Dilution and True Economic Gain From Cryptocurrency Block Rewards 

Dilution is the loss experienced by incumbent owners upon the creation of new ownership units (such as shares or tokens). Although many ad hoc patches to the U.S. tax code typically provide incumbents with some form of tax allowance for their loss, there appears to be no unified theory of accounting for dilution — for tax or any other purposes. When additions to one’s balance from newly created units are viewed as an income realization event, whereas dilution is not, net income is systematically overstated. The resulting overtaxation could be a serious hurdle to the adoption of proof-of-stake cryptocurrencies, which rely on token creation by incumbent owners as an integral part of network maintenance. In this article we quantify the potential for overtaxation — defined herein as the excess of taxable income under a strict realization approach over true economic income — for a real-world taxpayer holding cryptocurrency tokens.

Our example taxpayer is a Tezos staker — a token holder who acquires new Tezos cryptocurrency tokens by participating in the maintenance of the Tezos network. We present the pros and cons of different methods of accounting for dilution when the cryptocurrency’s aggregate network value, the taxpayer’s ownership balance, and the rate at which dilution happens are all time-varying. We conclude that the acquisition of those tokens should not be an income realization event, although any of the methods we propose would be preferable to an approach of strict realization that ignores dilution entirely. Tax policy aside, the methods we develop to quantify the economic value lost to dilution are independently interesting to investors and other finance and accounting practitioners.

I. Definition of Income

The total change in wealth caused by ownership of an asset (ΔWealth) is:

when capital appreciation is defined as the change in the asset’s value and can be positive or negative.

Different operational definitions of income imply that different components of the change in wealth are included in current income. Under the most comprehensive definition, known as Haig-Simons income, both components are included. Under a “strict realization” principle, income includes distributions only, for the rest will be realized if and when the asset share is sold.

The U.S. income tax is not based on a strict realization principle, however, and taxpayers are often allowed to deduct reductions in the value of their investments (with a corresponding reduction in the tax basis) when these are reasonably certain to have happened and are easy to quantify. The most obvious example is depreciation. If a business buys a car, it does not have to wait until the car is sold to a scrap yard to recognize an expense.

A less obvious example of a reduction in value is dilution. When owning a share of an asset, the capital appreciation is split into two components: the change in the value of the whole asset (prorated by the taxpayer’s initial share), and dilution, defined as the current asset value times the change in the fraction owned that occurs because of the creation of additional shares independent of the taxpayer’s purchases and sales:

Like depreciation, in many cases dilution results in an immediate explicit or implicit deduction for the taxpayer. Unlike depreciation, however, dilution is not a formally recognized taxable event and its treatment is determined on a case-by-case basis. For instance, for stock compensation, the corporation receives an offsetting deduction that indirectly benefits the shareholders being diluted. For a pro rata stock dividend, the distribution goes untaxed because it is automatically and exactly offset by dilution.

Cryptocurrencies consist of several tokens (units of accounting) in a network. If one accepts the uncontroversial premise that the value of a cryptocurrency network does not depend on the exact number of tokens it contains, then the creation of new cryptocurrency units results in dilution. Unlike random fluctuations in network value, which can give rise to both capital gains and losses, this dilution is sure to happen and sure to be detrimental to the taxpayer’s wealth.¹

As noted, dilution is fully and automatically accounted for under a Haig-Simons conception of income. Alternatively, dilution need not be accounted for if the acquisition of newly created tokens is not a realization event, as the combined effect will be accounted for at the time of sale. This is the position taken by one of us² on the grounds that new tokens are created by the taxpayer, and taxpayer-created property is not income under U.S. tax law. Under this approach, the true economic gains from both newly created tokens and purchased tokens will be accurately established, and can be taxed, at the time of those tokens’ sale. However, if new tokens are viewed as distributions (despite not being distributed by anyone) and are taxed in the year in which they are acquired, current law does not provide a way for the taxpayer being diluted by those tokens to obtain a corresponding deduction.

