Exhibit 4.5

bp

Maureen L. Johnson
BPXA Senior Vice President		BP Exploration (Alaska) Inc.
Greater Prudhoe Bay		900 E. Benson Boulevard
		Anchorage, Alaska 99508
		Tel: (907) 564 5671
		Fax: (907) 564 5000
		Email: johnsml@bp.com

VIA OVERNIGHT MAIL &
AS A SCANNED ATTACHMENT TO E-MAIL

October 11, 2006

Ms. Ming J. Ryan, Vice President
The Bank of New York
101 Barclay Street
New York, NY 10286

     Re: BP Prudhoe Bay Royalty Trust

Dear Ms. Ryan:

This is to confirm the consensus principles that have been developed with The Bank of New York (“Bank”), as Trustee of the BP Prudhoe Bay Royalty Trust (“Trust”), for applying the Alaska oil and gas production tax (“New Tax”), as amended by chapter 2, Third Special Session Laws of Alaska 2006 (“Act”), in the context of the Overriding Royalty Conveyance (“Conveyance”) and the overriding royalty interest (“ORRI”) thereunder that is owned by the Trust. These principles would resolve the two major issues presented by the Act: one, how the amount of New Tax chargeable against the ORRI will be determined under the Conveyance; and two, the extent, if any, to which the retroactivity of the New Tax under the Act is to be recognized for purposes of the Conveyance.

We understand the consensus principles to be the following:

1.

Calculation of the amount of New Tax chargeable against the ORRI . The amount of New Tax chargeable against the Trust’s ORRI under the Conveyance will be determined as follows:

a)

The taxable value per barrel equals the WTI Price determined under Section 4.3 of the conveyance, 1 minus the Chargeable Costs under Section 4.4 as adjusted by the Cost Adjustment Factor under Section 4.5.

Ms. Ming J. Ryan, Vice President
The Bank of New York
October 11, 2006
Page 2

	b)		The tax rate for the “progressivity” portion of the New Tax under section 011(g), enacted by § 5 of the Act, in chapter 55 of Title 43 of the Alaska Statutes 2 equals 0.25 percentage points times the amount by which the simple average for each calendar month of the daily taxable values per barrel under “a)” above exceeds $40 per barrel. If that average taxable value per barrel is $40 or less, the “progressivity” rate is zero. The $40 figure is not subject to adjustment over time.
	c)		The amount of New Tax chargeable against the ORRI equals the taxable value per barrel under “a)” above times the Royalty Production as defined in Article One of the Conveyance, times a rate equal to the sum of 22.5% plus the “progressivity” rate determined under “b)” above.

2.

Retroactivity of the New Tax . The tax chargeable against the ORRI under Section 4.6 for Prudhoe Bay oil produced during the period from April 1 to August 19, 2006, inclusive, is the amount of Old Tax as calculated under Section 4.6 for that production. For Prudhoe Bay oil produced on August 20, 2006 and thereafter, the tax chargeable against the ORRI under Section 4.6 is the amount of New Tax determined as prescribed in “1.” above for that production. The “progressivity” rate under the New Tax for August 2006 will be calculated under “1.b)” above using the average of the daily WTI Prices under Section 4.3 of the Conveyance for August 20 — 31, 2006, inclusive. 3

BP Exploration (Alaska) Inc. (“BPXA”), as Grantor of the Trust, agrees to these principles, not only because they represent the best interpretation of the Conveyance in light of the Act, but also because they offer the most reasonable and fair resolution of the issues for all interested parties, including the holders of beneficial Units in the Trust. These principles also preserve the historical nature and perception of those Units by investors on the New York Stock Exchange and in other markets where the Units may be bought and sold.

Assuming the Bank agrees to and approves the consensus principles set out above, we believe it is important, for those who will be implementing the terms of this agreement in the future, that BPXA explain and document within this letter why we (and, we believe, the Bank as well) view this agreement as the optimal outcome.

With respect to the computation of the amount of New Tax chargeable against the ORRI under Section 4.6 of the Conveyance, we believe the agreement reflects the best of the identified alternatives available for each of the significant aspects of this major issue. Significant among those aspects are the following:

Ms. Ming J. Ryan, Vice President
The Bank of New York
October 11, 2006
Page 3

A.

