The examples below is saying that, for BMNR to continue to issue new shares and buy more ETH, they need to do it when BMNR price is traded above its NAV (otherwise it would dilute the value for existing shareholders). However, this means the new shareholders need to be willing to buy the second offering at a price that is much higher than the market price of ETH.
Over time, unless BMNR can offer value differentiation, it is unlikely future investors would be willing to continue to buy their secondary offerings at a price that is much higher than NAV. Gradually, its stock price should stablize around it NAV + some premium reflecting its yield
Example 1: Assume BMNR always trade at the exact NAV
In reality, it should have a premium due to staking yield, but for simplicity, let's ignore that for now
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BMNR initially raises $100m and buys 10,000 ETH at $10,000 each.
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NAV = $100m / shares outstanding.
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Let’s say they issued 10m shares, so NAV/share = $10.
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Each share = claim on 0.001 ETH.
----- ETH doubles to $20,000 ------
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BMNR’s 10,000 ETH is now worth $200m.
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NAV/share = $200m / 10m shares = $20/share.
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Each share still = 0.001 ETH (10,000 ETH ÷ 10m shares).
----- Now BMNR issues new shares 5m shares at $20/share → raises $100m cash.
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They use that $100m to buy 5,000 ETH at $20k.
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New total: 15,000 ETH, worth $300m.
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Shares outstanding: 15m.
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NAV/share = $300m / 15m = $20/share.
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Each share = 0.001 ETH (15,000 ETH ÷ 15m shares).
In this example, each share of BMNR continues to track the same amount of ETH and therefore If BMNR continues to issue new shares to buy ETH, there is no difference than owning ETH itself
Example 2: Assume BMNR always trade above its NAV
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BMNR raises $100m at $10/share
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Issues 10m shares
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Buys 10,000 ETH @ $10k
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NAV = $100m / 10m = $10/share
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Each share = 0.001 ETH
------ ETH doubles from $10k to $20k -----
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10,000 ETH now worth $200m
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NAV = $200m / 10m = $20/share
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Each share = 0.001 ETH
----- Now BMNR issues new shares at $25 (above NAV = $20)
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BMNR issues 4m shares at $25 → raises $100m
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Uses cash to buy 5,000 ETH @ $20k
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Total ETH = 15,000
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Total assets = $300m
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Total shares = 14m
New NAV/share = $300m ÷ 14m = $21.43
New ETH/share = 15,000 ÷ 14m = 0.001071 ETH
So, for existing shareholders, they get 7% higher value than whatever is currently traded on the market。 However, since NAV is now $21.43, the new shareholders are overpaying $25 for assets worth $21.43, so their effective ETH price = $25 ÷ 0.001071 ≈ $23,333 per ETH (vs market price $20k)