In what follows we demonstrate that there is no one perfect method to account for this dilution. Accordingly, we propose three candidate methods, each with its own strengths and weaknesses. We then compare the results with an option for the tax treatment of block rewards that would disregard dilution. In 2014 IRS guidance stated that “mined” cryptocurrency tokens (such as bitcoins) are gross income at the tokens’ fair market value on the date received.³ This is a policy of strict realization because it fails to account for dilution. We call this policy of strict realization the cash value approach.

Our comparison is based on a specific cryptocurrency, Tezos, and we analyze both a stylized example (to build intuition) and a real-world example of a specific taxpayer. Dilution explains why the cash value approach systematically overstates taxpayer gain and is not desirable as a matter of tax policy. Our proposals therefore provide options for accounting for dilution, to make a realization-based annual tax fair. Each option results from a different but defensible approach to quantifying the economic value lost to dilution.

Because no one option is clearly superior, and because of the accounting complexity introduced by each option, we conclude that our results buttress arguments against a policy of annual taxation of reward tokens.

The lack of an obviously dominant option also implies that our discussion is independently interesting to investors in any assets subject to dilution. The accounting methods we develop suggest ways of decomposing investment returns into appreciation and dilution, and to produce consistent financial reporting of business income from cryptocurrency holdings.

II. Accounting for New Tokens

The aforementioned article presents a simple model for establishing true gains and losses from proof-of-stake cryptocurrency block rewards in light of dilution.⁴ That model is based on two key variables which illustrate the consequences of ignoring dilution. The first is the rate at which new tokens are added to the network: the token creation rate. The second is the percentage of the total supply of tokens that participate in network maintenance through staking: the staking rate.⁵ The model also excludes any changes in asset value, defined as the aggregate value of all tokens in the network. Later, we begin with this simplified model but then elaborate it to account for complications introduced when three parameters, held static in the simple model, are relaxed to account for their variance over time.

Tezos block rewards are the result of “staking” one’s tokens (either directly, or through delegation), and staking is required to maintain the Tezos network. Tezos tokens have a readily verifiable market value and, as noted, one option, the cash value approach, is to include reward tokens in gross income at their FMV on the date acquired. Tezos tokens are property for tax purposes while taxes must be paid in dollars, and dollars are also the unit of account for most accounting purposes.

Tezos token holders are eligible to create new reward tokens proportionate to their holding, that is, to their ownership share in the network. If all token holders stake their tokens and receive pro rata block rewards, everyone’s share would remain constant because block rewards would exactly make up for dilution. Then it would make sense to treat block rewards like pro rata stock dividends and exclude them from income. In this simplest case, when the staking rate is 100 percent, the token creation rate doesn’t matter. Whether each holder’s token balance increases by 10 percent or 1,000 percent, none experiences any gain and there should not be any income subjected to tax.

If some token holders do not participate in staking and therefore do not receive block rewards, then these “non-stakers” will see their share in the network decrease. If we know the token creation rate, then we know the effect of dilution on those who do not stake their tokens. The dilution rate is found from the reciprocal of the rate of increase of tokens in circulation. If the total supply of a cryptocurrency’s tokens increases by 50 percent over the course of a tax year, every non-staker will see his share in that supply decrease by one third; if the creation rate is 10 percent, the dilution is 9.09 percent.⁶

The token creation rate is not enough, however, to establish stakers’ gains from staking. Gains — both nominal and real — depend on the staking rate. Dilution affects stakers and non-stakers equally, but the extent to which stakers offset dilution through new tokens depends on how many stakers share in those tokens.⁷

We can use numbers drawn from Tezos to illustrate this simple model. In 2019 the total supply of Tezos tokens increased by about 5 percent, and so non-stakers’ dilution was approximately 4.8 percent.⁸ The staking rate varied over the course of the year, but averaged roughly 70 percent. Because the new tokens are divided among stakers, using these rough figures a Tezos staker would end the year with 0.05/0.7 = 7.14 percent more tokens. Accounting for the 5 percent new tokens, however, the true economic gain would be just (1 + 0.0714)/(1 + 0.05) = 2.04 percent.

