I’ve modeled and valued many royalty trusts; probably every one out there right now. Some are undervalued, some are overvalued, but the one that never ceases to amaze me as the most overvalued of them all is **BP Prudhoe Bay Royalty Trust (NYSE:BPT). **

I imagine that most people are in BPT for the same reason that most people are in any stock: capital appreciation and dividend yield. And BPT has them both. Since the end of the downturn, back in March of 2009, BPT has experienced capital appreciation of about 125%. Compare this to the S&P, which has had a return of about 60%, and crude oil, which has had a return of about 80%.. That’s pretty impressive for a royalty trust. Those returns don’t even include the distributions that BPT has been pumping out, which have yielded around 8 or 9 percent over the last few quarters. Sounds like the investment of the year, right?

To really understand and predict what the return on any royalty trust will be, there’s nowhere else to go but the trust’s 10-K. The 10-K can be found on the SEC website and it lays out every detail of the financial structure of the company. BPT has a fairly complicated model, as royalty trusts go, so it’s not unbelievable that the majority of people invested in it have not read the 10-K, nor do they have a real understanding of what they’re buying.

**Start at the very beginning…a very good place to start**

The first question we have to ask is: how much oil is BPT entitled to? Well, the 10-K clearly states that BPT has a 16.4246% interest in the **lesser** of a) 90,000 barrels a day, or b) the actual daily production of the underlying properties. So, for the sake of being conservative, let’s assume that the properties max out their 90,000 barrels a day, or even produce more than 90,000 barrels a day. Either way, the **absolute most** that BPT is entitled to is their 16.4246% of 90,000, or **14,782 barrels a day**.

For each barrel of oil produced, BPT has certain costs that get taken out of the sale price of the oil. The costs are as such:

a) The “chargeable cost” x “CPI index ratio”

b) Various taxes

We’ll start with the chargeable cost.

The charge cost is a set cost-per-barrel structure laid out in the corporate documents. In 2010, the chargeable cost per barrel was $14.50. Each year after, it slides up a buck or so, with the charge cost being $26.50 in the year 2020. The trust states that the chargeable cost per barrel increases at an uniform $2.75 per year after 2020.

As if that weren’t enough, this charge cost number is multiplied by what we will call the “CPI index ratio.” I don’t know who thought of this CPI index ratio, but it’s a doozie. Here’s how it goes: you take the current quarter’s CPI index number and divide it by 121.1 (the CPI number for January 1989). Don’t ask me why, but that’s what you have to do. So, let’s calculate the chargeable cost per barrel for the third quarter of 2010.

Chargeable costs for 2010: $14.50/barrel

CPI Index November 2010: 218.711

Remember, the equation is - **charge cost x (CPI number / 121.1)**

So:

14.5 x (218.711 / 121.1) = $26.21

The equation shows up that the chargeable cost per barrel is $26.21. That comes right out of the sale price for each barrel of oil to make the “taxable value” of each barrel of oil. So, the barrel of oil that was selling for $77.91 (average oil price over the quarter) now only brings in pre-tax revenue of $51.70 to the trust.

And we’re only getting started.

**Next: Taxes**

Being located in Alaska, the trust has some very intricate tax laws. I’ll break them down for you here now.

First of all, Alaska gets 25% off the top of the **tax value per barrel **(we will call that the TVPB). Remember, the tax value per barrel is the $51.70 number we came up with earlier. After the 25% off the top, there is a progressivity tax added on. The progressivity tax is based on the taxable value per barrel, and is laid out like this:

**TVPB between $30 and $92.50**: .004 x (tax value per barrel -30)

** TVPB is over $92.5: ** .25 + (.001 x (tax value per barrel – 92.5))

Note that the tax cannot exceed 50% in either scenario. What a relief.

Now that we know the tax structure, we can calculate the taxes on each barrel of oil. We will continue with the third quarter of 2010, when our taxable value per barrel was $51.70. It goes like this:

(51.70 x .25) + (51.70 x (.004 x (51.70 – 30))) = $17.41

Ouch. $17.41 per barrel. Add that to the $26.21 per barrel that was taken off for chargeable costs, and you end up with net income of $34.29 on a barrel of oil that sold for $77.91.

$77.91 - $26.21 - $17.41 = $34.29

From here it is fairly easy to figure out what the distribution will be for the quarter. There were 92 days in the third quarter of 2010 and there are 21.4 million shares outstanding, so the equation looks like this:

(14,782 x 92 x $34.29) / 21,400,000 = $2.09

BPT’s third distribution last year was, in fact, $2.09 per share. Right on.

