverage cost is spread out over 6 years. Hence 2.85% versus .5%.

 

 

Now it's also interesting to consider if the dividends grow. Assuming the dividend grows 10% per year, I assume you would calculate each new dividend as a % of the original strike price. Then you would add 1 to each "new" strike price dividend yield, compound them all together and multiply by the original strike. Doing this I get to an adjusted strike of $28.40.

 

So the cost of leverage is approximately 8.1% assuming GM grows the dividend by 10% per annum.

[racemize]

ordinary dividend:

 

COMMON STOCK:

Stock trades at $36.

$1.08 ordinary dividend is declared.

Stock now trades at $34.92 on dividend-EX date.

$1.08 + $34.92 = $36

 

WARRANT/CALL:

Option trades at $18

$1.08 ordinary dividend is declared

Option now trades at $16.92 on dividend-EX date (because the stock dropped by $1.08 on div-EX dates)

 

 

Better example?

 

Value of common stock portfolio didn't change one bit.

Value of option/warrant portfolio DECLINED by 6%

 

That 6% decline happens to be TWICE the dividend yield.

 

This is the best example.  I need to think about it, but it does require that the price actually drops by the dividend amount which is rational, but I'm not sure that the prices actually do that, as the dividend is coming out of earnings (for ordinary dividends).  That being said, these models never work unless you assume the stock drops by the dividend amount. 

 

I'm just going to go ahead and spell out my math/model, while still thinking about the above.

 

 

No dividend

Current Stock Price 40.87

Warrant Strike Price 18.33

Current Warrant Price 23.00

 

Solving for when the total return of stock = the total Return of Warrant at expiry.  Variables are current stock price (CSP), current warrant price (CWP), future stock price (FSP), warrant strike price (WSP); solving for FSP:

 

(FSP - CSP) / CSP = (FSP - WSP - CWP) / CWP

CWP*FSP - CWP*CSP = CSP*FSP - CSP*WSP - CSP*CWP

CSP*CWP = CSP*FSP - CWP*FSP

CSP*WSP / (CSP-CWP) = FSP

 

Ok, so now we plug in the nubmers to get FSP:

40.87*18.33 / (40.87-23) = 41.91

 

Thus, at 41.91, buying the common and buying the warrant will yield the same result, which is 41.91/40.87 - 1 = 2.54%, which can then be annualized.

 

 

With ordinary dividends

new variable: cumulative ordinary dividends = COD = 1.00

 

Again, solving for total return of stock = total return of warrant at expiry:

(FSP - CSP + COD) / CSP = (FSP - WSP - CWP) / CWP

CWP*FSP - CWP*CSP + CWP*COD = CSP*FSP - CSP*WSP - CWP*CSP

CWP*COD + CSP*WSP = CSP*FSP - CWP*FSP

(CWP*COD + CSP*WSP) / (CSP - CWP) = FSP

 

Plugging these numbers in to get FSP:

(23*1 + 40.87*18.33 / (40.87-23) = 43.21

 

(43.21+1) / 40.87 - 1 = 8.17% return, which can then be annualized

 

 

 

So, adding a 2.45% dividend has caused the breakeven growth to increase from 2.54% to 8.17%, or a difference of 5.63%

 

 

So yeah, now we can plainly see with my own math that Eric was right and I was wrong.  I'll go back to my cave now.

 

Thanks for sticking with me and making me work this out correctly (hopefully correctly anyway).

 

 

 

[ERICOPOLY]

Previously I put forth my method of computing cost of leverage -- the first part of the calculation was calculating how much is actually being borrowed (it's convoluted because you are prepaying interest to the very person you are borrowing from). 

 

But that of course wasn't the full cost of leverage, it was just the cost of the option premium component.

 

Missing is the cost of the excluded dividend (if any).

 

Because this portion of the cost isn't payable upfront, it's cost can just be added to the result of the prior calculation.

 

So a $1 dividend declared in a given year will cost 5% at $20 strike, it will cost 10% at $10 strike, and it will cost 100% at $1 strike.

 

Pretty funny isn't it.  Dividends make the leverage costs soar when the strike is lower.  So there is a point where the low strike options start to cost more than the at-the-money strike options.  Even though the at-the-money strike options are lower risk in a sizable common stock price decline (due to the higher put strike).