Determination of the taxable value under the New Tax for purposes of the Conveyance

The actual taxable value under the New Tax is calculated by starting with the spot price for Alaska North Slope crude oil (“ANS”) delivered on the U.S. West Coast, and subtracting from that spot price the actual costs of transportation to the West Coast from the “point of production” at the field. ⁴ From this “field value” are then subtracted the capital and operating expenditures incurred in the course of operating, developing and producing the field, and the result is the taxable “production tax value” (“PTV”). ⁵

None of these tax values and tax-deductible costs appears in the Conveyance. Even for the prior version (“Old Tax”) of Alaska’s oil and gas production tax — which was based on the same value of oil at its “point of production” ⁶ — the Conveyance did not calculate the amount of Old Tax chargeable against the ORRI on the basis of the ANS spot prices and actual transportation costs being used to calculate the amount of the real tax. Instead, Section 4.6 called for the use of the WTI Price under Section 4.3 and the use of flat $4.50/barrel (adjusted by the Cost Adjustment Factor under Section 4.5) as proxies for the actual ANS West Coast spot prices and transportation costs under the Old Tax. This allowed the chargeable Old Tax to be a function of WTI Price the same as the ORRI itself (see “C.” below at pp. 6-7).

Since taxable value under the New Tax is simply the taxable value at the “point of production” under the Old Tax minus field expenditures, it is reasonable ⁷ to continue to use the methodology under Section 4.6 to find the value at the “point of production” for the New Tax that was used for the Old Tax. This leaves the question of what to use as the deductible field expenditures in computing the chargeable New Tax under the Conveyance.

Ms. Ming J. Ryan, Vice President
The Bank of New York
October 11, 2006
Page 4

Two alternatives readily present themselves. One is to use the same field expenditures that BPXA will report for Prudhoe Bay under the New Tax. There are several drawbacks to this. For one thing, the field expenditures to be reported each month are estimates based on what the total deductible expenditures will be for the entire calendar year. Before the year ends it is impossible to know what the actual total expenditures will come to. The New Tax calls for a final reconciliation, by March 31 of the following year, of each month’s estimated deductible expenditures to the actual total expenditures for the year. ⁸  This estimation and reconciliation process will mean one or more restatements of the lease expenditures deducted in calculating the New Tax chargeable against the ORRI. Owners of beneficial Units in the Trust will have to be provided explanations of the changes each time such a restatement is made. In addition, in the course of these estimates and subsequent adjustments some Units will change hands, either to the advantage of the seller and disadvantage of the buyer, or vice versa, depending on whether the adjustments increase or decrease the amount of New Tax chargeable against the ORRI. Although Sections 3.2 and 3.3 address over- and under-payments of ORRI, they do so as an issue between the Trust and Grantor in order to keep them whole in light of the time-value of money, rather than addressing the issue of disparities between holders of Units in the Trust at different times relative to the times when adjustments are made for over- or under-payments. ⁹

Moreover, basing the chargeable New Tax on field expenditures actually deducted would introduce a new parameter into the calculation of the ORRI payments to the Trust and distributed to the beneficial Unit owners — the budget decisions of the working-interest owners in the Prudhoe Bay field. Unlike WTI spot prices, which Trust Unit owners can estimate for themselves, the Prudhoe Bay budget is something that the working-interest owners determine annually on the basis of the opportunities and economic conditions prevailing at that time, and even if they could be reliably predicted in advance, those budgets are not public information in any event. Thus, using actual field expenditures would introduce an element into the ORRI-payment equation that Trust Unit holders would generally know almost nothing about. But that new parameter would affect the Unit holders in two ways: changing the taxable

Ms. Ming J. Ryan, Vice President
The Bank of New York
October 11, 2006
Page 5

value upon which the New Tax is based, and changing the rate of “progressivity” if that taxable value is greater than $40/barrel.

The alternative to using the actual field expenditures would be to use a proxy or surrogate for the actual expenditures, most preferably something already in the Conveyance. As it turns out, there is such a potential proxy. For all but the years 1989 — 1991, the figures for annual Chargeable Costs per barrel appearing in the table in Section 4.4 are greater than the $4.50/barrel being used as a proxy for transportation costs in determining the “field value” under Section 4.6. Logically, to the extent the tabulated Chargeable Costs for a year are greater than $4.50/barrel, that excess cannot be for any costs between the “point of production” and the West Coast since the $4.50 allowance already covers those costs. Thus, the only thing remaining that the Chargeable Cost in excess of $4.50 might be for is costs incurred upstream of the “point of production” — that is, costs incurred in the operation of the field.

This idea that part of the annual Chargeable Costs figures set out in Section 4.4 could be for upstream costs is supported by the fact that Section 4.4(a) — (c) provides for reductions to the tabulated Chargeable Cost figures if certain additions to Proved Reserves fail to be made by their respective deadlines. Obviously, to add to Proved Reserves as contemplated in Section 4.4 would (and did) require the new investment of considerable sums of money as well as increased costs for operating those new investments. The “excess” Chargeable Costs figures beyond $4.50 could well be seen as a recognition of and response to those significant new investments and expenses.