So I can calculate the distribution. So what? Well, being able to calculate the distribution is the first step in being able to calculate the rate of return over the life of the trust.

**Calculating the future value of the trust**

BPT has a **set amount** of oil in the ground (63 million barrels), and once that oil is gone, the trust dissolves, and a share of BPT stock is worth zero. Zilch. Nada. The value of the trust is declining, and the key to figuring out what your return on investment will be is to figure out exactly when the value of the trust will be zero, and how much money you will get in distributions between now and then.

Once you know how to calculate the distribution for any given quarter, figuring out what the distribution will be for future quarters really only requires three pieces of knowledge: the cost of oil, BPT’s daily production, and the CPI index. There’s no way to know for sure what the future cost of oil will be, so the best that we can do it is use the crude oil futures curve. The curve actually goes out until the year 2019 and anything after that we can extrapolate using the current shape of the curve. Similarly, we have to extrapolate the future CPI number by using past data for the CPI, which is easily found on the Bureau of Labor web site. Finally, we can be sure that BPT won’t be cranking out 90,000 barrels a day forever, so you have to assume some decay in production.

Everyone’s calculations on this will be different, but if you get somewhere around $100/barrel for oil and a 280 CPI ten years from now, you’re on the right track. We also assumed a 4% decline in production, which is an industry standard. Keep in mind that these are **assumptions**, and they have a large impact on the valuation of the trust.

Using the current estimate of proved reserves (about 63 million barrels) and our production estimates that we got from declining the current production rates, we can get an estimate of when the trust’s wells will dry up. Our estimate is somewhere around the year 2025.

Now we are armed with all of the tools that we need to put it all together. Below is a simple table depicting all of the information we’ve put together so far. Note that the annual production number reflects BPT’s 16% share of the daily production.

*click to enlarge*

There it is, and yes, I DO show negative distributions for the last couple of years. How can that be? Well, given the increase in chargeable costs per barrel and the inflation of the CPI index, BPT actually starts to lose money on each barrel of oil around 2025. It’s ok though, because given our assumptions, the trust will be worthless (aka, $0 stock price) somewhere around 2025. Here’s the kicker - between now and then, you will receive a grand total of about $75 in distributions. Remember, people are buying it today for $130.

**Summing it up**

A simple internal rate of return function on excel will say more than I ever could. Given the current price of BPT and the assumptions laid out here, an investor buying BPT today and holding it can expect an internal rate of return of -8.62%. That’s an annual number, meaning that you lose 8% every year for the next 15 years. Ouch.

The obvious response to this claim would be “Yeah, well I’m not planning on holding it until 2025. I’ll just sell it when it starts to go down.” Surprisingly, this is the response of many of the investors that are active on the trust’s Yahoo message board when they are presented with the facts of the trust’s future. You’ll be hard pressed to find a single person that can give you a logical explanation of why BPT currently sells for $130; most of the investors just join the “I’ll just sell when it starts going down” chorus.

And why shouldn’t they? At the end of the day, a stock is worth what people are willing to pay for it. And if people want to pay $200 a share for BPT, then they will. Sooner or later, however, the inevitable will happen, and people will start to realize what this trust is actually worth and they will sell, and with them will be all of the people who said “I’ll just sell when it starts to go down.” When you’re in the middle of the herd of lemmings jumping off a cliff, you probably can’t see the cliff coming, let alone stop once it reaches you. The result will be a pretty sharp selloff of BPT, and holders of the trust will lose a lot of money.

So what’s my motive for writing this? Am I short this stock? No, I’m not. The market can be wrong for longer than I can be solvent. I guess you could say that I am simply trying to arm the everyday investor with a straightforward analysis of what they are getting into. Hopefully, this will get into the hands of someone who was counting on this stock for their retirement portfolio and advise them otherwise. Whatever the end result, there is no better reason to write this, except that it is right.

**So what IS it worth?**

In the same way that you can figure an internal rate of return on the current price, you can figure out what the share price would have to be now in order to get a 10% rate of return.

The magic number comes out to be $45.80 per share. **$45.80**. That’s a third of what BPT is trading for now. Unbelievable.

You want to know what else is unbelievable? Crude oil would have to be trading at $225 from now until 2025 **just to get your money back**. Once again, unbelievable.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.