[racemize]

After updating my spreadsheet (a few mental glitches in the process), it is pretty fascinating to look at the relationships.  GM is one of the ones affected the most, since the strike is ~0.5 of the current stock price.  Most of the other ones are much closer in terms of strike/current common price.

[ERICOPOLY]

actually, i need to think more about my last post.  i believe it may be that the cost of lost dividend is actually a cost on what is actually borrowed after taking into consideration all that prepaid warrant premium.

 

incidentally, i also worked out wahat madonnas "like a prayer" is about.  hot damn that's funny. think of tarantino in reservoir dogs when he explains the meaning of "like a virgin"

 

and this is my first post using my big TESLA computer screen -- i'm charging at the tesla supercharger at SpaceX

 

 

[racemize]

The BAC warrants will get a floor established to support the cost of leverage once a dividend is paid. 

 

Imagine if a $1 dividend were paid (it won't be that high, but just imagine).  That would be 7.5% of value versus what a regular call option offers.

 

So that large of a dividend, were it to be suddenly announced, would create quite a land grab for the warrants -- the price would spike right away.  They would suddenly be the best thing around, with effectively free options volatility premium (free embedded put) -- compared to a regular call options.  So for accounts that can't use margin loans  (like IRAs), it would be the best game in town and we'd see no more option decay.

 

Interestingly, a floor also gets established to support the cost of leverage when a dividend is paid for a call without dividend protection.  Let's say GM issues a dividend at 3% and the cost of leverage is at the 6% area due to the dividend.  That means that the cost of leverage can never fall below the 6% floor (assuming it is caused solely by the dividend) because if it did, it could be immediately aribitraged.  So, it would seem that floors are established for both dividend protected and unprotected leveraged vehicles when a dividend is paid.

 

However, it is obviously better to get the floor from getting the dividend protection than not.

 

I guess you were already saying that, but in the reverse way.  i.e., the A-warrants get the 7.5% of value because of the dividend floor that just got added to the calls without protection.

[racemize]

actually, i need to think more about my last post.  i believe it may be that the cost of lost dividend is actually a cost on what is actually borrowed after taking into consideration all that prepaid warrant premium.

 

Would you mind posting a cost of leverage example with the dividend after you have thought about it?  (Perhaps you already have).  txlaw and I have come up with different costs for various dividend scenarios and are working that out at the moment.

 

I'm curious to see if it matches the total return formula I derived earlier in the thread.  I would think they would match or at least that they will be fairly similar.

[racemize]

The BAC warrants will get a floor established to support the cost of leverage once a dividend is paid. 

 

Imagine if a $1 dividend were paid (it won't be that high, but just imagine).  That would be 7.5% of value versus what a regular call option offers.

 

So that large of a dividend, were it to be suddenly announced, would create quite a land grab for the warrants -- the price would spike right away.  They would suddenly be the best thing around, with effectively free options volatility premium (free embedded put) -- compared to a regular call options.  So for accounts that can't use margin loans  (like IRAs), it would be the best game in town and we'd see no more option decay.

 

Interestingly, a floor also gets established to support the cost of leverage when a dividend is paid for a call without dividend protection.  Let's say GM issues a dividend at 3% and the cost of leverage is at the 6% area due to the dividend.  That means that the cost of leverage can never fall below the 6% floor (assuming it is caused solely by the dividend) because if it did, it could be immediately aribitraged.  So, it would seem that floors are established for both dividend protected and unprotected leveraged vehicles when a dividend is paid.

 

However, it is obviously better to get the floor from getting the dividend protection than not.

 

I guess you were already saying that, but in the reverse way.  i.e., the A-warrants get the 7.5% of value because of the dividend floor that just got added to the calls without protection.

 

This is also about to be true for both the WFC and JPM warrants, as they are right at their dividend thresholds.  As the dividends increase, the warrants get increasingly more attractive than the calls.

[ERICOPOLY]

Interestingly, a floor also gets established to support the cost of leverage when a dividend is paid for a call without dividend protection.  Let's say GM issues a dividend at 3% and the cost of leverage is at the 6% area due to the dividend.  That means that the cost of leverage can never fall below the 6% floor (assuming it is caused solely by the dividend) because if it did, it could be immediately aribitraged.  So, it would seem that floors are established for both dividend protected and unprotected leveraged vehicles when a dividend is paid.