For 2006 the Chargeable Costs figure tabulated in Section 4.4 is $12.50, which after adjustment by the Cost Adjustment Factor for the Third Quarter is $19.63/barrel. Our current estimate of the 2006 operating and capital expenditures for Prudhoe Bay Unit operations, of which the initial participating areas are the largest part, and for transportation of Prudhoe Bay oil is $16 — $17 per barrel. Thus, using the adjusted Chargeable Costs for this year would result in less New Tax being charged against the ORRI than using our actual transportation and field-operation costs.

It must be acknowledged that the adjusted Chargeable Costs in the future may not always be greater than the actual field expenditures that BPXA would be deducting in computing its actual New Tax for the Prudhoe Bay field. In fact, we believe there is a significant possibility that in some years the adjusted Chargeable Costs would be less than BPXA’s actual Prudhoe Bay field expenditures, and in that event, the amount of New Tax chargeable against the ORRI under the present agreement would be greater than the actual New Tax being paid, and hence the ORRI payment would be less than it would have been using the actual field costs incurred. Whether this would happen, and if so, when or how often it might happen, would depend on future circumstances at that time ¹⁰ that cannot be predicted now.

Ms. Ming J. Ryan, Vice President
The Bank of New York
October 11, 2006
Page 6

B.

Determining the “progressivity” rate in the New Tax

“Progressivity” is a function of the extent to which the taxable PTV value of oil is greater than $40/barrel. The discussion just concluded above about determining the PTV value for calculating the amount of New Tax to be charged against the ORRI also applies here. The certainty in determining the taxable value that is gained by using adjusted Chargeable Costs as a proxy for actual transportation costs and field expenditures is matched by a similar certainty with respect to the “progressivity” rate. In other words, while the actual costs will be subject to the annual reconciliation by March 31 of the following year, the amount of the Chargeable Costs will be known at the time the ORRI payments are made to the Trust, and there will be nothing further for them to be reconciled to.

The use of a monthly average of WTI Prices to calculate a monthly “progressivity” rate, instead of calculating and applying a daily “progressivity” rate, is how that rate is required to be calculated under AS 43.55.011(g). The use of such a monthly “progressivity” rate, instead of a daily rate, to compute the daily ORRI amount net of chargeable New Tax is not inconsistent with Section 4.1.

“Progressivity” is a function of the extent to which the taxable PTV value of oil is greater than $40/barrel. The discussion contained in paragraph “A.” above about determining the PTV value for calculating the amount of New Tax to be charged against the ORRI also applies here. The certainty in determining the taxable value that is gained by using adjusted Chargeable Costs as a proxy for actual transportation costs and field expenditures is matched by a similar certainty with respect to the “progressivity” rate. In other words, while the actual costs will be subject to the annual reconciliation by March 31 of the following year, the amount of the Chargeable Costs will be known at the time the ORRI payments are made to the Trust, and there will be nothing further for them to be reconciled to.

C.

Preserving the perceived nature of the Trust Units in the market

We believe that since the Trust Units were first publicly offered, they have been perceived by many in the market as a means for them to make an investment reflecting their expectations about oil price trends. This is because the only variables affecting the amount of the ORRI payments to the Trust have been the spot price for WTI and one’s expectations about the rate of inflation in the future as reflected in the Cost Adjustment Factor. All the other factors in the calculation are fixed under the Conveyance, and it has been possible to compute what the ORRI payment as far into the future as one might want, just on the basis of one’s assumptions about WTI prices

infrastructure to market be built; technical and economic success in developing and applying new technology, and using existing technology in new ways, to produce viscous crude oil; and the willingness of other working-interest owners of the Prudhoe Bay field to commit to such investments and expenditures.

Ms. Ming J. Ryan, Vice President
The Bank of New York
October 11, 2006
Page 7

and inflation. ¹¹

This perception of the Trust Units will be maintained under the agreement. As before, the factors affecting the amount of future ORRI payments are future WTI prices, future inflation, and the volume of oil production subject to the ORRI. ¹¹

D.

Certainty

The agreement avoids uncertainties about the amount of ORRI payments under the New Tax. The WTI prices and adjusted Chargeable Costs will be definitively known under this agreement before the ORRI payments are made to the Trust. Apart from error, there will be no occasion or necessity to recompute any of the variable parameters affecting the calculation of the ORRI payments. This will be very different from the actual administration of the New Tax itself.