This simple model is adequate to explain why the cash value approach overstates gain from staking. Under the cash value approach, the tax authorities treat the 7.14 percent new tokens as income, overstating the true gain by 250 percent.

Among other shortcomings, this model does not address the dollar value of Tezos tokens. There is no reason to suppose that the value of a single token, expressed in dollars, will remain constant as new tokens are added to the supply. The more reasonable assumption for a basic model is that the total network value remains constant, so that income is a function of distributions and dilution but not changes in asset value. This was the approach taken in “Taxation of Block Rewards.” Assuming the value of the Tezos network holds constant, with 5 percent more tokens, at the end of the year the dollar value of a single token will be 95.24 percent what it was to start the year. With a 70 percent staking rate, a 5 percent token creation rate, and a constant network value, under the cash value approach stakers will show income of 6.97 percent of their initial share in the network.⁹

In real life, nothing remains constant. First, the value of the network expressed in dollars fluctuates — sometimes wildly. Second, the staking rate (and thus the dilution rate) varies over time; in 2019 it ranged between about 62 percent and 77 percent. (Note that, for a token holder who participates in validation, a higher number means less economic gain). Moreover, in practice reward tokens are not received in strict proportion to the tokens staked, especially over shorter periods of time.¹⁰ Finally, stakers’ balances change over time, as tokens are purchased or sold and as reward tokens are added to the balance.

Accordingly, a method of accounting for dilution must account for these three complications:

1. the taxpayer’s balance is time-varying;

2. the rate of dilution is time-varying; and

3. the value of the network is time-varying.

The first complication is just a matter of using the appropriate accounting technique, explained in the next section. The second complication can be dealt with by using the measured rate of dilution. The third complication is the challenging one, because there is not one correct way of handling it.

We can think of at least three defensible methods. None is philosophically superior in terms of being “closer” to the concept of “true” economic income, but the methods require different inputs and therefore have different strengths and weaknesses.

Suppose on January 1 a taxpayer buys 600 Tezos tokens at a price of $0.42 per token (or $252 total). The total supply of Tezos at that time was 10,000. Next, suppose that on December 31 the total supply of Tezos rose to 15,000 and the token price rose to $0.50. What is the cost of the dilution sustained by the taxpayer?

A. Method 1: Depletion

While on January 1 the taxpayer owned 600/10,000 = 6 percent of the total cryptocurrency network, on December 31 she owns 600/15,000 = 4 percent, or one-third less. For this reason, the taxpayer takes a depletion charge equal to one-third of the tax basis of her investment, or¹¹:

The advantage of this method is that it does not require a market price and it is instead entirely based on transactions that happened in the past. The only data requirement is the total number of tokens outstanding at two points in time. Moreover, it is consistent: The depletion deduction is guaranteed to be less than the tax basis. Because of this consistency property, this method is suited for financial reporting to shareholders by a business that owns tokens.¹² Disregarding dilution altogether, as in the cash value method, would result in overstated business income, potentially distorting management compensation or shareholder perception of value. On the other hand, accounting for dilution using an inconsistent method could result in the business holding the tokens at negative book value, also an undesirable result.

B. Method 2: Market-Based

The market capitalization of Tezos went from $4,200 ($0.42 x 10,000) to $7,500 ($0.50 x 15,000), a 79 percent increase in network value, while the taxpayer’s position went from $252 to $300 (a 19 percent return). The difference in return (79 percent - 19 percent = 60 percent of $252, or $150) must be mathematically caused by dilution. Equivalently, if the taxpayer had owned 6 percent of all Tezos in circulation on December 31, her position would have been worth $450 (6 percent x 15,000 x $0.50). Because her position is only worth $300, the value lost to dilution is $150 ($450 - $300).