 

However, it is obviously better to get the floor from getting the dividend protection than not.

 

I guess you were already saying that, but in the reverse way.  i.e., the A-warrants get the 7.5% of value because of the dividend floor that just got added to the calls without protection.

 

 

Yes, a floor gets established for the value of the premium in the call with no dividend protection.  Only, the floor will be $0.    The premium won't fall below $0, because of the arbitrage.

 

Once the dividend is large enough, there will be negative utility to own the call.  At that point, the best strategy would be to exercise the call and grab the dividend (or sell it back to the market for someone else to do this arbitrage). 

 

So the floor in the calls for the option premium is $0 if there is no dividend protection.  The premium also can't go negative due to arbitrage.

 

You can think of a 100% dividend to imagine this clearly -- even though it's not a realistic example for an ordinary dividend.

 

So yes, you are right.  At a certain point the floor for cost of leverage (after premium goes to $0) will be just the cost of not getting the dividend.

[ERICOPOLY]

I could be wrong about how much the arbitrage supports the warrants.

 

Let's say I try to do this arbitrage.  I purchase the warrant and write a call.  What price will I get for the call?  For a high dividend scenario, who is going to do this trade without wanting to buy the call for a slightly negative option premium?  Once he's bought it, he exercises it and sells the underlying, thereby locking in his negative premium.

 

But that leaves my warrant unhedged again.  Hmm...

 

What if instead the warrant is simply supported by the lowest-cost strategy of hedged leverage?  I mean, suppose a trader is using portfolio margin an puts to leverage the common.  Further suppose the cost of leverage in his strategy is only 3%.  Won't this guy be motivated to short the warrants?  His arbitrage would be to earn the spread on cost of leverage between the two strategies.  Although he would have a cost of borrow for the warrant that he is shorting.

 

Complicating his trade would be the rising volatility premium in the warrants if the stock pulled back down near warrant strike.  But his strike prices on his margined stock puts could be quite high -- providing protection.  Like for example, if we're talking about BAC at $30 and he is doing this arbitrage with $20 strike puts.... and if that's only costing him 3%, then it would seem to negate some worry.  Of course, he takes on interest rate risk still and of course he is paying cost to borrow the warrants for shorting.

 

Maybe somebody who isn't just rambling could chime in.

[thepupil]

Eric, I explored doing that with the expensive BAC Warrants, but the cost of borrow was prohibitive,  indicating many already are shorting the warrants.

[racemize]

I could be wrong about how much the arbitrage supports the warrants.

 

Let's say I try to do this arbitrage.  I purchase the warrant and write a call.  What price will I get for the call?  For a high dividend scenario, who is going to do this trade without wanting to buy the call for a slightly negative option premium?  Once he's bought it, he exercises it and sells the underlying, thereby locking in his negative premium.

 

But that leaves my warrant unhedged again.  Hmm...

 

What if instead the warrant is simply supported by the lowest-cost strategy of hedged leverage?  I mean, suppose a trader is using portfolio margin an puts to leverage the common.  Further suppose the cost of leverage in his strategy is only 3%.  Won't this guy be motivated to short the warrants?  His arbitrage would be to earn the spread on cost of leverage between the two strategies.  Although he would have a cost of borrow for the warrant that he is shorting.

 

Yes, I was trying to figure that out this morning.  I'm not sure I've reached any solid conclusions.

 

Let's say the BAC has a $1 dividend and the leaps start having a cost of leverage of 7% due solely to the missed dividends.  Would we expect it to trade at a higher cost of leverage than 7%?  Perhaps, but I guess we could ignore it now for now.

 

So if someone is looking at Leaps with a 7% dividend-adjusted cost of leverage, and the warrants are trading at 5% dividend-adjusted cost of leverage, then clearly the buyer would go for the warrants.  (Unless they wanted less raw gains and a shorter duration).  I guess I was thinking (and I think this is what you are saying) that the warrants should trade at least at the same cost of leverage as the Leaps?

 

How much is there a possibility that the cost is just too high and people stop writing LEAPs?  Probably, people would still be writing them in some amounts, but that's a lot of cost, since it is 7% for dividends plus any additional expected gains.

