6.5 Modigliani & Miller (“M & M”): “Proposition One” The Formula

In the following discussion, it is important to keep in mind the arguments already presented to this point.

Before we get further into it, let’s (re-) state the underlying restrictive assumptions:


  1. Markets are perfect
    • Managers and investors share identical information about the firm’s future earnings prospects
  1. Corporations and investors can borrow at the same rate
  2. There are no taxes, no transaction costs
    • This restriction enables M&M to assert that investors can “create” their own dividend policy.
    • Investors are indifferent as between receiving dividends or the allowing the corporation to instead retain earnings


“Proposition I”: “The Irrelevance Proposition”

This (first of numerous) proposition(s) states that Capital Structure does not matter.  Therefore, the value of a company’s assets and hence (if the balance sheet is to match) the (market) value of its capital – including both its debt and equity, is the present value of its operating earnings (EBIT) discounted a rate of return commensurate with its risk, as defined by the standard deviation of the firm’s EBIT. We can say this formally as:

V = D + E = EBIT / R


V =

M =

… the market value of the firm

… the market value of the firm’s assets

D + E = … the market value of the firm’s total capital.
EBIT = … Operating earnings
R = … a discount rate commensurate with the firm’s operating/business risk


Some of the implications include:

  1. Changes in capital structure alter the respective risks of the capital components, but not the overall firm risk or value. This is to say succinctly that a levered (or unlevered) Beta for any given capital component is independent of firm (i.e., operating or unsystematic) risk. The respective Betas of the firm’s capital can change with no change in overall firm Beta.
    • If there are no taxes or transaction costs, stock prices and equity capital costs are also unaffected.
  1. There is a significant dichotomy between the firm’s business- and financial-risks.
    • EBIT, i.e., operating profit, is generated by the firm’s assets (and management’s skill in exploiting the assets).
    • Business risk has to do with the variability of the firms’ operating cash earnings (EBITDA). Financial risk has to do with financing choices and its proportionate distribution amongst lenders (i.e., paying interest) and owners (i.e., paying dividends and retaining additional earnings).
    • Increasing leverage passes on more financial risk to shareholders.
  1. The discount rate, which is used, is the required return on the firm’s assets, and is based on the variability of EBIT and thus ROA as well.
  2. In the absence of debt (i.e., an all-equity capitalization structure) the return on equity will equal the return on assets: ROA = ROE.
    • If there is no debt, EBIT = NI, EQ = TA, and EBIT / TA = NI / EQ.
      •  Remember: we are still ignoring Taxes.
    • This also says that leverage can potentially enhance ROE (vs. ROA) similar to what we saw with the DuPont Model.
  1. Although this model, as it is, does not neatly – or at all – conform to actual market conditions, M&M have nonetheless, provided us with some valuable insights.


M&M offered additional propositions, increasingly relaxing earlier assumptions and providing additional alternatives.

    • M&M do not address stock pricing – unless you assume no taxes (i.e., Prop I). That’s the domain of the DDM.
    • M&M focus on the firm’s overall risk and value, not bond or stock prices.



Business Risk = f (σ EBIT, σ ROA)

Financial Risk = f (σ NI, σ EPS, σ ROE)


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Corporate Finance Copyright © 2023 by Kenneth S. Bigel is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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