ERICOPOLY

I am saying that if you run the equation today on the WFC warrant, it will spit out the correct answer because it doesn't matter if you give your dividends to the Pope, or if you reinvest them into the stock. All the share conversion adjustment does is give credit to the fact that you've reinvested it into the stock rather than having given it to the Pope. So ignore it.

You just agreed (above) that it doesn't matter to the banker what you invest the money in that you borrowed. You only owe him interest on the money borrowed.

It would be the same as with the GM formula. You just treat 34 cents as the missed dividend cost expressed as a percentage of the strike price. You'll get a more accurate leverage cost estimate as compared to GM. After all, GM won't keep a dividend at 1.20 for each year -- they would raise it a bit each year. But WFC's lost dividend cost is capped at 34 cents -- so it doesn't have the complexity of the GM case. So here is what we used for the GM formula (an approximate result it spits out): 17.65*1.x^5.5=18.33*1.065^5.5 You would just rework it with WFC's numbers. using the maximum lost WFC dividend yield on the right hand side of the equation. So if the WFC strike price were $38 (I'm not sure if it is, but just for an example) then the missed dividend yield would be 3.57%. Thus, you would have for the right side of the WFC equation: =38*1.0357^5.5 Assuming 5.5 years left on the WFC warrant and 38 for the strike (I think both numbers are different, but I'm too lazy to look them up)

Another simple way to think about it is that the lender is letting you borrow $13.30 per class A BAC share. His conditions are that the interest rate is fixed and that you prepay him all of the interest. So your cost of interest on that $13.30 is a static cost. It's simply the interest you owe for borrowing $13.30. Now, compare that to borrowing $13.30 from your local banker. Does he charge you a higher interest rate if you invest it in BAC shares and then reinvest your BAC dividends into more shares? Of course he doesn't -- he charges you interest rate on that $13.30 no matter how you invest it. You could give it to the Pope and it still is going to be the same amount of money you owe in interest.

You can think of BAC common stock as being logically identical to a warrant with 0 strike and full dividend protection (adjustment). My formula computes the cost of leverage of BAC common to be zero. This is the correct results. It's correct because there is no option premium to the common, and there is no loss from dividends. It does not matter at all how many shares this common (with full dividend protection) converts to in the end.

The reason why it works for the BAC warrants is because you have two independent costs. The option premium has nothing to do with the costs from lost dividends. And with BAC, the only lost dividend is 1 cent per quarter. So the formula works almost perfectly at approximating BAC "A" warrant cost of leverage, except that it will be off slightly for not taking into account the prices at which the lost 1 cent dividend quarterly dividend would be invested in to the common. I'm compounding that lost dividend cost (against the strike price) which is slightly wrong because it depends on how many new common shares could be purchased with that lost 1 one cent dividend. But... it will be damn close. That 1 cent dividend can't purchase many shares so there is little to be skewed. Now, if the BAC class "A" warrant had a 0 cent adjustment hurdle (rather than 1 cent), then I believe the calculation would be perfect. After all, you start out with the option premium being your only cost -- and that's the only cost truly because there is no lost dividend.

You are making my head hurt forcing fractions into my thinking. So I'd rather just "unfraction" and reverse the Citi split and then solve. Sort of like if you asked me to compute the rate at which 0.1 grows to 0.2, and if I didn't want to deal with fractions, I would just multiple both by 10 and then solve. I'd get the same result either way. In math you can multiply both sides of the equation by 10 and you aren't screwing things up -- you just make things easier to think about and work with.

Actually, I got a slightly different result (compared to txlaw) from my modified formula. They were very close, but a little bit different. I wonder if it's due to this effect: 1) The common stock owner would be reinvesting the dividend into extra shares. Therefore the dividend needs to be multiplied by the FULL amount of shares. The total share count grows each year when the dividends are reinvested. 2) My computation that compounds the warrant strike by 6.5% takes this into account (I think). It grows the dividend effectively as if it were reinvested into additional shares, each paying 6.5% worth of missed dividend cost. Each year, the dividend cost is 6.5% bigger than the prior year because there are more shares. Do you agree that makes sense? If you ignore the effect of the missed dividend growing each year (due to the increasing share count of reinvested dividends), then the computation comes out wrong. So I think if you want best accuracy you can't simply add 6.5% to .69%. It's relatively close though, but for the sake of exactness it misses by a bit. so this is still my best stab at it: 17.65*1.x^5.5=18.33*1.065^5.5 EDIT: Well, it's better than nothing because it does at least recognize that the share count is rising after each dividend. However, it might not be adjusting the share count properly because it would depend on how many shares are purchased with the dividend. A higher stock price would result in fewer added shares, and a lower stock price would result in greater added shares. This is why the BAC "A" warrant dividend protection formula takes into account stock price when it adjusts the warrants for paid dividends. So, now how do you adjust the formula when you can get more than one share per warrant? weeeeee..... You don't need to. The gap in value is on the initial share, not on the additional shares from dividend reinvestment formula. In other words, there is no option premium assigned to those additional shares as they are bought with the dividend. So you only need to compute the rate of compounding to close the gap on the initial share purchased. EDIT: the "gap" I'm referring to is the option premium. You subtract it off the strike price, then get a number. At what rate does that number compound to get back to strike? That's the cost of leverage from the option premium alone. That rate doesn't change even after the warrant has undergone the dividend reinvestment simulation that results in higher number of shares at conversion.