[ERICOPOLY]

I could be wrong about how much the arbitrage supports the warrants.

 

Let's say I try to do this arbitrage.  I purchase the warrant and write a call.  What price will I get for the call?  For a high dividend scenario, who is going to do this trade without wanting to buy the call for a slightly negative option premium?  Once he's bought it, he exercises it and sells the underlying, thereby locking in his negative premium.

 

But that leaves my warrant unhedged again.  Hmm...

 

What if instead the warrant is simply supported by the lowest-cost strategy of hedged leverage?  I mean, suppose a trader is using portfolio margin an puts to leverage the common.  Further suppose the cost of leverage in his strategy is only 3%.  Won't this guy be motivated to short the warrants?  His arbitrage would be to earn the spread on cost of leverage between the two strategies.  Although he would have a cost of borrow for the warrant that he is shorting.

 

Yes, I was trying to figure that out this morning.  I'm not sure I've reached any solid conclusions.

 

Let's say the BAC has a $1 dividend and the leaps start having a cost of leverage of 7% due solely to the missed dividends.  Would we expect it to trade at a higher cost of leverage than 7%?  Perhaps, but I guess we could ignore it now for now.

 

So if someone is looking at Leaps with a 7% dividend-adjusted cost of leverage, and the warrants are trading at 5% dividend-adjusted cost of leverage, then clearly the buyer would go for the warrants.  (Unless they wanted less raw gains and a shorter duration).  I guess I was thinking (and I think this is what you are saying) that the warrants should trade at least at the same cost of leverage as the Leaps?

 

How much is there a possibility that the cost is just too high and people stop writing LEAPs?  Probably, people would still be writing them in some amounts, but that's a lot of cost, since it is 7% for dividends plus any additional expected gains.

 

People would perhaps still be writing the LEAPS (they could buy the common and write the LEAP -- collecting the dividend on the common and profiting on the harm done to the LEAPS).  But why would someone want to purchase the LEAPS?  I think that's what you meant?

[racemize]

Yes, that's what I meant, haven't been getting enough sleep lately...

 

I guess I'm wondering, if people stop buying the Leaps because they get too expensive (maybe?) then it stops being a floor for the warrants.  Do you agree?

[ERICOPOLY]

Yes, that's what I meant, haven't been getting enough sleep lately...

 

I guess I'm wondering, if people stop buying the Leaps because they get too expensive (maybe?) then it stops being a floor for the warrants.  Do you agree?

 

Yes.

 

It sounded good in theory to believe one could just write LEAPs as an arbitrage on the warrant dividend, but it may be hard to find such an idiot to purchase the LEAPs in real-time.

 

 

[txlaw]

actually, i need to think more about my last post.  i believe it may be that the cost of lost dividend is actually a cost on what is actually borrowed after taking into consideration all that prepaid warrant premium.

 

Would you mind posting a cost of leverage example with the dividend after you have thought about it?  (Perhaps you already have).  txlaw and I have come up with different costs for various dividend scenarios and are working that out at the moment.

 

I'm curious to see if it matches the total return formula I derived earlier in the thread.  I would think they would match or at least that they will be fairly similar.

 

Let me see if I can sort of describe the way that I'm calculating cost of leverage for these GM warrants, which is to treat a warrant buy as a leveraged buy of the common, where the principal balance is completely forgiven in case of wipe out.  Constructive criticism welcome.

 

Strike price      =  $18.33  =  Loan principal amount

Common price  =  $40.27  =  Economic rights bought today (minus div collection)

Option price      =  $22.62  =  Cash outlay today

Intrinsic value  =  $21.94  =  Cash outlay attributable as down payment

Time premium  =  $ 0.68  =  Cash outlay attributable as pre-paid interest for 5.5 year loan

Div (possible)    ~  $ 1.20  =  Additional interest sweeped by the market on an annual basis

 

The strike price is like the principal amount for a balloon payment loan.  In 5.5 years or so, I can take full ownership of a share of GM common by making a cash outlay equal to the principal amount. 

 

The differential between the strike price and the common price today -- the intrinsic value of the option -- is equivalent to the cash down payment required for this non-recourse loan transaction.  I have to outlay $21.94 today as down payment to get this leveraged deal. 

