Corporate Finance - Comparing Projects With Unequal Lives
There are two methods used to make the adjustments:
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 IRR of Machine A is equal to 8.3%.
The IRR of Machine B is equal to 15.5%.
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%.
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
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.
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.
Career Education & ResourcesLearn about the difficulty of the CFA exams with a description of the tests, some statistics on pass rates and suggestions that can help you pass the exams.
ProfessionalsBecome one of the elite who pass these exams by using these simple study methods.
Financial AdvisorsPotential financial advisors, analysts or asset managers have many credentials and degrees from which to choose. Here's a look at the CFA vs. the MBA.
Your PracticeIf you want to become an RIA all you have to do is pay a $165 fee to the SEC and pass the Series 65 exam. Is the bar set too low?
ProfessionalsTo pass the CFA exam, get organized, develop an effective study program and review.
ProfessionalsHere are some pros and cons to consider before you take the CFA charter plunge.
ProfessionalsFinding that first finance job is not easy, but these five tips can boost your chances even before you graduate.
ProfessionalsThe right accounting certification can open the doors of opportunity.
ProfessionalsA financial analyst researches companies and economic conditions to make business, sector and industry recommendations.
Career Education & ResourcesRead about what it takes to become a financial analyst in a corporation or securities firm, and learn how far you can rise in the profession.
A professional designation given by the CFA Institute (formerly ...
Professionals who help individuals manage their finances by providing ...
Formerly known as the Association for Investment Management and ...
A financial professional who studies various industries and companies, ...
Understand the differences between a Chartered Financial Analyst and a Certified Financial Planner. Learn how each approaches ... Read Answer >>
Understand what it means to hold the Chartered Financial Analyst designation. Learn how a candidate can work to become a ... Read Answer >>
Understand what types of positions a Chartered Financial Analyst can hold. Learn what is available to those who have only ... Read Answer >>
Learn who benefits most when expenses are prepaid. Individuals and businesses often make payments, such as rent or insurance, ... Read Answer >>
If you are looking specifically for an investment banking position, an MBA may be marginally preferable over the CFA. The ... Read Answer >>
You may still pass the Chartered Financial Analysis (CFA) Level I even if you fare poorly in the ethics section, but don't ... Read Answer >>