That decision by GM is interesting. Imported cars are very expensive in Australia due to the import duties. What if there are no longer any domestically produced cars?

Regarding their cost of labor... I remember in the late 1990s (around 1999) my Australian engineer cousins were envious about our pay rates here in the US. Did that change?

Looks like they want to stimulate the economy by lowering the Australian dollar instead of cutting rates: http://finance.yahoo.com/news/aud-usd-dives-below-0-135000747.html The Australian Dollar took an unexpected spill this morning after Reserve Bank of Australia Governor Glenn Stevens surprised markets with overly dovish commentary. Noting that the economy won't likely be influenced by further rate cuts, Governor Stevens suggested that the economy would fare better if the AUDUSD traded closer to $0.8500. I would tend to believe that foreign property investors would hate this kind of thinking.

Actually, I got a slightly different result (compared to txlaw) from my modified formula. They were very close, but a little bit different. I wonder if it's due to this effect: 1) The common stock owner would be reinvesting the dividend into extra shares. Therefore the dividend needs to be multiplied by the FULL amount of shares. The total share count grows each year when the dividends are reinvested. 2) My computation that compounds the warrant strike by 6.5% takes this into account (I think). It grows the dividend effectively as if it were reinvested into additional shares, each paying 6.5% worth of missed dividend cost. Each year, the dividend cost is 6.5% bigger than the prior year because there are more shares. Do you agree that makes sense? If you ignore the effect of the missed dividend growing each year (due to the increasing share count of reinvested dividends), then the computation comes out wrong. So I think if you want best accuracy you can't simply add 6.5% to .69%. It's relatively close though, but for the sake of exactness it misses by a bit. so this is still my best stab at it: 17.65*1.x^5.5=18.33*1.065^5.5 EDIT: Well, it's better than nothing because it does at least recognize that the share count is rising after each dividend. However, it might not be adjusting the share count properly because it would depend on how many shares are purchased with the dividend. A higher stock price would result in fewer added shares, and a lower stock price would result in greater added shares. This is why the BAC "A" warrant dividend protection formula takes into account stock price when it adjusts the warrants for paid dividends.

I rather prefer just using my first equation that computes the cost of the option premium. Take that result which is .69% Then add 6.5% Get result of 7.19% Much simpler than modifying that equation like I recently did -- which ultimately just makes it needlessly complicated

I believe it solves the problem where the dividends from the common are immediately reinvested into the common stock. I guess so, but you have to know the common price at those points to get an actual number, right? I see it like this. For the common, a $40 stock with $1 dividend. Now it's $1 in cash and $39 in stock. Reinvest the $1 into stock. Now you have $40 in stock. So for the common, just pretend like nothing ever happened (instantaneous reinvestment). $40 in stock is $40 in stock. Therefore, we only need to think about what effect the MISSED dividend has on the warrant. That's what my calculation does, by adjusting the strike price.

I believe it solves the problem where the dividends from the common are immediately reinvested into the common stock.

This seems to match txlaw's result: this time, I'm just taking 18.33 (the strike) and compounding it by the annual missed dividend rate. The reason why I think it makes sense to compound the strike price is because the first year's missed dividend expense get's compounded 4.5 more times, the second year's missed dividend expense get's compounded 3.5 more times, etc... So that effectively works in a way that it solves the time value of money problem. He used 1.20 for the annual dividend and therefore 6.5% for the annual dividend cost (1.20/18.33=.065) He used 68 cents for the option premium 18.33 is the option strike he used 5.5 years 18.33-.68=17.65 17.65*1.x^5.5=18.33*1.065^5.5 solving for x, I get about 7.19% annualized cost. That's 6.5%+.69%=7.19% .69% is the annualized cost of the option premium -- he estimated it to be 1%. It was just an estimate. I compute it to be .69% using my first equation which calculates it precisely (17.65*1.x^5.5=18.33). So we come to the same result. Hooray! EDIT: I reworded the explanation in the first paragraph

Here is another aspect of txlaw's calculation that differs: I'm not sure if he recognized it, but the formula I provided to Packer solves for that. It's a pretty easy formula to use. But that formula only tells you what the pre-paid interest really cost you -- it doesn't account for the cost of the lost dividends.