 

Additionally, I have to pay pre-paid interest (the time premium) of $0.68 today. 

 

In order to get the nominal interest rate associated with the pre-paid interest, I have to solve for a rate that generates annual coupon payments with an NPV equal to the total amount of the pre-paid interest.  For simplicity's sake, let's say that comes out to 1% based on the discount rate I use.  And that rate, btw, should be keyed off the loan principal amount, aka the strike price.

 

BUT, additionally, the dividends that go along with my common ownership rights are swept away by the market, unlike if I simply use portfolio margin to buy the common.  If the dividend starts next year at $1.20 (~3% yield), that's a $1.20 annual cost that must be assigned to the loan principal amount, aka the strike price.  So I would get an additional interest rate of $1.2/$18.33, which equals approximately 6.5%. 

 

So my total cost of non-recourse leverage for $18.33 worth of borrowing (an LTV of 46%) is 6.5% + 1% = 7.5%.  If the dividend ratchets up over five years, then my interest rate goes up.  Of course, this does not take into account the "risk free" rate I could obtain for 5.5 years with that $18.33 worth of cash that I didn't have to outlay today, which somewhat mitigates the (potential) high interest rate.

 

Bottom line is that the cost of leverage depends on the dividends that GM decides to go with over the next couple of years, as there is no dividend protection.

[hyten1]

looks about right, now the question is what should one do if you own a great deal amount of the B warrant (in the event dividend starts or before in preparation) :)

 

 

actually, i need to think more about my last post.  i believe it may be that the cost of lost dividend is actually a cost on what is actually borrowed after taking into consideration all that prepaid warrant premium.

 

Would you mind posting a cost of leverage example with the dividend after you have thought about it?  (Perhaps you already have).  txlaw and I have come up with different costs for various dividend scenarios and are working that out at the moment.

 

I'm curious to see if it matches the total return formula I derived earlier in the thread.  I would think they would match or at least that they will be fairly similar.

 

Let me see if I can sort of describe the way that I'm calculating cost of leverage for these GM warrants, which is to treat a warrant buy as a leveraged buy of the common, where the principal balance is completely forgiven in case of wipe out.  Constructive criticism welcome.

 

Strike price      =  $18.33  =  Loan principal amount

Common price  =  $40.27  =  Economic rights bought today (minus div collection)

Option price      =  $22.62  =  Cash outlay today

Intrinsic value  =  $21.94  =  Cash outlay attributable as down payment

Time premium  =  $ 0.68  =  Cash outlay attributable as pre-paid interest for 5.5 year loan

Div (possible)    ~  $ 1.20  =  Additional interest sweeped by the market on an annual basis

 

The strike price is like the principal amount for a balloon payment loan.  In 5.5 years or so, I can take full ownership of a share of GM common by making a cash outlay equal to the principal amount. 

 

The differential between the strike price and the common price today -- the intrinsic value of the option -- is equivalent to the cash down payment required for this non-recourse loan transaction.  I have to outlay $21.94 today as down payment to get this leveraged deal. 

 

Additionally, I have to pay pre-paid interest (the time premium) of $0.68 today. 

 

In order to get the nominal interest rate associated with the pre-paid interest, I have to solve for a rate that generates annual coupon payments with an NPV equal to the total amount of the pre-paid interest.  For simplicity's sake, let's say that comes out to 1% based on the discount rate I use.  And that rate, btw, should be keyed off the loan principal amount, aka the strike price.

 

BUT, additionally, the dividends that go along with my common ownership rights are swept away by the market, unlike if I simply use portfolio margin to buy the common.  If the dividend starts next year at $1.20 (~3% yield), that's a $1.20 annual cost that must be assigned to the loan principal amount, aka the strike price.  So I would get an additional interest rate of $1.2/$18.33, which equals approximately 6.5%. 

 

So my total cost of non-recourse leverage for $18.33 worth of borrowing (an LTV of 46%) is 6.5% + 1% = 7.5%.  If the dividend ratchets up over five years, then my interest rate goes up.  Of course, this does not take into account the "risk free" rate I could obtain for 5.5 years with that $18.33 worth of cash that I didn't have to outlay today, which somewhat mitigates the (potential) high interest rate.

 

Bottom line is that the cost of leverage depends on the dividends that GM decides to go with over the next couple of years, as there is no dividend protection.

