Corporate Finance - Comparing Projects With Unequal Lives

As mentioned previously, NPV and IRR can sometimes lead to conflicting results in the analysis of mutually exclusive projects. One reason for this potential problem is the timing of the cash flows of the mutually exclusive projects. As a result, we need to adjust for the timing issue in order to correct this problem.

There are two methods used to make the adjustments:
1. Replacement-chain method
2. Equivalent annual annuity

Example:
Once again, assume Newco is planning to add new machinery to its current plant. There are two machines Newco is considering, with cash flows as follows:

Figure 11.8: Discounted cash flows for Machine A and Machine B



Compare the two projects with unequal lives using both the replacement-chain method and the equivalent annual annuity (EAA) approach.

1. Replacement-Chain Method
In this example, Machine A has an operating lifespan of six years. Machine B has an operating lifespan of three years. The cash flows for each project are discounted by Newco's calculated WACC of 8.4%.
  • NPV of Machine A is equal to $2,926.
  • NPV of Machine B is equal to $1,735.
     
The initial analysis indicates that Machine A, with the greater NPV, should be the project chosen.
  • The IRR of Machine A is equal to 8.3%.
  • The IRR of Machine B is equal to 15.5%.
     
This analysis indicates that Machine B, with the greater IRR, should be the project chosen.
The NPV analysis and the IRR analysis have given us differing results. This is most likely due to the unequal lives of the two projects. As such, we need to analyze the two projects over a common life.

For Machine A (project 1), the lifespan is six years. For Machine B (project 2), the lifespan is three years. Given that the lifespan of the longest project is six years, in order to measure both over a common life, we must adjust the lifespan of Machine B to six years.

Because the lifespan of Machine B is three years, the lifespan of this project needs to be doubled to equal the six-year lifespan of Machine A. This indicates that another Machine B would have to be purchased (to get two machines with a lifespan of three years each) to get to the six-year lifespan of Machine A - hence, the replacement-chain method.

The new cash flows would be as follows:

Figure 11.9: Cash flows over a common life

  • NPV of Machine A remains $2,926.
  • NPV of Machine B is now $3,098 given the adjustment.

The initial analysis indicates that Machine B, with the greater NPV, should be the project chosen. Recall, this is different from our first analysis where Machine A was chosen given its greater NPV.

  • The IRR of Machine A remains 8.3%.
  • The IRR of Machine B remains 15.5%.
Look Out!
Note, while the NPV has changed given the additional cash flows, the IRR for the projects remain the same.



This analysis indicates that Machine B, with the greater IRR, should be the project chosen. Recall, this is the same as our first analysis, where Machine B was chosen given its greater IRR.

With the cash flows adjusted with the replacement-chain method, both the NPV and the IRR arrive at the same conclusion. With this adjusted analysis, Machine B (project 2), should be the project accepted.

2. Equivalent-Annual-Annuity Approach
While easy to understand, the replacement-chain method can be time consuming. A simpler approach is the equivalent-annual-annuity approach.

This is the procedure for determining EAA:

1) Determine the projects' NPVs.
2) Find each project's EAA, the expected payment over the project's life, where the future value of the project would equal zero.
3) Compare the EAA of each project and select the project with the highestEAA.

From our example, the NPV of each project is as follows:
-NPV of Machine A is equal to $2,926.
-NPV of Machine B is equal to $1,735.

To determine each project's EAA, it is best to use your financial calculator.

- For, Machine A (project 1), our assumptions are as follows:

i = 8.4% (the company's WACC)
n = 6
PV = NPV = -2,926
FV = 0
Find PMT

For Machine A, the EAA (the calculated PMT) is $640.64.

- For Machine B (project 2), our assumptions are as follows:

i = 8.4% (the company's WACC)
n = 3
PV = NPV = -1,735
FV = 0
Find for PMT

For Machine B, the EAA (the calculated PMT) is $678.10.

Answer
Machine B should be the project chosen as it has the highest EAA, which is $678.10, relative to Machine A whose EAA is $640.64.

Inflation Effects on Capital Budgeting Analysis
Inflation exists and should not be forgotten when making capital-budgeting decisions. It is important to build inflation expectations into the analysis. If inflation expectations are left out of the capital-budgeting analysis, the NPV calculated from the biased cash flows will be incorrect.

