Capital Budgeting Essay (Derived from Chapter 17: Long-Term Investment Analysis) Title: The Lorie-Savage Problem BUS 505 – Multinational Economics of Technology Table of Contents 1. 0Introduction – Lorie-Savage Problem3 1. 1 Thesis Statement3 2. 0Supporting Research4 3. 0Conclusions and Recommendations6 References7 1.
0 Introduction – Lorie-Savage Problem The Lorie-Savage problem is a problem introduced in 1955 that addresses the issue in how to allocate capital (or resources) among competing investment opportunities with constraints on the available resources. (Lorie & Savage, 1955, p. 29) In defining this problem, Lorie-Savage structures it by outlining three separate scenarios: 1) Given the cost of capital, what group of investments should be selected? 2) Given a fixed sum for capital investment, what group of investment proposals should be undertaken? 3) How to select the best among mutually exclusive alternatives? Lorie-Savage go on to state that the traditional method used at the time to drive investment decisions and maximize company profits and net worth is the rate-of-return method (now more commonly known as the internal-rate-of-return (IRR) method).It is clear that the authors have some reservations with this method part of their journal article is dedicated in proving that IRR has severe flaws and at times will not result in maximizing the net worth of a company from IRR based investment decisions.
(Lorie & Savage, 1955, p. 239) 1. 1 Thesis Statement The research below will demonstrate that the Lorie-Savage problem shows that the IRR method has severe flaws and therefore investment decisions should be made utilizing alternate, superior methods; the summarized research below ill demonstrate this thesis statement. These methods are the modified-internal-rate-of-return (MIRR) and net-present-value (NPV). Also additional methods using a technique known as ‘genetic programming’ has also shown to have superior results over IRR. 2.
0 Supporting Research As stated previously, the general solution methods for the Lorie-Savage problem are rate-of-return (or internal rate of return (IRR)) and net-present value (NPV) with additional techniques using genetic algorithms was found that also addresses the Lorie-Savage problem.Lorie-Savage state in their journal article their reservations on using IRR and provide examples to support that notion, in particular the situation of ranking of mutually exclusive projects. (Lorie & Savage, 1955, pp. 236-239) The flaws with the IRR method can be described in one way by relating it to the concept of Jensen’s Inequality, discovered in 1906, that states that for convex functions, the function of the expectation is always less than or equal to the expectation of the function itself.IRR is a curved function of cash flow, but the simulated values for the calculated IRR is expected to be linear, thus producing inherent biases. Jensen’s Inequality proves that these inherent biases will emerge when simulating IRR, which can lead to incorrect decisions unless these biases are identified and reported up front and early.
(Brown, 2006, p. 197) However, all is not lost with the IRR method.The modified-internal-rate-of-return (MIRR) method has been introduced that takes an additional step beyond the IRR method as it takes into account the risk of reinvestment, as well as adjusting the discount rate for those reinvestments given the risk provided. This is a significant improvement beyond the original IRR method, which also has advantages over NPV, primarily due to the fact that the reinvestment of future cash flows is specifically addressed. (Kierulff, 2008, pp.
328-329) In writing their paper Lorie-Savage essentially changed the opinion in the academic world in showing the advantages of NPV over IRR. Osbourne, 2010, p. 234) This was achieved by employing an implementation of trial and error using ‘Lagrange Multipliers’ with their defined equation: y-p1c1-p2c2, resulting in a decision to invest based on a positive final value from this equation. (Lorie & Savage, 1955, p. 234) Turns out this is an Integer Programming optimization problem as it has identified constraints with the end output being to either accept an investment (using the integer 1), or decline (using the integer 0). Since the Lagrange Multipliers are real values, this is more specifically classified as a Mixed Integer Programming problem.
Trick, 1998) Their research proved to be revolutionary as this strayed from the traditional accepted method in using IRR, and this research has evolved since. One example of this is demonstrated where Seymour Kaplan introduced the concept of applying the Generalized Lagrange Multiplier (G. L. M.
