用数学阐释“BMNR们”的金钱游戏

比推Опубліковано о 2025-08-18Востаннє оновлено о 2025-08-18

作者丨Theclues

Twitter丨@follow_clues

原标题丨BMNR的金钱游戏


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股权稀释的核心机制:增发会改变每股权益的分配,导致价值从现有股东转移到新股东,除非某些理想条件(如市场完全接受增发且不调整估值)持续成立。下面我用数学计算说明为什么这个效应在现实中无法回避,最终会破坏“永恒循环”的逻辑。

1. 例子假设

  • 初始状态:
    公司资产:100亿美元 ETH(净资产 = 100亿美元,假设无负债)。
    市值:110亿美元(意味着市场给出10%溢价,可能基于增长预期或投机)。
    假设总股本为 S 股,则:
    每股净资产(NAV) = 100/S 亿美元。
    每股股价 = 110/S亿美元(溢价 = 10% )。

  • 行动:融资50亿美元(增发新股),全部买入50亿美元 ETH。

  • 为了使股价不变,增发必须以当前股价100/S定价。这是一种“市场价增发”。

2. 计算增发后的情况(假设以市场价增发,股价不变)

  • 增发股数:募集50亿美元,需要新股数 N=0.4545S。

  • 新总股本: 1.4545S。

  • 新总资产:100 + 50 = 150亿美元 ETH。

  • 新每股净资产: 150/1.4545S亿美元(比初始100/S增加约3.13%)。

  • 新市值(假设市场接受股价不变):160亿美元。

  • 新溢价:10/150=6.67%(从10%降到6.67%)。

表面上看,每股股价不变110/S,每股净资产甚至略增。

但这里隐藏了稀释效应

  • 价值转移发生:新增的50亿美元资产被所有股东(旧 + 新)分享。现有股东的股权比例从100%降到68.75%。他们原本拥有100亿美元资产的全部,现在只拥有150亿美元的68.75%(≈103.13亿美元),净增3.13亿美元。但如果没有增发,他们本可拥有110亿;这里,新股东以“折扣”方式分享了部分增值(因为溢价压缩)。

  • 并非真实增值:增发的50亿美元是外部资金注入,不是公司内部创造的价值。它的“增值”只是会计幻觉——类似于你把别人的钱存入自家银行,然后声称家庭财富增加了。

  • 溢价压缩是预警:初始10%溢价反映市场对“增长潜力”的乐观(如期待更多增发循环)。但每次增发都稀释这个潜力,导致溢价逐步下降(从10%到6.67%,下次更低)。

  • 为什么?因为公司本质上是“ETH持有壳”,无独特业务,市场会逐渐视其为ETH ETF(市值 ≈ 净资产,溢价 → 0)。一旦溢价为0,进一步增发就无法以高于净资产的价格进行,否则没人买单。

3. 如果持续循环,效应会放大并破坏模型

假设重复例子几次(每次融资相当于当前资产的50%,以当时股价增发,假设股价不变):

  • 第1轮后:资产150亿,市值160亿,溢价6.67%。

  • 第2轮:融资75亿(50% of 150),新股数 ≈0.46875S'(S'为当前股本),新资产225亿,新市值235亿,溢价 ≈4.44%,每股净资产增但溢价继续降。

  • 第3轮:类似,溢价降至≈3%。

经过几轮,溢价趋近0。这时:

  • 增发价格被迫等于每股净资产(无溢价空间)。

  • 每股净资产不再增加:例如,资产A,股本T,增发0.5A(以A/T定价),新股数=0.5T,新资产1.5A,新每股=1.5A / 1.5T = A/T(不变)。

  • 循环失效:无“股价上涨”驱动下次增发,模型从“增值”转为“零和”——新资金只是稀释旧股,无净益。

这正是稀释效应的显现:早期靠溢价掩盖,后期暴露,导致价值转移(新股东低成本进入,旧股东权益摊薄)。

4. 如果不是市场价增发,稀释更明显(贴近“平价增发”场景)

5. 为什么这个效应在实践中无法回避

  • 市场不是无限理性或乐观:你的假设依赖市场永远接受“股价不变”,但投资者会计算稀释(用EV/EBITDA或NAV折扣模型)。一旦意识到模型无内在现金流(无分红、只靠ETH持有),FOMO转为恐慌,股价提前崩。

  • 数学本质:稀释是算术必然。除非增发带来的增长率 > 稀释率(Gordon模型:价值 = \frac{D}{r – g},g为增长,但g依赖外部ETH涨,非永续),否则价值不增。

总之,BMNR的新股东通过增发,不断蚕食老股东的权益,只是掩盖在ETH上涨之中。其他币股也是类似,增发规模/当前市值比例越大,稀释效应越快!


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