This method is more complex, as it requires additional information: the price of Tezos at two points in time, in addition to the number of tokens outstanding. The main advantage of this method is that it is accurate: Unlike the depletion method, this definition captures the true economic cost of dilution under FMV (or Haig-Simons) accounting, that is, the third term in equation (2). For this reason, this method is suited for any business purposes that require measuring the true economic cost of dilution, such as performance attribution in an investment portfolio.

Unlike the depletion method, moreover, this method is not consistent. In the extreme, if on December 31 the price of Tezos rises to $1 (twice the previously assumed value), the value lost to dilution is $300 (2 x $150), more than the original cost basis of $252, resulting in negative book value. This problem happens precisely because this method allows the taxpayer to deduct the full market value cost of dilution without requiring her to first realize the market value of her unrealized capital gains (that is, it uses the Haig-Simons approach on the “minus” side but not on the “plus” side).

A less obvious consequence of this inconsistency is that the greater the unrealized capital gain, the greater the taxpayer’s deduction is! Thus, a higher Haig-Simons income (a larger increase in market value of wealth) results in a lower taxable income. For this reason, this method would likely be deemed too favorable to the taxpayer and thus unacceptable as a method of determining taxable income.

C. Method 3: Imputed Dilution

The prior two methods highlight an apparently unsolvable trade-off between consistency and accuracy. On one hand, the market value of rewards is counted as current income, and thus it seems appropriate to offset it using the market-value cost of dilution. On the other hand, the market-value cost of dilution can be greater than the combined value of income from rewards and the taxpayer’s basis in the original tokens. Accounting for tokens at FMV (that is, setting taxable income equal to Haig-Simons income) solves the trade-off but creates well-known problems, which is why the taxation of unrealized gains and losses on an FMV basis has found very limited application in real-world tax systems.¹³

A potential solution to this conundrum is to directly adjust rewards for an imputed cost of dilution. In our example, the total supply of tokens grows in a year by 50 percent (from 10,000 to 15,000). Our taxpayer begins the year with 600 tokens and would have to acquire 300 additional tokens to maintain her proportionate share in the network. In practice, however, she may receive more than 300 tokens if other token holders choose not to participate in validation. For instance, suppose that 75 percent of tokens participate in validation (that is, the staking rate is 75 percent). In that case, our taxpayer should expect to receive 5,000 * 600/(10,000 * 0.75) = 400 tokens. Of these, 300 (75 percent of all tokens received) compensate the taxpayer for dilution, and the remaining 100 (25 percent) constitute a transfer from non-validators to validators, that is, income.

While the explanation is somewhat complicated, the resulting math is very simple. Under this proposal, taxable income is calculated as:

This method has two main advantages, both deriving from the fact that it does not affect the tax basis of, nor does it require any knowledge of, existing tokens, and income is defined at the level of individual reward transactions. First, as will be clear in the following section, this method greatly simplifies accounting. Second, while it is an approximate method, it does come close to solving the apparently unsolvable trade-off between accuracy and consistency, as it roughly captures only the realized portion of the FMV cost of dilution.

This resolution, however, comes at the cost of generality because it embeds knowledge specific to the Tezos network. This is a high cost: While the concept of staking rate exists in some form for most proof-of-stake cryptocurrencies (that is, those cryptocurrencies for which network maintenance is performed by token owners, and thus dilution accounting is most relevant), the rule proposed here is not guaranteed to be easily applicable to every existing and future cryptocurrency. Thus, the greater simplicity in accounting is offset by a greater complexity in regulation — namely, the potential for having as many distinct practical implementations of this method as there are cryptocurrencies.¹⁴

Also, the loss of generality is with respect to the taxpayer’s behavior as well. The imputed dilution method essentially assumes that the taxpayer engages in staking directly and without pause throughout the entire tax reporting period. A taxpayer who stakes intermittently or delegates to others could plausibly earn less than necessary to keep up with the creation of new tokens. For this taxpayer, the true net income from holding Tezos is negative, but taxable income is positive. This happens because the taxpayer only gets an allowance for dilution when staking but gets diluted all the time.

