Explaining the money game of "BMNRs" with mathematics

Author丨Theclues

Twitter丨@follow_clues

Original Title丨BMNR's Money Game

The core mechanism of equity dilution: A capital increase will change the distribution of equity per share, leading to a transfer of value from existing shareholders to new shareholders, unless certain ideal conditions (such as the market fully accepting the capital increase without adjusting the valuation) continuously hold. Below, I will explain with mathematical calculations why this effect is unavoidable in reality and will ultimately undermine the logic of the "eternal cycle."

1. Example assumption

• Initial State:
  Company assets: $10 billion ETH (net assets = $10 billion, assuming no liabilities). Market Cap: $11 billion (implying a 10% premium given by the market, possibly based on growth expectations or speculation). Assuming the total share capital is S shares, then: Net Asset Value (NAV) per share = 100/S billion USD. Share price = 110/S million USD (Premium = 10% ).
• Action: Raise $5 billion (issue new shares), fully purchase $5 billion worth of ETH.
• In order to keep the stock price unchanged, the new issuance must be priced at the current stock price of 100/S. This is a "market price issuance."

2. Calculate the situation after the increase in issuance (assuming the increase is at market price, with the stock price remaining unchanged)

• Additional shares issued: Raised $5 billion, requires new shares N=0.4545S.
• New total share capital: 1.4545S.
• New total assets: 100 + 50 = 150 billion USD ETH.
• New net asset value per share: 150/1.4545S billion USD (an increase of approximately 3.13% compared to the initial 100/S).
• New market capitalization (assuming the market accepts the stock price unchanged): $16 billion.
• New premium: 10/150=6.67% (down from 10% to 6.67%).

On the surface, the stock price remains unchanged at 110/S, and the net asset per share has even slightly increased.

But there is a hidden dilution effect here:

• Value transfer occurs: An additional $5 billion in assets is shared among all shareholders (old + new). The existing shareholders' equity ratio drops from 100% to 68.75%. They originally owned the entirety of $10 billion in assets, and now they only own 68.75% of $15 billion (≈ $10.313 billion), a net increase of $313 million. However, without the new issuance, they could have owned $11 billion; here, the new shareholders share part of the appreciation at a "discount" (due to the premium compression).
• Not real value added: The 5 billion dollars issued is external funding injection, not value created internally by the company. Its "value increase" is just an accounting illusion - similar to you depositing someone else's money into your own bank and then claiming that your family's wealth has increased.
• Premium compression is a warning: the initial 10% premium reflects market optimism about "growth potential" (such as expectations for more issuance cycles). However, each issuance dilutes this potential, leading to a gradual decline in the premium (from 10% to 6.67%, and lower next time).
• Why? Because the company is essentially an "ETH holding shell" with no unique business, the market will gradually see it as an ETH ETF (market value ≈ net asset, premium → 0). Once the premium is 0, further issuance cannot be done at a price higher than the net asset, otherwise no one will buy.

3. If the cycle continues, the effect will amplify and disrupt the model.

Assume the example is repeated several times (each financing is equivalent to 50% of the current assets, issued at the current stock price, assuming the stock price remains unchanged):

• After Round 1: Assets 15 billion, Market Value 16 billion, Premium 6.67%.
• Round 2: Financing 7.5 billion (50% of 150), new shares ≈0.46875S' (S' is the current equity), new assets 22.5 billion, new market value 23.5 billion, premium ≈4.44%, net assets per share increase but premium continues to decrease.
• Round 3: Similar, the premium drops to ≈3%.

After several rounds, the premium approaches 0. At this point:

• The price of the additional issuance is forced to equal the net asset value per share (with no premium space).
• Net asset per share no longer increases: For example, asset A, equity T, issuing 0.5A (priced at A/T), new number of shares = 0.5T, new assets 1.5A, new per share = 1.5A / 1.5T = A/T (unchanged).
• Cycle failure: Without the "stock price increase" driving the next issuance, the model shifts from "appreciation" to "zero-sum" - new funds merely dilute old shares, resulting in no net gain.

This is exactly the manifestation of the dilution effect: initially covered by premiums, later exposed, leading to value transfer (new shareholders entering at low cost, old shareholders' equity diluted).

4. If it is not a market price issuance, the dilution is more significant (closer to the "par value issuance" scenario)

5. Why this effect cannot be avoided in practice

• The market is not infinitely rational or optimistic: your assumption relies on the market always accepting "constant stock prices," but investors will calculate dilution (using EV/EBITDA or NAV discount models). Once they realize that the model has no intrinsic cash flow (no dividends, relying solely on holding ETH), FOMO turns into panic, and stock prices collapse ahead of time.
• Nature of Mathematics: Dilution is an arithmetic inevitability. Unless the growth rate from new issuance is greater than the dilution rate (Gordon model: value = \frac{D}{r – g}, where g is growth, but g depends on external ETH rise, not perpetual), value does not increase.

In summary, the new shareholders of BMNR continuously erode the rights of old shareholders through issuance, merely masked by the rise of ETH. Other coins and stocks are similar; the larger the ratio of issuance scale to current market value, the faster the dilution effect!