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An extension of Merton’s (1974) model (EMM) taking account of the firm’s payments and generating a new statistical distribution for the firm value is suggested. In an open log-value space, this distribution evolves from the initially normal to negatively skewed one. When payments are zero or proportional to the firm value, EMM turns into the Geometric Brownian model (GBM). We show that Modigliani-Miller Propositions (MMPs) and the no-arbitraging principle (NAP) result from the use of GBM with no payments. For a firm with payments, MMPs hold for short times and are false for time intervals exceeding a year. In contradiction with MMPs, the asset structure affects the firm value at the perfect market, and at the market with taxes, debt decreases the firm value even when there are no bankruptcy costs. NAP always holds for the entire market for short time deals. For long-term investments, the firm’s mean year returns decline in time intervals whose length depends on the firm’s initial conditions and its business environment. In these conditions, NAP does not hold for the whole market, but it temporarily holds for individual stocks as far as the mean year returns of the firms issuing them remain constant and fails when the mean year returns begin to decline.

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Extensions of Merton's model (EMM) considering the firm's payments and generating new types of firm value distribution are suggested. In the open log-value/time space, these distributions evolve from initially normal to negatively skewed ones, and their means are concave-down functions of time. When payments are set to zero or proportional to the firm value, EMM turns into the Geometric Brownian model (GBM). We show that risk-neutral probabilities (RNPs) and the no-arbitraging principle (NAP) follow from GBM. When firm's payments are considered, RNPs and NAP hold for the entire market for short times only, but for long-term investments, RNPs and NAP just temporarily hold for individual stocks as far as mean year returns of the firms issuing those stocks remain constant, and fail when the mean year returns decline. The developed method is applied to firm valuation to derive continuous-time equations for the firm present value and project NPV.

We use Extended Merton model (EMM) for estimating the firm's credit risks in the presence of inflation. We show quantitatively that inflation is an influential factor making either a benign or adverse effect on the firm's survival, supporting at the microeconomic level New Keynesian findings of the nonlinear inflation effect on output growth.Lower inflation increasing the firm's expected rate of return can raise its mean year returns and decrease its default probability. Higher inflation, decreasing the expected rate return, makes the opposite effect. The magnitude of the adverse effect depends on the firm strength: for a steady firm, this effect is small, whereas for a weaker firm, it can be fatal. EMM is the only model taking account of inflation. It can be useful for banks or insurance companies estimating credit risks of commercial borrowers over the debt maturity, and for the firm's management planning long-term business operations.