III. A Stylized Example

Methods 1 and 2 isolate the losses from dilution regardless of whether token holders stake their tokens. If annual taxation is predicated on the receipt of reward tokens as a realization event, the more important case involves the token holder who stakes his tokens and as a result acquires reward tokens during the year.

Suppose that after having purchased 600 tokens on January 1, our taxpayer acquires 140 Tezos reward tokens on May 26 when the total supply is 12,000 and the price is 0.5, and then another 260 reward tokens on October 19 when the total supply is 14,000 and the price is 0.6. The next table shows that cumulative reward income as of December 31 is $226, if rewards are measured at their FMV on the date received (that is, the cash value approach). What is the total “true” income, net of dilution?

Table 1

Date	XTZ: USD	XTZ				USD
		Supply	Balance	Award	Purch.	Balance	Award	(Cum.)
1/1	0.42	10,000	600		600	252.00		0.00
5/26	0.50	12,000	740	140		370.00	70.00	70.00
10/19	0.60	14,000	1000	260		600.00	156.00	226.00
12/31	0.50	15,000	1000			500.00	0.00	226.00

Because the total supply of Tezos tokens changes at every reward transaction, any dilution allowance must be calculated upon every transaction starting from the previous transaction. For reporting purposes, the resulting income figures can be aggregated at arbitrary frequency.¹⁵

This section does not deal with the imputed dilution method. Because the cost of dilution is calculated on a per-transaction and not on a per-period basis, there is no need to worry about time-varying balances.

A. Depletion Method

For instance, on May 26 we calculate depletion for the first time just one instant before the balance changes for the first time. Depletion is calculated as the original tax basis (252) times the relative change in share. The preexisting tokens used to be the entirety of the tokens (10,000/10,000), whereas now they are only five-sixths (10,000/12,000), resulting in a one-sixth drop in share:

The total new book value on May 26 after the reward transaction is then calculated as the remaining book value of the initial Tezos tokens (252 - 42) plus the new book value of the reward tokens (0.5 * 140):

On October 19, upon recording a new transaction, once again we take stock of the intervening depletion:

And so forth. Note that depletion could be computed more frequently and regardless of transactions, but it has to be computed at least upon every transaction, that is, every time the number of tokens changes.

The results are summarized in Table 2, which shows that true income calculated this way is $117.60. Therefore, compared with this method, taxing reward income without any dilution allowances results in taxable income that is 92 percent greater.

Table 2

	Depletion Method (USD)
Date	BV	Depletion	Net Income	(Cum.)
1/1	252.00			0.00
5/26	280.00	-42.00	28.00	28.00
10/19	396.00	-40.00	116.00	144.00
12/31		-26.40	-26.40	117.60

B. Market Value Method

Up to May 26, the taxpayer’s return has been 19 percent (price increase from $0.42 to $0.50). In the same period, however, the market capitalization of the network has increased from $4,200 to $6,000, a 42.9 percent increase. In the absence of dilution, the taxpayer would have realized an additional return of $60, or 23.8 percent (42.9 percent - 19 percent) of her initial investment of $252.

Once again, the procedure is repeated at every transaction. On May 26, after receiving the first reward, the taxpayer’s Tezos position is worth $370. On October 19, before receiving the second reward, the position has experienced a return of 20 percent (price increase from $0.50 to $0.60), while market value has increased by 40 percent. The loss to dilution is therefore:

And so forth. The results are summarized in Table 3, which shows that true income calculated this way is $56.29. Therefore, compared with this method, taxing reward income without any dilution allowances results in taxable income that is 302 percent greater.