In addition to the foregoing considerations about how the New Tax is to be applied for purposes of the Conveyance, the other major issue regarding the enactment of the New Tax is its retroactivity under the Act, which makes the New Tax applicable to oil and gas production beginning April 1, 2006. In this regard we acknowledge, as representatives of the Bank have pointed out, that Section 4.1 provides in pertinent part:

The Royalty Interest entitles Grantee to receive ... for each calendar quarter ... the sum of the product for each day in such quarter of (1) the Royalty Production and (2) the Per Barrel Royalty .... [Emphasis added]

We agree that this calls for a daily calculation of a “product” that is, in effect, a calculation under the Conveyance of the contractual amount of the ORRI payment obligation arising for each respective day during a given calendar quarter.

With respect to the retroactivity of the New Tax, therefore, the amount of tax chargeable against the ORRI was determined contractually under Section 4.6 on the basis of the Alaska tax law in effect in real time on each day beginning April 1 ^st of this year. Thus, when the Act came into effect on August 20 ^th and thereupon became retroactive to April 1 ^st , the contractual amounts of “daily” chargeable tax under Section 4.6 had already been determined for the days prior to August 20, and those determinations had been made on the basis of the Old Tax. The Act does not purport to alter the contractual obligations arising under the Conveyance prior to August 20 when the Act came into effect, and even if it did, it could not alter them under the Impairment of Contracts clauses of the United

Ms. Ming J. Ryan, Vice President
The Bank of New York
October 11, 2006
Page 8

States and Alaska constitutions. ¹²

We concur with the view expressed by the Bank’s representatives that the foregoing analysis regarding the Act’s retroactivity in the context of the Conveyance represents the best interpretation of the Conveyance and the most defensible position on this issue of retroactivity.

Accordingly, when the New Tax did become applicable and chargeable against the ORRI beginning August 20 ^th , the most appropriate and fairest way to apply the “progressivity” portion of the New Tax is to treat the period of August 20 — 31, when the New Tax was applicable, as a “month” for purposes of determining the “progressivity” rate. If the chargeable tax for the days in August before the 20 ^th was indeed contractually determined in real time each day under the Old Tax, then when the New Tax becomes applicable on the 20 ^th , those prior days in August do not exist for purposes of the calculating the amount of New Tax chargeable against the ORRI, and the effect is the same as if Prudhoe Bay were first coming into production on that date. It would be inconsistent to include those prior August days for purposes of computing the “progressivity” rate for the portion of August when the New Tax is chargeable.

I am signing and mailing to you two counterpart originals of this letter. If the statement of our understanding of the consensus principles, appearing on pp. 1-2 of this letter, does indeed accurately state the Bank’s understanding of and agreement with them, please have a duly authorized officer of the Bank execute the “AGREEMENT AND APPROVAL” appearing below on behalf of the Bank in each counterpart, and then kindly send one fully executed counterpart original back to me for BPXA’s records. The other will be for the Bank’s records. As an interim confirmation pending my receipt of the original counterpart, I would ask you to email a scanned copy of it to Mark Dennehy, who has been in direct contact with you previously regarding this matter.

BPXA believes the understanding and agreement to the consensus principles as outlined in this letter is a fair and reasonable resolution to the issues raised by applying the New Tax in the context of the Conveyance. However, it is recognized there may be issues outside the matters contained in this letter affecting the Trust Unit holders’ and BPXA’s interests. This letter and the understanding of and agreement to the consensus principles between the Bank, as Trustee, and BPXA, are not intended to waive any other rights, obligations or remedies available to them under law or the BP Prudhoe Bay Trust. Further, in the event of future amendments or changes to Alaska’s oil and gas production tax laws, or should the understanding of and agreement to the consensus principles on pp. 1-2 be invalidated by operation of law or by a court of competent jurisdiction, BPXA and

Ms. Ming J. Ryan, Vice President
The Bank of New York
October 11, 2006
Page 9

the Bank, as Trustee, expressly agree to reserve all rights, powers and remedies, they may have available to them under law or the BP Prudhoe Bay Royalty Trust.

On behalf of BPXA, I should like to take this opportunity to express our thanks and appreciation to the Bank and its representatives for the attention and constructive cooperation shown in seeking and achieving a resolution to these issues that is reasonable and fair from all perspectives for those concerned.

AGREEMENT AND APPROVAL I, the undersigned, certify that I am an officer of The Bank of New York (“Bank”) duly authorized to execute this AGREEMENT AND APPROVAL, and in such capacity, I hereby acknowledge that the consensus principles have been accurately and fully set forth on pages 1 - 2 of the foregoing letter, and do agree to and approve those principles on behalf of the Bank, as Trustee of the BP Prudhoe Bay Royalty Trust.