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金融 1958

《資本成本、公司財務與投資理論》

法蘭哥·莫迪利亞尼 與 默頓·米勒

公司怎麼融資——舉債還是發股——並不改變它值多少。

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In depth · the introduction

公司若把一部分錢靠借貸籌來,而不是全部發股票賣掉,它會因此更值錢嗎?兩位經濟學家證明:在完美的市場裡,答案乾脆是「不會」。

核心思想

一家公司值多少,取決於它的資產預期能賺多少。它怎麼為這些資產付錢——賣股、借債,或兩者混搭——不過是把同一塊餅,在投資者之間切得不同罷了。法蘭哥·莫迪利亞尼與默頓·米勒在 1958 年證明:在一個沒有稅、沒有別的摩擦的市場裡,這些切片加起來永遠不會比整塊餅更多(也不會更少)。借債看起來便宜,但這份便宜,恰好被它甩給留下來的股東的那份額外風險所抵消。

它是怎麼來的

1950 年代,多數專家相信每家公司都有一個理想的負債量——借進恰到好處的廉價債務,使資本成本最低、公司價值最高。莫迪利亞尼(經濟學家)與米勒(金融學者),同在匹茲堡的卡內基理工,用一件純經濟學的工具來攻這道題:套利。倘若一家有槓桿的公司當真比一家完全相同、卻無槓桿的公司更值錢,你大可自己借一點錢,複製出那家有槓桿公司的回報,再買下便宜的那家,憑空賺一筆。既然天上不會一直掉餡餅,這兩家公司就必須一樣值錢。這套論證乾淨得近乎令人惱火——而且它是對的。

它為何重要

它把一個含糊的實務問題,變成了一條鋒利的定理,並給了金融學一個前所未有的基準。一旦你知道在無摩擦的世界裡融資無關緊要,你就能問那個真正有用的問題:在這裡,是哪一種摩擦讓它變得要緊?是稅(利息可抵扣,於是債務能省下一筆稅)?是破產的危險(債太多,遇上糟糕的年景就會沉沒)?是經理與投資者之間的不信任?關於「該借多少」的每一條實務經驗,如今都被理解為對 MM 的這些偏離之一。

一個日常的比方

默頓·米勒愛用一塊披薩來講它。整塊披薩就是這家公司。你可以把它切成兩大片,或八小片,把一些片分給放貸人、一些片分給股東——但無論怎麼切,都不會切出更多披薩。餅的大小由麵團決定,而非由刀決定。債務與股權,不過是同一份晚餐切出的、形狀不同的片而已。

一個面板,用滑桿給公司加債。左側的柱子分成股權與債務兩段,無論怎麼切分,總高度不變。右側的圖顯示:隨著債務增加,股東要求的回報沿直線上升,而公司的平均資本成本始終保持水平。

它在故事裡的位置

莫迪利亞尼–米勒是現代金融的奠基石之一,與馬科維茨的分散化投資組合(1952)奠基於同一個十年,又早於布萊克–斯科爾斯為期權定價(1973)一代人——後兩者也在本館——它們共用同一台引擎:在一個不可能憑空賺錢的市場裡,價格靠無套利彼此對齊。兩位作者後來都獲得了諾貝爾經濟學紀念獎。每一門金融課至今仍從這裡講起,因為你若不先弄懂「債務本不要緊」的那個世界,就無法弄懂債務為何要緊。

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