Table 3

	Market Value Method (USD)
Date	Ret%	Mkt Cap	Mkt Cap Ret %	MV Dilution	Net Inc.	(Cum.)
1/1		4,200				0.00
5/26	19.0%	6,000	42.9%	-60.00	10.00	10.00
10/19	20.0%	8,400	40.0%	-74.00	82.00	92.00
12/31	-16.7%	7,500	-10.7%	-35.71	-35.71	56.29

IV. Real-World Example

We now apply these methods to a real taxpayer’s participation in the Tezos network and compute the taxpayer’s total taxable income for 2019.

We use four methods:

1. The “cash value method” (include rewards in gross income at their FMV on the date received, with no deductions for dilution).

2. The “market value method” (dilution allowance based on market value of dilution loss).

3. The “depletion method” (dilution allowance based on fraction of initial investment).

4. The “imputed dilution method” (taxable income is computed already net of dilution allowance as the portion of reward tokens’ FMV that exceeds the rewards expected in a 100 percent staking scenario).

This taxpayer staked his Tezos tokens throughout 2019, initially by delegating them to others, and later by delegating them to himself and directly operating a computer running the Tezos software that validated transactions. His initial balance on January 1, 2019, was 102,708 tokens. On several occasions during the year, he added to his staking balance through purchases of tokens. These purchases totaled 98,554 tokens. On two occasions he reduced his staking balance, selling a total of 460 tokens. During 2019 the taxpayer acquired 8,876 tokens as a result of staking; these tokens were added to his balance on more than 100 different days. His token balance at the close of 2019 was 209,678.

The total supply of Tezos on January 1, 2019, was 781,346,794. During 2019, the supply increased by 39,529,621 tokens or 5.06 percent,¹⁶ and at the end of the year the total supply was 820,876,415. The market price of a single token began the year at $0.49 and trended upward, ending the year at $1.32, an increase of 169 percent. The value of the total token supply started the year at $356,735,257 and ended the year at $1,085,198,621, an increase of 182 percent.

The taxpayer’s 8,876 reward tokens, after adjusting for reward tokens as well as deposits and withdrawals over the course of the year, reflect an annual increase in tokens caused by staking of 5.74 percent.¹⁷ The taxpayer reported the gains from his reward tokens by establishing their FMV on the date they became spendable.

The chart above reports the taxpayer’s cumulative income under each of the three methods.¹⁸ The outcomes are very different, but under any definition of true economic income the cash value approach drawn from the 2014 IRS guidance results in a substantial overstatement of taxpayer income and results in overtaxation.

Note that the “depletion” method is sensitive to the tax basis of the existing position on January 1. To show how the result differs, we provide four different assumptions for the tax basis:

• zero basis (as if the taxpayer had, for example, obtained the tokens for free) — a lower bound;

• basis = market value of tokens on January 1, 2019 (as if they had been bought on that date — a reasonable approximation of the situation of most taxpayers);

• basis = $4.46/token (all-time high — a practical upper bound); or

• basis = $10/token (an arbitrarily high number — a theoretical quasi-upper bound).

The results are reported in the following table, in which “income overstatement” is calculated as (taxable income under cash value method - taxable income under depletion method) / absolute value of taxable income under depletion method.

Table 4

Rationale	Basis on 1/1/2019 (USD)	Income Overstatement
Most conservative	$0	32.90%
Market value	$46,886	93.18%
$4.46 per token	$458,079	162.59%
$10 per token	$1,027,084	116.74%

While the result is sensitive to the assumption, the estimated income overstatement is at a minimum 32.9 percent.

V. Conclusion

In this article we have examined three methods to account for dilution in proof-of-stake cryptocurrencies. The creation of new tokens (“block rewards”) is often used as a device to encourage network maintenance and always results in dilution. Quantifying the economic effect of dilution is important for proof-of-stake cryptocurrencies in particular, as their networks are maintained by token owners as opposed to third-party miners. Therefore, to participate in network maintenance and obtain block rewards, one must suffer dilution as well. If block rewards are taxed as realized income, without a way to quantify the effect of dilution, cryptocurrency owners are likely to suffer from overtaxation.

