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Option theoretic implications of taking Tesla private

Discussion in 'TSLA Investor Discussions' started by jhm, Aug 11, 2018.

  1. jhm

    jhm Well-Known Member

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    I'd like to carve out a space for a more theoretical discussion of how options theory can help us understand the implications of taking Tesla private. The offer to exchange a common share for the shareholder's choice of a private share or $420 cash is itself an option. Once shareholders approve the transaction a common share actually becomes a defacto option with the private share as the underlying. This metamorphosis from stock to option is subtle and complex. Many of our expectations about how a stock should behave fly out the window because it starts to behave more like an option. Likewise commonly traded options on Tesla will morph from being an option on a stock to an option on an option on a private company. So conventional behavior around trades option can break down over the course of this transaction. Trading strategies will adapt. So with all this in play, I think it will benefit us all to gain an option theoretic understanding into what this transaction implies.

    Put-Call Parity
    Under normal conditions, put-call parity holds when for stock at price X, strike K, and put and call option with the same expiration

    X = K + Call(X, K) - Put(X, K)

    So usually prices of options and the underlying will tend to trade near parity subject to illiquidity or bid/ask spreads. So basically there is a small transaction cost to trade.

    Put-call parity also implies that the implied volatility of a call is identical to the that of the paired put option. We think of implied volatility as a measure of demand for an option as it relates to the premium an option buyer is willing to pay. It there is stronger demand for a put option than for its paired call option, the implied volatility of the put goes higher than that for the call. This imbalance means the price of the put option becomes higher than parity. It is usually short lived through traders who seek arbitrage opportunities. But in extreme markets it can become pronounced and sustain. This happens when shares become extraordinarily hard to borrow for shorting. Basically shorts are willing to pay a premium to keep adding to their short position when the supply of shares to borrow is exhausted. This imbalance also motivates sophisticated longs to write put options as a way to harvest the premium bears are willing to pay them.

    Taking Tesla private has the potential to violate put-call parity. Specifically shorts have expanded the supply of long position from 170M shares to 205M. 35M shares shorted will be forced out of circulation by the time all shares have converted. Redeemable shares will be scarce, and shorts will need them to close their positions. In the event of a short squeeze, shorts may pay a premium for call options so as to limit their losses. Other traders may pay a premium for call options so as to speculate on the short squeeze. Meanwhile, put options will lose value. The cash out offer of $420 put a floor on the value of a share at conversion and this floor will decrease the implied volatility of put options. So the question is whether implied volatility for call options will collapse with puts or remain high through a speculation and hedging in a short squeeze. I believe there is a substantial risk of imbalance. I expect calls to trade above parity as we approach the take-private transaction.

    Synthetic Longs
    Put-call parity suggests a way to synthesize having a long position from a portfolio of cash and options. Specifically, the synthetic long portfolio consists of:

    Long 1 call strike K expiring T
    Short 1 put strike K expiring T
    Cash $K × exp(-r(T-t))

    The cash earns the risk free rate r. At time T, this portfolio has the equivalent value as a share of stock, $X(T). Therefore, under conditions of put-call parity the value of the stock and the synthetic long portfolio are equivalent.

    Let's consider how an institutional investor might use this. Suppose also that this investor is unable to hold private shares. The investor believes that Tesla will be taken private in or before Merch. It must then find some reasonable way to exit a large holding of Tesla shares, say 1M. One option is to convert shares into synthetic long positions. Consider this trade.

    Sell 1M shares Tesla at $355/sh for $355M
    Buy 10k Merch call contracts strike $420 for $23M
    Sell 10k Merch put contracts strike $420 for $85M

    The cash out proceeds are $417M which can earn $3M or more interest by Merch. So cash is worth $420M in Merch. Thus, the investor has realized the cash out value well in advance of the completion of the take-private transaction.

    Now the investor is also short puts and long calls. If the transaction fails and the price of Tesla is below $420 in Merch, then the investor can use the cash to buy shares back at strike. Likewise if the transaction fails but Tesla is above $420, it uses the call option plus $420M cash to repurchase all the shares. So in the event of a failed take-private attempt, the investor continues to own 1M shares of Tesla as if nothing had happened.


    If the take-private transaction happens as planned, then the puts expire worthless. Now the investor is sitting on $420M cash plus 10k call contract. This is clearly better than waiting to cash out shares in Merch. At the outset of this trade the call options are worth $23M. This is essentially the value that the take-private offer is transferring to a cash out shareholder. The cash option is actually worth $443 = $420 + $23. The investor can decide how to trade this call option. In the event that demand for private shares is high or there is a short squeeze, the value of the call option can appreciate.

