An entrepreneur owns a business and bears significant risks/rewards from the business. Casual observations and empirical studies have shown that active businesses account for a large fraction of entrepreneurs’ total wealth and that entrepreneurial firms tend to have highly concentrated ownership. Moreover, entrepreneurs often face liquidity constraints. Lack of diversification and liquidity constraints cause business decisions (capital accumulation and entry/exit) and household decisions (consumption/saving and asset allocation) to be highly interdependent. In a recent survey of research, Quadrini (2009) discusses the importance of borrowing constraints and non-diversification on entrepreneurial career choice, entrepreneurial saving/investment, and economic development/growth.
We study the effects of liquidity constraints and non-diversification on entrepreneurial entry, capital accumulation/asset sale, consumption, portfolio allocation, and exit decisions in a dynamic framework. We then use the entrepreneur’s optimal decision rules to deliver an operational and analytically tractable framework for the cost of capital as well as the private valuation of an entrepreneurial firm.
Entrepreneurial Finance, as an academic field, offers no theoretical guidance on how to calculate the cost of capital for entrepreneurial firms. Non-diversifiable risk and other frictions that entrepreneurs face invalidate the textbook risk-return and capital budgeting analysis. Consider a project valuation exercise. Suppose that the standard capital asset pricing model (CAPM) works if this project is evaluated by a firm owned by diversified investors. The standard valuation technique is based on complete diversification and thus leaves no room for an idiosyncratic risk premium.
However, when the project is evaluated by an entrepreneurial firm whose owner is heavily exposed to the project’s subsequent performance and cannot fully diversify, we expect that the entrepreneur not only demands the systematic risk premium but also an additional “private” equity idiosyncratic risk premium. What are the determinants of this idiosyncratic risk premium? We provide an operational and economic framework to answer this fundamental question that arises in Entrepreneurial Finance. Our calibration exercise suggests that this idiosyncratic risk premium is likely to be significant for non-diversified entrepreneurs.
Our agent has a preference for intertemporal consumption smoothing. This preference separates the elasticity of intertemporal substitution (EIS) from risk aversion, i.e. an Epstein-Zin (1989) non-expected utility. The agent optimally chooses the timing to become an entrepreneur. Doing so forgoes the outside option (e.g. earning constant wages over time) and requires a fixed start-up cost. The entrepreneur also chooses the initial firm size. The entrepreneurial project/idea is defined by a capital accumulation/production technology.
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Dynamics of Entrepreneurship under Incomplete Markets
