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What determines whether an investment should be made using debt vs. equity?

For example, startups are often financed with equity, while mortgages are always financed using debt. What characteristics about the investment (like risk, uncertainty, information, duration, etc) inform whether one or the other type of instrument is most efficient?

I would love a precise answer, in particular if there is a text book answer for this.

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Equity is for the bulls; debt is for the bears.

It depends on what kind of capital is available for financing and what the group needing capital can offer in terms of security. Early stage startups have nothing to offer but future returns (especially if they are cash-flow negative). A high risk investment with little collateral and a high burn rate may not be able to find debt financing at any interest rate, but there may be an investor willing to take an equity position. Alternatively, a bank may not see much upside in a single-family home, so would not be willing to take an equity position, but would be willing to except a lower rate of return on a 80% LTV.

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