Valor presente

Economics Letters 84 (2004) 427 – 432
www.elsevier.com/locate/econbase

Present value criterion: the case of differing borrowing and lending rates
Liqun Liu *, Andrew J. Rettenmaier, Thomas R. Saving
Private Enterprise Research Center, Texas A&M University, College Station, TX 77843-4231, USA Received 1 March 2004; accepted 9 March 2004
Available online 4 June 2004

Abstract This paperexamines the present value criterion in a capital market with differing borrowing and lending rates. The more general present value criterion not only extends its applicability, but also enables us to better understand some features of the traditional present value criterion for a perfect capital market. D 2004 Elsevier B.V. All rights reserved.
Keywords: Present value criterion; Project evaluationJEL classification: G31; D92

1. Introduction In an environment of certainty and perfect capital markets, the welfare foundation of the net present value (NPV) criterion for project evaluation has long been established (Fisher, 1930; Hirshleifer, 1958). That is, any non-satiated investor will choose an independent investment project if and only if its NPV is positive. Further, an investor willchoose a project with the largest NPV from a set of mutually exclusive projects. On the other hand, the internal rate of return (IRR) of a project may either have multiple or no solutions, rendering the IRR criterion for project evaluation non-applicable in those situations. Moreover, when choosing among mutually exclusive projects, even if all projects have unique, positive internal rates ofreturn, a direct comparison of project IRRs may produce a ranking different from the NPV criterion (Lorie and Savage, 1955). This latter drawback of IRR is also inherited by all so-called ‘‘modified internal rate of return’’ (MIRR) concepts,1 as well as by
* Corresponding author. Tel.: +1-979-845-7723; fax: +1-979-845-6636. E-mail address: LLIU@TAMU.EDU (L. Liu). 1 See Bernhard (1979) for a criticalreview of various versions of MIRR. 0165-1765/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2004.03.013

428

L. Liu et al. / Economics Letters 84 (2004) 427–432

Teichroew et al.’s (1965) rate of return approach based on the concept of uncovered project balances. Thus, in selecting from a set of mutually exclusive projects using any rate of returncriterion, one has to compare the projects in the set pair by pair and calculate incremental rates of return. In contrast, direct comparison of the projects’ NPVs reveals the best project. The extra effort associated with using any rate of return criterion to select from a set of mutually exclusive projects clearly gives the NPV criterion an advantage. However, the NPV criterion has its ownlimitations. For example, it is not clear what discount rate to use when the interest rate is uncertain. This is especially troublesome since it is possible for the NPV to either increase or decrease as the discount rate increases (Ramsey, 1970; Bernhard and Norstrom, 1980; Oehmke, 2000). These conclusions on the merits and shortcomings of the present value criterion are conducted in a perfect,frictionless capital market framework, where funds can be lent (or reinvested) and borrowed without limit at the same interest rate. In this paper we examine the present value criterion in a more realistic and more general framework, in which the borrowing rate exceeds the lending rate. In this case, a project’s traditional NPV is not well defined. We build on two generalized present values originallydeveloped by Pye (1966): the ‘‘neutralizing present value’’ (NPVN) and the ‘‘generating present value’’ (NPVG).2 With these two generalized present values, Pye established the welfare foundation for the present value criterion in a capital market with differing borrowing and lending rates: (i) accepting an independent project with a positive NPVN will make every non-satiated investor better off...