    Let's consider the case where demand for private shares is high enough that the price of private shares is above $420. In this case, the price of Tesla shares will converge to the price of private shares. The Merch call option is actually an option on the private shares, since at expiration above strike common share and private share are swapped. Suppose the price of the private share is around $450 plus random noise. That random noise is key. It is based on the implied volatility of an option on private shares. The bigger the IV, the more valuable the call option. Even if the expected price is just $30 over the strike, the option could see valuations twice this high or more. Thus, it is attractive to hold onto this call option long enough to be sure that the market has priced it well. Certainly the market cannot price it well until there is a prospectus for private Tesla and the shareholders have approved the transaction.

    Shareholder Dynamics
    I believe institutional and other sophisticated investors (especially those not planning to continue with private Tesla) will see value in converting shares into synthetic long portfolios. It gives them exposure to upside value beyond the $420 cash out value. But this strategy also impacts how actual shares circulate.

    First, when a synthetic long is created, effectively a synthetic short is also created for the counterparties in options trade. This supply of synthetic short positions can become an attractive alternative to borrowing shares to short. So as longs go synthetic, it becomes cheaper for shorts to go synthetic as well. Specifically a cheap DTM put should be quite attractive to shorts. The irony here is that shorts may be encouraged to stay in the game because puts become so cheap. Meanwhile, brokers may want to rein in borrowed shares as this trade exposes them to complex credit exposure through a take-private transaction. Brokers may elect to restrict the supply of shares available to be shorted. This would only push shorts harder into puts and synthetic short positions.

    Both longs cashing out and shorts have motivation to gravitate to synthetic positions. This can derisk the potential for a short squeeze. We could see short interest (borrowed shares) decline even while shorts maintain a very large short position via synthetic shorts. If this is orderly it could appear that shorts are closing though the share price remains relatively stable. It's just a migration from borrowed shares to synthetic short positions with no real impact on price. It only appears that shorts are covering when they are not. This does not mean there won't be fireworks, but simply that things can appear to be mild on the surface while massive wealth transfer happens in the options market. Once shorts have peacefully migrated into puts, the value of those puts will implode.

    Funding the Cash Out Offer
    Finally, I would point out that Musk and friends who put up the cash out money have an opportunity to raise that cash through writing out options to expire in Merch. Investment bankers can customize this for them. But the essence of what they are doing is granting a massive put option to Tesla shareholders in exchange for the privilege of taking Tesla private.

    Increasing the strike on this massive out option decreases the value of the call option on private shares that shareholders receive in the transaction. Specifically, where Y is the price of a private share and X the price of a common share, the offer is

    K + Call(Y, K, t, T)

    in exchange for a common share. We do not really know how to price this because private shares are not in circulation to be traded just yet. What we can observe, however, is

    K + Call(X, K, t, T)

    That is we can think of common shares as a proxy for private shares. After all, they are both instruments of equity in Tesla, though they are not identical instruments. Private equity should be less volatile than common equity, which would have implications for implied volatility. Nevertheless, at the time of exchange T,

    X(T) = max(K*, Y(T))

    where K* is the cash out level, now $420. So these converge

    Call(X, K*, t, T) -> Call(Y, K*, T, T)

    as t -> T. This is why it is important not to sell the call option too soon.

    At any rate the value of the offer, K + Call(Y, K, t, T), is not as sensitive to the cash out strike K. Increasing K by one dollar decreases value of the call by a fraction of a dollar. If one believes that the value of private Tesla is substantially greater than what one has with public Tesla, then you want to capture that value in the call option. We can all watch Call(X, K*, t, T) trade in the meantime. All shareholders will want that to go very high.

    In negotiating around the cash out level, whether it should be higher than $420, we need to appreciate fact that the cost of the put option to raise the funds is a cost that will be borne by all private shareholders. If that cost is too high, the transaction will become uneconomical to do and could cancel the whole deal. So there is an unbound to how much the non-private shareholders can get in concessions from private shareholders. But short of this the more value is extracted the less valuable private shares become. That is, increasing K decreases Y. So the total value of the transaction, K + Call(X, K, t, T), is optimized at some value of K where both non-private and private shareholders can share optimally in this transaction. Some value midway between current share prices (around $355) and the value of a private share ($525, my totally subjective impression) is likely where the deal creates the most value for all current shareholders. So $420 is in the ballpark, maybe $440 or $460 is in the cards, but going to far could undermine any value in the transaction for all shareholders.