[ERICOPOLY]

The time premium of .68 -- I wonder what the market is expecting for dividend reinstatement?

 

I expect the premium would decay at somewhat of an accelerated pace when a significant dividend is reinstated.

 

So over a short time period that could easily get expensive.  Or at least, no longer look like such a bargain.

 

What if it went from .68 to zero in one month?  Okay, perhaps an exaggerated example.  And ultimately, it's only 68 cents so not that big of a deal -- but the cost of leverage on an annualized basis would be high.

 

Still, it can't exceed 68 cents -- leverage costs can be high for short periods and it's not a big deal in the grand picture of things. 

 

 

[racemize]

txlaw, that calculation looks like it will be at least close to the right cost of leverage.  However, my answer comes in slightly lower (some of this has to do with your 1% rounding from 0.65% I think).

 

Although I derived the formula earlier, here are the basics for what I am doing:

 

I determine the common price at which the total return of the common matches the total return of the warrant, which I believe should be the equation that gives the same cost of leverage that Eric is calculating.  However, it is possible that it is answering a slightly different question than Eric's, but returns very similar results.

 

In any event, the initial equation is:

 

Total Returns of Common = Total Returns of Warrant @ some future stock price, OR:

(Future Stock Price - Current Stock Price + cumulative dividends) / (Current Stock Price) = (Future Stock Price - Strike Price - Current Warrant Price) / Current Warrant Price

 

Solving for Future Stock Price gives you:

Future Stock Price = (Current Warrant Price * Cumulative Dividends + Current Stock Price * Warrant Strike Price) / (Current Stock Price - Current Warrant Price)

 

So, this is the number that tells you the stock price that makes the total return of the common = the total return of the warrant, from today's prices, based on the entered cumulative dividends.

 

If I plug in your value of $1.20 per year, I get:

Cumulative Dividends = 6.6 (22 quarters left @ 0.3 per quarter)

 

Now, using Current Stock Price = $40.34

Current Warrant price = $22.57

Warrant Strike = 18.33

Future Stock Price = $49.99

 

Checking my work:

Total Return for Stock = (49.99 + 6.6 - 40.34) / 40.34 = 40.3% return

Total Return for Warrant = (49.99-22.57-18.33) / 22.57 = 40.3% return

 

Annualizing that number = 6.25% cost of leverage. (from 0.63% with no dividend)

 

Would appreciate any faults with the above, if there are any.

[hyten1]

racemize, sorry a quick question why "I determine the common price at which the total return of the common matches the total return of the warrant"?

 

sorry for my dense brain. if i use dividend of $0 for all 22 quarters using your formula i get a price of $41.61. so this is telling me if no dividend the warrant and common will have the same return if stock is at approx $41 (which is close to where that stock is trading at right now). what does it mean if the actual stock is lower or higher than $41.61?

 

 

hy

 

txlaw, that calculation looks like it will be at least close to the right cost of leverage.  However, my answer comes in slightly lower (some of this has to do with your 1% rounding from 0.65% I think).

 

Although I derived the formula earlier, here are the basics for what I am doing:

 

I determine the common price at which the total return of the common matches the total return of the warrant, which I believe should be the equation that gives the same cost of leverage that Eric is calculating.  However, it is possible that it is answering a slightly different question than Eric's, but returns very similar results.

 

In any event, the initial equation is:

 

Total Returns of Common = Total Returns of Warrant @ some future stock price, OR:

(Future Stock Price - Current Stock Price + cumulative dividends) / (Current Stock Price) = (Future Stock Price - Strike Price - Current Warrant Price) / Current Warrant Price

 

Solving for Future Stock Price gives you:

Future Stock Price = (Current Warrant Price * Cumulative Dividends + Current Stock Price * Warrant Strike Price) / (Current Stock Price - Current Warrant Price)

 

So, this is the number that tells you the stock price that makes the total return of the common = the total return of the warrant, from today's prices, based on the entered cumulative dividends.

