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Proper Risk Resolution in Replacement Chain Analysis
Abstract
This paper Identifies situations in which the widely recommended procedures for evaluating mutually exclusive projects with unequal lives may result in incorrect project rankings. These situations arise from the failure of conventional techniques to place alternatives on an appropriate equivalent-risk basis and may occur whether a net present value or equivalent annual annuity approach is utilized. We develop alternative discounted cash flow procedures which correctly reflect the nature of risk. In so doing, we address the following important issues: 1) the choice of the discount rate to be used in calculating the net present value of a series of replications of a project: 2) the choice of a discount rate for calculating the equivalent annual annuity for a series of replications: and 3) the selection of an appropriate common-life horizon for comparison of alternative projects.
The relative performance of six capital budgeting decision procedures for dealing with risk was studied using Monte Carlo computer simulation of long sequences of capital rationing decisions involving risk. Five of the decision procedures included either subjective or objective risk assessment and used common measures of worth: Net Present Value, Internal Rate of Return, and Payback Period. The sixth decision procedure was random selection. Also investigated were (1) the effects of errors in risk assessment and (2) the effectiveness of the decision strategy to prefer opportunities with short-term capital recovery periods to reduce the exposure to risk of the capital invested.
When evaluating mutually exclusive projects of unequal lives and with differing risk, standard approaches such as the constant chain of replacement, lowest common multiple and equivalent annual value techniques are usually applied. In using these techniques to rank projects, a critical issue is the manner in which uncertainty in the cashflows is resolved through time. We explore the applicability of net present value techniques to the problem of valuing assets with unequal lives, emphasising the use of equivalent annual value and lowest common multiple methods, and the correct choice of discount rate. Our results have direct application to practical capital budgeting problems such as choosing the optimum lifespan for a single asset, choosing between assets with different lifespans, and deciding whether to “run an asset for another year”.
This study compares two discounting methods for evaluating multi-period stochastic income streams that are identical and independent over time. These two methods are based on the single-risk-adjusted-dlscount factor (SRADF), and the certainty-equivalent-discount factor (CEDF) They involve two alternative assumptions regarding the time pattern of the exchange rate between flaky and riskless Income streams. We demonstrate that the standard SRADF method leads to a different result than that implied by the CEDF method when the time horizon is longer than one period
This paper provides a criterion that can be applied to evaluate mutually exclusive investment options with different economic lives in an inflationary environment. This criterion - denoted as the equivalent real annual cost procedure - is more computationally efficient thatn the alternative "replacement chain" approach. Moreover, the equivalent real annual cost method is remarkably similar in its calculations and in its intuitive appeal to the well known equivalent annual cost method.
This paper is concerned with the valuation of multiperiod cash flows in a world where prices are determined according to the Sharpe-Lintner-Black model of capital market equilibrium. We find that the current market value of any future net cash flow is the current expected value of the flow discounted at risk-adjusted discount rates for each of the periods until the flow is realized. The discount rates are known and non-stochastic, but the rates for the different periods preceding the realization of a cash flow need not to be the same, and the rates relevant for a given period can differ across cash flows. The risk adjustments in the discount rates arise because of uncertainties about reassessments through time of the expected value of a flow and the relationships between these reassessments and the corresponding reassessments of the expected cash flows of all firms.
We embed the Sharpe-Lintner, two-parameter asset pricing theory in an intertemporal general equilibrium model. The investment opportunity set changes stochastically over time; in general the short-term and long-term interest rates and the distribution of the rate of return of the market portfolio are non-stationary. This non-stationarity, which is admissible in the Sharpe-Lintner model, has two implications: First, it may bias econometric methods which fail to explicitly take into account the non-stationarity. Second, the sequential application of the Sharpe-Lintner model in the discounting of stochastic cash flows becomes computationally complex and of little practical use.