LG 6 12.5 Capital Budgeting Refinements
LG 5 LG 6 12.5 Capital Budgeting Refinements
Refinements must often be made in the analysis of capital budgeting projects to accommodate special circumstances. These adjustments permit the relaxation of certain simplifying assumptions presented earlier. Three areas in which special forms of analysis are frequently needed are (1) comparison of mutually exclusive projects having unequal lives, (2) recognition of real options, and (3) capital rationing caused by a binding budget constraint.
COMPARING PROJECTS WITH UNEQUAL LIVES The financial manager must often select the best of a group of unequal-lived proj-
ects. If the projects are independent, the length of the project lives is not critical. But when unequal-lived projects are mutually exclusive, the impact of differing lives must be considered because the projects do not provide service over compa- rable time periods. This is especially important when continuing service is needed from the project under consideration. The discussions that follow assume that the unequal-lived, mutually exclusive projects being compared are ongoing. If they
were not, the project with the highest NPV would be selected.
The Problem
A simple example will demonstrate the basic problem of noncomparability caused by the need to select the best of a group of mutually exclusive projects with differing usable lives.
Example 12.7 3 The AT Company, a regional cable television company, is evaluating two proj- ects, X and Y. The relevant cash flows for each project are given in the following
table. The applicable cost of capital for use in evaluating these equally risky proj-
CHAPTER 12
Risk and Refinements in Capital Budgeting
Project X
Project Y
Initial investment
Annual cash inflows
Project X Calculator Use Employing the preprogrammed NPV function in a financial cal- culator, we use the keystrokes shown at the left for project X and for project Y to
Input Function
CF 0 find their respective NPVs of $11,277.24 and $19,013.27.
CF 1 Spreadsheet Use The net present values of two projects with unequal lives also
CF 2 can be compared as shown on the following Excel spreadsheet.
38000 CF 3
10 I A B C
COMPARISON OF NET PRESENT VALUES OF TWO PROJECTS WITH
NPV
Solution
1 UNEQUAL LIVES
2 Cost of Capital
3 Year-End Cash Flows
4 Year
Project X
Project Y
Project Y
13 Choice of project
Project Y
CF 5 Entry in Cell B12 is
CF 6 =NPV($C$2,B6:B11)+B5. 10 I Copy the entry in Cell B12 to Cell C12.
Entry in Cell C13 is =IF(B12>=C12,B4,C4). Solution
NPV
Ignoring the differences in project lives, we can see that both projects are acceptable (both NPVs are greater than zero) and that project Y is preferred over project X. If the projects were independent and only one could be accepted, project Y—with the larger NPV—would be preferred. If the projects were mutu- ally exclusive, their differing lives would have to be considered. Project Y pro- vides 3 more years of service than project X.
The analysis in the preceding example is incomplete if the projects are mutu- ally exclusive (which will be our assumption throughout the remaining discus-
PART 5
Long-Term Investment Decisions
must consider the differing lives in the analysis; an incorrect decision could result from simply using NPV to select the better project. Although a number of approaches are available for dealing with unequal lives, here we present the most efficient technique—the annualized net present value (ANPV) approach.
Annualized Net Present Value (ANPV) Approach
annualized net present value The annualized net present value (ANPV) approach 6 converts the net present (ANPV) approach
value of unequal-lived, mutually exclusive projects into an equivalent annual
An approach to evaluating
amount (in NPV terms) that can be used to select the best project. 7 This net
unequal-lived projects that
present value based approach can be applied to unequal-lived, mutually exclusive
converts the net present value of unequal-lived, mutually
projects by using the following steps:
exclusive projects into an
Step 1 Calculate the net present value of each project j, NPV j , over its life, n j ,
equivalent annual amount (in
using the appropriate cost of capital, r.
NPV terms).
Step 2 Convert the NPV j into an annuity having life n j . That is, find an annuity that has the same life and the same NPV as the project.
Step 3 Select the project that has the highest ANPV.