As an example, suppose Newco unintentionally leaves out its inflation expectations when determining the plant addition. Since inflation expectations are included in the WACC, and PV of each cash flow is discounted by the WACC, the NPV will be incorrect and have a downward bias.

 

Types of Risk


Related Articles
  1. Investing Basics

    Capital Budgeting: Capital Budgeting Decision Tools

    Once projects have been identified, management then begins the financial process of determining whether or not the project should be pursued. The three common capital budgeting decision tools ...
  2. Investing Basics

    Capital Budgeting: The Capital Budgeting Process At Work

    This tutorial will conclude with some basic, yet illustrative examples of the capital budgeting process at work. Example 1: Payback PeriodAssume that two gas stations are for sale with the following ...
  3. Personal Finance

    An Introduction To Capital Budgeting

    We look at three widely used valuation methods and figure out how companies justify spending.
  4. Fundamental Analysis

    Calculating the Internal Rate of Return Using Excel

    The internal rate of return on investments is explained and illustrated in different investment scenarios.
  5. Fundamental Analysis

    Internal Rate Of Return: An Inside Look

    Use this method to choose which project or investment is right for you.
  6. Forex

    Understanding Internal Rate Of Return

    Internal rate of return, or IRR, is one of the most popular methods of evaluating potential projects. Learn more about this important metric.
  7. Professionals

    What Exactly Do Project Managers Do?

    While supervision is one important part of the job, a lot more goes into project management than just watching everyone work.
  8. Budgeting

    Why You Suddenly Can’t Buy Gift Cards

    Fraud liability falls on the party ill-equipped to handle consumers’ chip-and-pin cards. Merchants are scaling back gift card sales to protect themselves.
  9. Investing

    What's Capitalization?

    Capitalization has different meanings depending on the context.
  10. Stock Analysis

    5 Stocks With Solid Cash Flow

    While a company's reported earnings may not tell the whole story, cash flow usually does.
RELATED TERMS
  1. Net Present Value - NPV

    Net Present Value (NPV) is the difference between the present ...
  2. Internal Rate Of Return - IRR

    A metric used in capital budgeting measuring the profitability ...
  3. Total Project Approach

    A way to compare net income or contribution margin results by ...
  4. IRR Rule

    A measure for evaluating whether to proceed with a project or ...
  5. Net Present Value Rule

    A rule stating that an investment should be accepted if its net ...
  6. Modified Internal Rate Of Return ...

    While the internal rate of return (IRR) assumes the cash flows ...
RELATED FAQS
  1. How do you use discounted cash flow to calculate a capital budget?

    Learn how discounted cash flows are used in creating capital budgets as a part of the net present value and internal rate ... Read Answer >>
  2. Which is a better measure for capital budgeting, IRR or NPV?

    In capital budgeting, there are a number of different approaches that can be used to evaluate any given project, and each ... Read Answer >>
  3. Do you discount working capital in net present value (NPV)?

    Learn why changes in net working capital (NPV) should be included in net present value calculations for analyzing a project's ... Read Answer >>
  4. What is the formula for calculating net present value (NPV) in Excel?

    Understand how net present value is used to estimate the anticipated profitability of projects or investments and how to ... Read Answer >>
  5. What is the formula for calculating internal rate of return (IRR) in Excel?

    Understand how to calculate the internal rate of return (IRR) using Excel and how this metric is used to determine anticipated ... Read Answer >>
  6. What is the difference between present value and net present value?

    Understand the difference between the present value and net present value calculations and how these formulas are used in ... Read Answer >>
Hot Definitions
  1. Over-The-Counter - OTC

    Over-The-Counter (or OTC) is a security traded in some context other than on a formal exchange such as the NYSE, TSX, AMEX, ...
  2. Quarter - Q1, Q2, Q3, Q4

    A three-month period on a financial calendar that acts as a basis for the reporting of earnings and the paying of dividends.
  3. Weighted Average Cost Of Capital - WACC

    Weighted average cost of capital (WACC) is a calculation of a firm's cost of capital in which each category of capital is ...
  4. Basis Point (BPS)

    A unit that is equal to 1/100th of 1%, and is used to denote the change in a financial instrument. The basis point is commonly ...
  5. Sharing Economy

    An economic model in which individuals are able to borrow or rent assets owned by someone else.
  6. Unlevered Beta

    A type of metric that compares the risk of an unlevered company to the risk of the market. The unlevered beta is the beta ...
Trading Center