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金融 1958

《资本成本、公司财务与投资理论》

佛朗哥·莫迪利亚尼 与 默顿·米勒

公司怎么融资——举债还是发股——并不改变它值多少。

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In depth · the introduction

公司若把一部分钱靠借贷筹来,而不是全部发股票卖掉,它会因此更值钱吗?两位经济学家证明:在完美的市场里,答案干脆是「不会」。

核心思想

一家公司值多少,取决于它的资产预期能赚多少。它怎么为这些资产付钱——卖股、借债,或两者混搭——不过是把同一块饼,在投资者之间切得不同罢了。佛朗哥·莫迪利亚尼与默顿·米勒在 1958 年证明:在一个没有税、没有别的摩擦的市场里,这些切片加起来永远不会比整块饼更多(也不会更少)。借债看起来便宜,但这份便宜,恰好被它甩给留下来的股东的那份额外风险所抵消。

它是怎么来的

1950 年代,多数专家相信每家公司都有一个理想的负债量——借进恰到好处的廉价债务,使资本成本最低、公司价值最高。莫迪利亚尼(经济学家)与米勒(金融学者),同在匹兹堡的卡内基理工,用一件纯经济学的工具来攻这道题:套利。倘若一家有杠杆的公司当真比一家完全相同、却无杠杆的公司更值钱,你大可自己借一点钱,复制出那家有杠杆公司的回报,再买下便宜的那家,凭空赚一笔。既然天上不会一直掉馅饼,这两家公司就必须一样值钱。这套论证干净得近乎令人恼火——而且它是对的。

它为何重要

它把一个含糊的实务问题,变成了一条锋利的定理,并给了金融学一个前所未有的基准。一旦你知道在无摩擦的世界里融资无关紧要,你就能问那个真正有用的问题:在这里,是哪一种摩擦让它变得要紧?是税(利息可抵扣,于是债务能省下一笔税)?是破产的危险(债太多,遇上糟糕的年景就会沉没)?是经理与投资者之间的不信任?关于「该借多少」的每一条实务经验,如今都被理解为对 MM 的这些偏离之一。

一个日常的比方

默顿·米勒爱用一块披萨来讲它。整块披萨就是这家公司。你可以把它切成两大片,或八小片,把一些片分给放贷人、一些片分给股东——但无论怎么切,都不会切出更多披萨。饼的大小由面团决定,而非由刀决定。债务与股权,不过是同一份晚餐切出的、形状不同的片而已。

一个面板,用滑块给公司加债。左侧的柱子分成股权与债务两段,无论怎么切分,总高度不变。右侧的图显示:随着债务增加,股东要求的回报沿直线上升,而公司的平均资本成本始终保持水平。

它在故事里的位置

莫迪利亚尼–米勒是现代金融的奠基石之一,与马科维茨的分散化投资组合(1952)奠基于同一个十年,又早于布莱克–斯科尔斯为期权定价(1973)一代人——后两者也在本馆——它们共用同一台引擎:在一个不可能凭空赚钱的市场里,价格靠无套利彼此对齐。两位作者后来都获得了诺贝尔经济学纪念奖。每一门金融课至今仍从这里讲起,因为你若不先弄懂「债务本不要紧」的那个世界,就无法弄懂债务为何要紧。

The original document
Original source text
Franco Modigliani & Merton H. Miller · The American Economic Review 48(3): 261–297 · June 1958
The question
A firm can raise the money to buy its assets by issuing shares (equity) or by borrowing (debt), in any mix it likes. The reigning view held that there was an optimal mix — some debt is cheap, so a little leverage should lower the overall cost of capital and raise the firm's value. Modigliani and Miller asked whether that is actually true in a market where investors can borrow and lend on the same terms as firms.
Proposition I
…the market value of any firm is independent of its capital structure and is given by capitalizing its expected return at the rate ρ_k appropriate to its class.
The proof is an arbitrage argument. If two firms with the same expected earnings sold for different prices merely because one was levered and the other not, an investor could replicate the levered firm's payoff by borrowing on personal account (homemade leverage), buy the cheaper firm, and pocket a riskless profit. Such trades would erase the price gap. It follows that the weighted average cost of capital is the same whatever the debt–equity mix.
Proposition II
If the average cost of capital is fixed, then loading on cheap debt cannot be a free lunch: the expected return that the remaining shareholders demand must rise just enough to offset it. Proposition II states this precisely — the cost of equity equals the pure-equity rate ρ_k plus a risk premium equal to the debt-to-equity ratio times the spread between ρ_k and the interest rate. The two movements cancel, and the average cost of capital stays flat.
What is assumed away
The result lives in a frictionless world: no taxes, no bankruptcy or distress costs, no asymmetric information, and firms and investors borrowing at the same rate. The authors knew these were idealisations; the value of the theorem is as a benchmark. In a 1963 correction the same authors added the corporate income tax, under which interest is deductible — a tax shield that does make leverage raise value, up to the point where distress costs begin to bite.
[ … ]
Carnegie Institute of Technology · 1958