) method with Integer Programming, using the Lorie-Savage problem as a basis for comparison, that found favorable results in the effectiveness of G. L. M. in producing optimal solutions using NPV to make investment decisions. Kaplan, 1966, p.
1136) Building on this research was the introduction of using genetic algorithms (GA) to solve capital budgeting problems in allowing financial analysts to find optimal investment combinations for various situations, such as the multiple tax-structures a company may encounter. (Berry & Manongga, 2006, p. 96) Expanding on the GA implementation was research conducted that incorporated fuzzy set theory on problems when investment parameters contained scant or vague information and therefore had great uncertainty.Xiaoxia Huang created a new mean variance model using fuzzy variables and the GA approach that produces optimal capital budgeting decisions with “fuzzy available capital, fuzzy investment outlays, and fuzzy annual net cash flows”. (Huang, 2008, pp.
35, 45) These are only a few of the extensions researched on the solutions of IRR, NPV and genetic algorithms in helping to solve the capital budgeting dilemma in terms of which technique is the best to use. This is a rigorous debate with no clear cut answer. Osbourne states that NPV is super to the orthodoxIRR method; all while making no mention of the advantages MIRR has over both. (Osbourne, 2010, p. 238) (Kierulff, 2008, p. 328) One of the premier textbooks in the area of finance titled “Principles of Corporate Finance” by Brealey, Myers, and Allen, states the IRR is misleading due to the fact that managers may make a decision based on the largest discount rate and not the largest NPV.
(Brealey, Myers, & Allen, 2008, p. 130) 3. 0 Conclusions and Recommendations While there is no clear answer, it is widely accepted that IRR is the least advantageous when compared to the other methods.Yet IRR is highly likely to continue to be used by executives and managers due to their general familiarity with IRR (as well as their client’s familiarity). (Brown, 2006, p.
5) What a finance professional should take from this topic is that he/she needs to realize and accept that there is no general solution to the issue of which method is best to use to make the decision(s) on how “to ration available capital or liquid resources among competing investment opportunities” (as stated in the Lorie-Savage paper on page 229. What a finance professional should do is become knowledgeable with each method’s advantages and shortcomings. (Brown, 2006, p. 5) In doing so, his/her credibility is established and the subsequent investment decisions will in-turn be made by those who are well informed. References Berry, R.
H. , & Manongga, D. H. (2006). Integrating genetic algorithms and spreadsheets: a capital budgeting application.
Intelligent Systems in Accounting, Finance & Management , 14 (3), 87-97. Brealey, R. A. , Myers, S. C.
, & Allen, F. 2008). Principles of Corporate Finance. New York, NY, USA: McGraw-Hill Companies Inc.
Brown, R. J. (2006). Sins of the IRR. Journal of Real Estate Portfolio Management , 12 (2), 195-199. Huang, X.
(2008). Mean-variance Model for Fuzzy Capital Budgeting. Computers & Industrial Engineering , 55 (1), 34-47. Kaplan, S.
(1966). Solution of the Lorie-Savage and Similar Integer Programming Problems by the Generalized Lagrange Multiplier Method. Operations Research , 14 (6), 1130-1136. Kierulff, H.
(2008). MIRR: A Better Measure .Business Horizons , 51 (4), 321-329. Lorie, J.
H. , & Savage, L. J. (1955).
Three Problems in Rationing Capital. The Journal of Business , 28 (4), 229-239. Osbourne, M. J. (2010).
A resolution to the NPV–IRR debate? The Quarterly Review of Economics and Finance , 50 (2), 234-239. Trick, M. (1998). A Tutorial on Integer Programming. Retrieved April 05, 2011, from Michael Trick's Operations Research Page, Carnegie Mellon University: http://mat.
gsia. cmu. edu/orclass/integer/node2. html#SECTION00020000000000000000
