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This paper aims to clarify how contingent convertible bond (CoCo) as a debt financing instrument affects a firm's investment policy, agency cost of debt, and capital structure. We consider endogenous and exogenous conversion thresholds, respectively. Under the exogenous case, there is an explicit optimal fraction of equity allocated to CoCo holders upon conversion, such that the agency cost reaches zero. Numerical analysis demonstrates that under an endogenous conversion threshold, CoCo induces overinvestment, a higher leverage, a possible bigger agency cost, and a stronger incentive to increase risk. But if the conversion threshold is exogenously determined, almost the opposite holds true.

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The paper considers the option of an investor to invest in a project that generates perpetual cash flows, of which the drift parameter is unobservable. The investor invests in a liquid financial market to partially hedge cash flow risk and estimation risk. We derive two 3-dimensional non-linear free-boundary PDEs satisfied by the utility-based prices of the option and the cash flows. We provide an approach to measure the information value.A numerical procedure is developed. We show that investors have not only idiosyncratic-risk-induced but also estimation-risk-induced precautionary saving demands. A growth of estimation risk, risk aversion or project risk delays investment, but it is accelerated if the project is more closely correlated with the market. Partial information results in a considerable loss, which reaches the peak value at the exercising time and increases with project risk and estimation risk. The more risk-averse the investor or the weaker the correlation, the larger the loss.

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