    Conclusion
    I hope this illustrates some of ways option theoretic analysis can provide clarity into the value, dynamics and opportunities in the take-private transaction. I do believe this transaction is in the benefit of all shareholders. Tesla will definitely not want to burn bridges. I believe there may be future opportunities to invest in Tesla that could be attractive non-private investors. For example, bonds or even preferred stock may be offered. At this point, however, it is import to think through the strategic options one has to personally benefit from the deal. Going synthetic may be worth considering if you need to cash out.

    All the best.
     
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  2. jhm

    jhm Well-Known Member

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    Need to correct this.

    X = K×exp(r(T-t))+ Call(X, K) - Put(X, K)

    Or to fully spell out the time dependence,

    X(t) = K×exp(r(T-t))+ Call(X(t), K, t, T) - Put(X(t), K, t, T)

    for t <= T.
     
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  3. ggr

    ggr Roadster R80 537, SigS P85 29, M3P 80k

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    Not trying to pick out a typo here, but in your entire article you refer to "Merch". Is this meant to be a hypothetical future date? Or something else that you actually mean? If it's a typo for "March" I can fix it for you.
     
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  4. TrendTrader007

    TrendTrader007 Active Member

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    Wow! Amazing analysis
    I converted all my common stock as well as OTM calls into DITM calls last week expiration J19 . I am a bit nervous about losing time premium and liquidity as the privatization deal nears. Any thoughts on that would be highly appreciated
    For what it’s worth my TA chart read suggests SP far exceeding $420 to $520 to 530s within the next 4 to 5 weeks followed my a sharp sell off in Tsla shares
     
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  5. jhm

    jhm Well-Known Member

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    Ha, you caught it. Musk said the short shorts are coming in Merch. So that must be the month this all goes down. So yes it is the hypothetical month this stuff happens. But I did get quotes for March options.
     
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  6. jhm

    jhm Well-Known Member

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    #6 jhm, Aug 11, 2018
    Last edited: Aug 11, 2018
    Sure, I happen to hold a 2020 LEAP with 360 strike. Assuming the transaction goes through at $420, the value at maturity is a minimum of $60, but I also get exposure above that. The first $60 is not really doing anything for me though. Holding $60 cash plus a LEAP with strike 420 would have the same after puts with strike below 420 lose all their value. That is, the market does not know that 420 is a definite floor now. So I can't just yet get all the value out without selling puts like the synthetic long.

    Let's break this down. My 360 call is equivalent to a bull call spread from 360 to 420 and a 420 call. Once the market is convinced that the the take-private deal is sure to go through, the call spread (long 360 call, short 420 call) should approach its maximum payout of $60. (If it doesn't, then you have an interesting arbitrage opportunity.) But the 420 call gains value so long as IV does not plummet. The key here is that the market needs to figure out that the private share is more valuable than a common share. So it is not clear when this will happen or even if the market is smart enough to figure it out. We do still have shorts actively sowing disinformation and general confusion. But if the market figures this out (or expects a short squeeze) the 420 call could see some big gains.

    When Elon first tweeted about considering going private, the initial reaction was that calls above 420 strike would lose value. That was knee jerk to the idea of a cash only deal. The cash or private share option is much more subtle. Far too many investors just don't seem to get it. So it is a curious bet whether the market will really figure it out in time. Buying a 420 call may be a really cool contrarian play, betting that the market will figure it out in time.

    So what is interesting here is that the strategy needs to be sensitive to when the market learns things and how it figures out the implications of the transaction. Of course, if the market does not figure out the value of private Tesla, the best strategy may simply be to convert to private shares. What's needed for that is is just a common share.

    I'll convert most of my shares, but for my own 360 call, I think I'll just hold onto it and see how it goes.

    Edit. Looking back at your question, I see I missed the time decay and liquidity question. Yeah liquidity could be a big problem with all the complexity of the transaction. I would also worry about time decay once the transaction is approved by shareholders, when the put options under 420 should lose value quickly. The problem is that IV for call option on private shares could be low, even though there is a step up from common shares to private. My view is that private shares will be lower volatility and therefore higher value than the common shares. So as the call option transitions from being based primarily on common shares to conceptually on private shares, there could be a step up on the price of the call, but after that time decay could be heavy. And there is also the risk that the market just does not value the private shares highly which could also lead to value decline. So I think one wants to be quick to harvest a gain.
     
