The Cash-Cap Model: A Two-State Model of Firm Dynamics

Ali Kakhbod, Max Reppen, Tarik Umar, Hao Xing - May 28, 2022

How does a firm’s optimal cash, issuance, default, payout, and investment policies vary over its life cycle? To answer this question, we relax the assumption of homogeneity in size in models of firm dynamics. Our Cash-Cap model has two state variables: cash and capital. We find support in the data for new predictions: (1) issuance-to-capital ratios decrease convexly in capital, (2) payout-to-capital ratios are concave in capital, (3) investment-to-cash holdings sensitivities decrease in capital, and (4) cash holdings-to- volatility sensitivities increase in capital. We prove the uniqueness of the model solution and convergence of the numeric algorithm.

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