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Asymptotic Behavior of the Net Present Value
Abstract
The net present value (NPV) of an investment is typically estimated by discounting the expected future cash flows at a rate, which is an estimator of the risk adjusted rate of return R. The estimator of the risk adjusted rate of return R is based on the historical record of the returns of comparable investments and is derived by utilizing models such as the Capital Asset Pricing Model. The paper examines the asymptotic behavior of the estimator of the NPV under assumptions and regularity conditions. In particular, it is assumed that the investment will never be completely wiped out or, alternatively, that the investor will have some capital protection and cut the losses at a preset level. The error of estimation is approximated up to an order of o(t -1/2), where t denotes the size of the sample used to estimate R. The discussion concludes with three applications: the case of independent identically distributed observations, truncated regression and censored regression.
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