 

If I plug in your value of $1.20 per year, I get:

Cumulative Dividends = 6.6 (22 quarters left @ 0.3 per quarter)

 

Now, using Current Stock Price = $40.34

Current Warrant price = $22.57

Warrant Strike = 18.33

Future Stock Price = $49.99

 

Checking my work:

Total Return for Stock = (49.99 + 6.6 - 40.34) / 40.34 = 40.3% return

Total Return for Warrant = (49.99-22.57-18.33) / 22.57 = 40.3% return

 

Annualizing that number = 6.25% cost of leverage. (from 0.63% with no dividend)

 

Would appreciate any faults with the above, if there are any.

[racemize]

Hi Hyten, if it trades below the price that comes out of the formula at expiry, then the common was better, and if it is above, then the warrant was better.

[txlaw]

txlaw, that calculation looks like it will be at least close to the right cost of leverage.  However, my answer comes in slightly lower (some of this has to do with your 1% rounding from 0.65% I think).

 

Although I derived the formula earlier, here are the basics for what I am doing:

 

I determine the common price at which the total return of the common matches the total return of the warrant, which I believe should be the equation that gives the same cost of leverage that Eric is calculating.  However, it is possible that it is answering a slightly different question than Eric's, but returns very similar results.

 

In any event, the initial equation is:

 

Total Returns of Common = Total Returns of Warrant @ some future stock price, OR:

(Future Stock Price - Current Stock Price + cumulative dividends) / (Current Stock Price) = (Future Stock Price - Strike Price - Current Warrant Price) / Current Warrant Price

 

Solving for Future Stock Price gives you:

Future Stock Price = (Current Warrant Price * Cumulative Dividends + Current Stock Price * Warrant Strike Price) / (Current Stock Price - Current Warrant Price)

 

So, this is the number that tells you the stock price that makes the total return of the common = the total return of the warrant, from today's prices, based on the entered cumulative dividends.

 

If I plug in your value of $1.20 per year, I get:

Cumulative Dividends = 6.6 (22 quarters left @ 0.3 per quarter)

 

Now, using Current Stock Price = $40.34

Current Warrant price = $22.57

Warrant Strike = 18.33

Future Stock Price = $49.99

 

Checking my work:

Total Return for Stock = (49.99 + 6.6 - 40.34) / 40.34 = 40.3% return

Total Return for Warrant = (49.99-22.57-18.33) / 22.57 = 40.3% return

 

Annualizing that number = 6.25% cost of leverage. (from 0.63% with no dividend)

 

Would appreciate any faults with the above, if there are any.

 

Honestly, it's very hard for me to follow this line of thinking.

 

But perhaps the cost of leverage is different because of compound interest?

[hyten1]

yes that is right, it seem like you are trying to answer a different question? i put your equation into a spreadsheet, using different dividend amounts along with current prices (stock, warrant, strike etc.) i can determine at what point (how much dividend would it take) to make the common a better investment vs the warrant.

 

as for the cost of leverage question. it doesnt seem obvious (at least to me) how you extract the cost of leverage number out from these equations/exercise.

 

some findings:

- $0 dividend warrant is better

- $1-$2 dividend  warrant is better if common is approx $45 or higher

- etc.

 

so i guess everyone can take an educated guess as to how much dividend will be paid out from now  until 2019 and determine what you think the stock will trade at which will then allow you to determine if common or warrant is a better way to go.

 

hy

 

Hi Hyten, if it trades below the price that comes out of the formula at expiry, then the common was better, and if it is above, then the warrant was better.

[ERICOPOLY]

The background on how I came up with that equation...

 

1)  I don't know how to use Excel, so I wasn't going to go there

2)  I didn't want to have to plot two lines on a graph and find the point of intersection

 

So I just reasoned that the option premium is a cost that would have to be overcome in order to do just as well as the common.

 

So you subtract the option premium from the strike price to get a number.  Then you just have to ask at what rate that number needs to compound to get back to the strike price.  That rate will be the precise, exact breakeven point versus the regular common stock.

 

Were it to come up short, you would have not met the option premium hurdle -- so it would certainly have underperformed the common.  Were it to come up in excess of the options premium, then you would for certain have outperformed the common stock as you've exceeded the amount paid for the premium.

 

Make sense?

 

I'm not sure if it's in any text books or if it's used elsewhere -- probably, but I just came to this on my own out of avoidance of Excel.

 

So the option premium results in a "hole" in the value versus the common if the stock never appreciates before expiry -- the only way to break even versus the common is to precisely fill in that hole.