Our methods attempt to reconcile the underlying economics of block rewards and dilution with a realization-based system. This turns out to be a formidable challenge. We propose a depletion method, which is consistent — that is, it never results in a depletion allowance greater than the cryptocurrency’s initial cost basis — but inaccurate, as it does not measure the true market value cost of dilution. Next we propose a market-based method, which is accurate but inconsistent. Finally, we propose an imputed dilution method which is simple and offers a practical compromise between accuracy and consistency, but at the cost of generality — that is, it only works under specific assumptions.

It is therefore natural to conclude that instead of allowing proof-of-stake validators to realize the value of their dilution, it is simpler and fairer to allow them not to realize the value of their block rewards until sold.

Aside from tax, the methods we develop can be useful for valuation and management of cryptocurrency portfolios and inventories. The depletion method is suitable for reporting under delegated management, when realization matters and consistency matters more than correctness. The market-value method is likely more useful for cryptocurrency valuation and portfolio management, when total income (realized plus unrealized) matters. While in that context FMV accounting is both easy and best, our method is still useful to decompose investment performance into rewards, dilution, and actual asset appreciation.

VI. Appendix: Data Excerpt and Calculations

Table 5

Date	XTZ ($)	# Tokens	Rewards (XTZ)	Rewards (USD)	Rewards (USD, Cum.)
1/1/2019	0.4805	781,457,300	0.00	0.00	0.00
1/2/2019	0.4738	781,564,265	44.12	21.20	21.20
1/3/2019	0.4785	781,673,212	0.00	0.00	21.20
1/4/2019	0.4714	781,780,984	0.00	0.00	21.20
1/5/2019	0.4781	781,889,615	44.14	20.81	42.01
1/6/2019	0.4794	782,000,032	0.00	0.00	42.01
1/7/2019	0.4753	782,110,563	0.00	0.00	42.01
1/8/2019	0.4702	782,218,411	44.16	20.99	63.00
...
12/24/2019	1.5138	820,104,596	0.00	0.00	9,027.49
12/25/2019	1.3758	820,215,207	0.00	0.00	9,027.49
12/26/2019	1.4010	820,324,794	166.35	228.87	9,256.36
12/27/2019	1.3629	820,436,878	0.00	0.00	9,256.36
12/28/2019	1.3249	820,549,859	0.00	0.00	9,256.36
12/29/2019	1.3260	820,662,081	113.34	150.16	9,406.52
12/30/2019	1.3029	820,773,664	0.00	0.00	9,406.52
12/31/2019	1.3220	820,876,415	0.00	0.00	9,406.52

Table 6

Cum. USD	Depletion		Market Value		Imputed dilution
Date	Depletion	Income	MV Dilution	Income	Income
1/1/2019	6.63	-6.63	6.98	-6.98	0.00
1/2/2019	13.05	8.15	13.64	7.26	16.83
1/3/2019	19.58	1.62	20.49	0.41	16.83
1/4/2019	26.05	-4.85	27.17	-6.27	16.83
1/5/2019	32.56	9.45	34.00	8.01	33.22
1/6/2019	39.18	2.83	40.96	1.05	33.22
1/7/2019	45.81	-3.80	47.86	-5.86	33.22
1/8/2019	52.27	10.73	54.53	8.24	49.44
...
12/24/2019	4,542.81	4,484.68	7,726.91	1,339.40	2,460.33
12/25/2019	4,563.02	4,464.47	7,765.77	1,300.55	2,460.33
12/26/2019	4,583.05	4,673.31	7,804.97	1,494.41	2,498.30
12/27/2019	4,603.56	4,652.80	7,843.99	1,455.38	2,498.30
12/28/2019	4,624.22	4,632.14	7,882.23	1,417.15	2,498.30
12/29/2019	4,644.74	4,761.78	7,920.23	1,529.43	2,524.14
12/30/2019	4,665.16	4,741.36	7,957.38	1,492.29	2,524.14
12/31/2019	4,683.96	4,722.56	7,992.08	1,457.58	2,524.14