Conceptual Problems in the Use of Risk-Adjusted Discount Rate for Risky Negative Cash Flows

Anastasia  Blaset Kastro; Nikolay  Kulakov

doi:10.17323/j.jcfr.2073-0438.15.1.2021.67-76

Anastasia Blaset Kastro All-Russian Research Institute of Metrology Service, Moscow, Russia https://orcid.org/0000-0002-9756-4077
Nikolay Kulakov The Moscow Investor Club, Moscow, Russia https://orcid.org/0000-0002-5574-0466

DOI: https://doi.org/10.17323/j.jcfr.2073-0438.15.1.2021.67-76

Keywords: nonconventional project, net present value, NPV, risk, risk adjusted discount rate, RADR, negative cash flows, risk premium, risk penalty

Abstract

This paper examines the risk adjusted discount rate (RADR) method for evaluating risky nonconventional projects, which has been hotly debated over the last century [1]. Economists face the contradiction of using the NPV rule to evaluate projects with different levels of risk. According to the theory of investments, the higher the project risk, the greater the return for the investor. Therefore, an increased discount rate is used to evaluate a riskier project, as a result, the project’s NPV decreases and the project is deemed less attractive or even unprofitable for investment. However, the NPV of a nonconventional investment project may increase through increasing the discount rate, and then the investor, following the NPV rule, will choose a riskier project out of two projects with the same yield. That does not correspond to the hypothesis about rational investor behavior.

We continue the study of the RADR method. Recently, published works [2–4] have proposed a solution to the debatable RADR problem. The GNPV method was used for evaluating risky nonconventional projects. We will evaluate these aspects of the recent literature. We examine the fallacy of the main arguments (to maintain value additivity and preclude arbitrage) justifying the application of a single rate to discount risky opposite sign cash flows. The future cash flows are estimated independently of the transactions preceding them, which seems illogical, so a risk penalty formula which adjusts the discount rate applied to risky negative cash flows is applied. The risk penalty is determined depending on the risk premium in the case of symmetric and asymmetric distribution of cash flow values.

Our results are applicable to a diverse range of business applications, including but not limited to well-known asset pricing models, short position analysis, determining fair insurance premiums, and calculating appropriate RADRs for public private partnerships.

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