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  7. jhm

    jhm Well-Known Member

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    I should warn people that I am a lousy options trader. I work in quantitative finance, but not trading. I am more of a theoretician, modeler and analyst. So my interest here is more about using option theory to illuminate dynamics than to get into tactical issues around trading options. Other folks are much more skilled than me in that.
     
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  8. winfield100

    winfield100 Active Member

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    Thank you, as a holder of stock and not authorized to do options, I read your college level presentation about 6x and am vaguely starting to understand. Planning to stay if allowed with a 20-40 year time horizon.
    the salient part is, for me
    " Specifically shorts have expanded the supply of long position from 170M shares to 205M. 35M shares shorted will be forced out of circulation by the time all shares have converted. Redeemable shares will be scarce, and shorts will need them to close their positions."

    about 21% of shares will vanish (35M divided by 170M)

    It would seem to be against my best interests, as desiring to go private, to create synthetic long positions while creating a synthetic short position in the process for a short to "hide in"
    {as an aside, i'm getting an extreme amount of semi-polite vitriol when i point out the 35,000,000 vanishing shares}
    again thank you for your intro level college course in comment number 1, which i am re-reading a lot
    [i will go back to lurk mode]
     
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  9. bdy0627

    bdy0627 Active Member

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    The premium of the J20 calls over earlier dated ones is very likely lost money. For instance, the current premium on a J20 $360 call is $63.0. Intrinsic value of the call is $60. So, assuming the stock trades near $420, anyone buying those calls now and holding them almost to the delisting date would lose 5%. The J19 at the same strike has a premium of $40.7. Those would yield a gain of 47% if the stock is near $420 near the expiration date. I personally think the time safety of J20s is not worth paying for given the situation. J19s still seem worth the time since this may take 4+ months. March 2019 calls may be worth the extra time safety. Maybe June calls too, but that would be as far out as I would consider paying for. The alternative of selling J20s to others makes more sense to me than buying them.
     
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  10. bhzmark

    bhzmark Supporting Member

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    Great job. Still digesting. I couldn't help think how the convertible debt plays into this.

    Apparently a common investment is to buy the convertible debt and also sell calls matching the conversion option in the debt to monetize it into a decent overall lower risk yield. So many of the debt holders will have already sold calls for likely ~360 march 2019. Or similarly sell short at over 360 with plans to cover with the conversion, or buy on mkt if lower. That should account for almost 1B of short activity as a byproduct of the convertible notes.

    It seems that buying those notes with their converts is one way the buying group might participate in the transaction?
     
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  11. Johan

    Johan Funds for M3 secured. Contingent on wife aproval.

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    @jhm thanks for taking the time to write this up. Hopefully it will be possible to go back after the deal has completed and check whether reality corresponded a lot of only partly with theory.
     
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  12. jhm

    jhm Well-Known Member

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    Yes, good to think through this. The common stock as it approaches this transaction becomes quite similar to a convertible bond. In both you have a expiration date with a big cash payment or option to have shares instead.

    Some longer dated convertible bonds could be a way to gain exposure to private shares without actually holding private shares. Specifically I am thinking that these bonds have some provision to adjust the conversion option to private shares. So the bondholder can expect cash payment or a certain number of private shares at maturity.

    The idea of shorting against the box, say writing call options hedged by the convertible bonds intrinsic call option so as to make income could also be a strategy for current shareholders planning to cash out. Holding the common shares you can write a covered call. If this call has strike at the cash out value (nominally $420 but it could negotiate up), then the proceeds of the sell of the call is one way to cash out the implied call option embedded in holding common shares as they approach the transaction. In the event of a short squeeze, this could be enormously attractive, selling a call with the share price is wicked high. But of course that value could be obtained simply by selling the shares too. But if you want to cash out while anticipation of a squeeze drives up the price of options ahead of share movement, selling the call could give could lock in that gain.
     
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  13. jhm

    jhm Well-Known Member

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    Yep, I bought it quite awhile back. It is not really an optimal expiration date for playing the take-private transaction. So Merch is it, but I don't know which month Merch is.
     