Anyways, to be nitpicky a missed 25 cent dividend paid out quarterly does not have the same cost as a missed $1 dividend paid out annually. However, I have only so much patience for being too exact.

I am only talking about how he deals with the cost of the lost dividend to the option. He's just saying that it cost a percentage of the strike price. So let's say you borrow $10 (the strike price) and you miss a $1 dividend. That's a 10% cost. Compare that to borrowing $10 from your local banker at a 10% interest rate. After a year, it cost you $1. So he's right about that, I think. The only time you have to worry about reinvestment of the dividend is when you are dealing with the common. So it's a problem for you to overcome when you are fixing up your spreadsheet, but it's not something that txlaw has to deal with because he didn't take a stab at the common.

I thought your way was an iteration back on Eric's--shouldn't you use Eric's new way to calculate it? I don't think so. They way I do it makes the most intuitive sense for calculating leverage to me. I think if Eric's way is right, our cost of leverage should come out the same (plus or minus NPV effects). I think it might have to do with you guys using a compound interest rate. But my brain is fried at this point. You and Eric are approaching it in a very different manner than I am, so I don't think I can comment too intelligently as to the way you are doing it. Perhaps Eric can. The compound interest rate is the right way to deal with the option premium (my first equation that I gave to Packer). However, I think my attempts to modify it today are stuffed up. By implication, since my second iteration today came to the same result as Racemize's spreadsheet, perhaps his spreadsheet too is stuffed up (if it comes to the same result). And I think they are stuffed up for the reason that Racemize and I both suspected -- the summing up of the dividends. We're acting like the missed dividend all comes at the end. As if it were one huge whopping dividend payment missed at the very end of the term. However, that's wrong, because the dividends are missed every step of the way. That meshes with txlaw's sustpicion that the error has to do with compounding rate. We can't use the compounding rate to deal with the missed dividends because we are doing no adjustment for the time value of the missed dividends. For example, $1 is 5% of $20. But if you compound $20 by 5% for two years, you don't get $22. Our methods of computing it therefore arrive at a different cost in the missing dividend scenario.

I have a feeling that it turns into one of the equations where you get the big greek Sigma letter in it.

I do indeed have the suspicion. No idea what to do with it though. But I think your model also has the same mistake. Because you don't do anything with your dividend, you're also effectively just summing it. Instead, you could be reinvesting it in the stock in real time as it gets paid out.

Ok, I'll do the same analysis as the prior post for this formula and see what it spits out: 17.75*1.x = 6.6+18.33 = 24.93 ----> 40.4% gross return This is exactly the same as my formula. I think we have a winner. Edit: Your formula is prettier/easier. sadface. I'm glad it comes to the same result as yours. Either it's right or we are both wrong. My first iteration had at least one significant problem 1) when Y was so big that it overwhelmed the number it was subtracted from -- that generates a negative number

Or it could be this: $17.75*1.x^5 = Y+$18.33 What's your opinion? I did have a large beer at lunch which is making this relatively more difficult. Would appreciate input. EDIT: Do you have a nagging suspicion that the dividends can't just be summed because their value depends on when they are paid out? Time value of money thing.

Okay, I'm done with my thinking on this now (I know, famous last words). Let's say you own a $10 call option and miss a $1 dividend. The value of your call option drops by $1. Now it's worth $9. It has to compound by 11.11% in order to get back to $10 value. So the cost of leverage (from this dividend alone) is actually 11.11%, not 10%. GM stock at todays close: $40.16 GM "B" warrant price: $22.41 GM "B" warrant strike: $18.33 Let Y = sum total of expected future dividends over the option period. Let X = cost of leverage rate $40.16 - $22.41 = $17.75 ($17.75 - Y)*1.x^5 = $18.33 I used time period of 5 years for simplicity, even though it's not exactly 5 years to expiry. Does this formula make sense to you guys? I introduced "Y" to account for the lost dividends.