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  14. winfield100

    winfield100 Active Member

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    #14 winfield100, Aug 13, 2018
    Last edited: Aug 13, 2018
    where is the "like" button for "totally confused, but willing to learn after reading 7 times" :confused:
    I _think_ you use the proceeds of selling the covered call to by the convertable bond IF I understand you.
    So where do I get one of those bonds (too late most likely, but..)
    :)I expect both Google and college level texts are my friends:)
    I shall spend a bit researching to stretch my mind
     
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  15. jhm

    jhm Well-Known Member

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    Once the transaction is sure, the value of Tesla share is future cash plus a call option (on a private share). You could see your shares and get straight cash and you may miss out on the full value of the call. But if you want to capture the value of that call while continuing to hold shares, you can sell call options. This gives you some cash upfront and later you can do what you want with the share. Also what you do with cash is a separate matter. You could certainly buy bonds if you like, but this is not really the point.

    The point I was making about convertible bonds is that they are future cash plus call option on stock. Some callable bondholders try to capture (monetize) the value of embedded call option by selling calls on the stock. This gives them cash upfront and the rest of the bond is just future cash. This sort of investor just want to hold a straight bond and generate cash along the way. So selling call options adds to the cash that is generated along the way.

    For a non-private investor, the advantage of holding a convertible bond that matures well after the take-private transaction is that it gives you exposure to the private stock without actually owning private stock. Think of it this way if you want to own private stock but cannot actually hold private stock, your next best alternative could be to own convertible bonds. Again the convertible bond is future cash (straight bond) plus a call option on the (private) stock. So in this case, what is most attractive about the convertible bond is the embedded call option not so much the bond side. Suppose you really wanted just the call option but not the cash from the bond. You could borrow money to buy the convertible bond. The money you borrow basically nets out the straight bond portion of the convertible bond. What is left is mostly just a call option.
     
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  16. lmaccaro

    lmaccaro Member

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    Agree with your last line. I'm not sure if this is shorts not understanding the 'first principles of market physics" (scary, for them) or intentional FUD.
     
  17. jhm

    jhm Well-Known Member

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    #17 jhm, Aug 14, 2018
    Last edited by a moderator: Aug 14, 2018
    Let me just post here that a Mar Put 420 is currently priced at $87.54.

    https://www.nasdaq.com/symbol/tsla/option-chain/190315P00420000-tsla-put

    We can watch this over time. If the deal is to go thru on or before this March expiration date at cash out $420 or above, then the price of this contract should decline, perhaps losing 99% of its current value.

    So I'm noting the price now, so that we can track its descent.
     
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  18. jhm

    jhm Well-Known Member

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    Another way to think about the price of this put is that it is the incremental value of the take-private transaction to the current price of a share, $351. This has total value of about $439. On 171 shares outstanding, Musk and partners would be offering $14.9B to current shareholders to put this deal through by March.
     
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  19. jhm

    jhm Well-Known Member

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    https://www.nasdaq.com/symbol/tsla/option-chain/200117P00420000-tsla-put
    It's not bad to look further out to Jan 20 puts strike 420. Bid/Ask $103.50 / $106.85, while the stock is at $347.64.

    This contract will also go to $0 if the take-private deal goes through before the expiration date. You can see that it is advantageous to Musk to get this done asap. The longer the deal takes the further we go out the option chain and the more expensive these puts get. So valuing the transfer of value from Musk and partners to shareholders via the nearest dated put option shows that this is a cheaper if done more quickly.

    Another thing about this whole analysis is that anyone can trade in these put contracts that will lose value under a take-private transactions. We might call these the shadowed puts. Under the transaction, all shadowed puts go to zero. If one want to speculate about the deal, you can sell or buy these shadowed puts. You would sell if you though the deal would go through earlier or at a cash out value at or above the strike. You would buy these puts if you thought such a deal would not happen and would leave the stock diminished in value.


    Advice to shorts: If the Saudis offer to sell you cheap puts, buy. ;)
     
  20. jhm

    jhm Well-Known Member

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    Current stock $336.3/share.
    The Mar 19 420 put bid / ask spread is now $95 / $97.5.
    The Jan 20 420 put bid / ask spread is now $110.5 / $115. This is up from Tuesday as the stock price has tumbled.

    Check out the Mar 19 340 call with bid / ask spread $44.35 / $45.60. If one was sure of the take-private deal and wanted to cash out, you could sell shares at $336 and buy a call at $45. If the call goes to 80 (= 420 - 340), this is 78% gain. Thus, you $336 share could leverage up to $597 (= 336*80/45). That would be one way to cash out in style.
     
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