Overview
This lecture explains how to compare mutually exclusive projects with different lifespans using the Equivalent Annual Annuity (EAA) method, rather than Net Present Value (NPV) alone.
Comparing Projects with Different Lives
- NPV is usually used to select the best project, but problems arise when project lifespans differ.
- Simply choosing the project with the highest NPV may not account for differences in project duration.
Example: Server A vs. Server B
- Server A: lasts 3 years, costs $10,000, $1,000 annual maintenance, NPV at 10% = -$12,487.
- Server B: lasts 2 years, costs $7,000, $2,000 annual maintenance, NPV at 10% = -$10,471.
- Both NPVs are negative, reflecting costs.
Equalizing Project Lives
- To compare projects with different lives, assume each can be replaced by an identical project until reaching a common timeframe.
- This approach allows fair yearly cost comparisons.
Equivalent Annual Annuity (EAA) Method
- EAA converts a project’s NPV into an equal annual cost using the annuity formula.
- Formula: EAA = NPV / [ (1 - 1/(1+r)^n )/ r ], where r = discount rate, n = project life.
- Compare EAA values instead of total NPVs for projects with unequal lives.
Application to the Example
- For Server A: EAA = -$5,021 per year.
- For Server B: EAA = -$6,033 per year.
- Although Server B has a higher NPV, Server A has a lower annual cost using EAA.
- Correct choice is Server A, as it is less costly per year.
Limitations and Assumptions
- Assumes projects can be replaced with identical versions at end of life.
- EAA is suitable for repeatable, ongoing investments, not one-time purchases.
Key Terms & Definitions
- Net Present Value (NPV) — The present value of all cash flows associated with a project.
- Equivalent Annual Annuity (EAA) — The annual cost of a project, calculated so its present value equals the project's NPV.
- Discount Rate (r) — The interest rate used to discount future cash flows.
Action Items / Next Steps
- Practice calculating EAA for sample projects.
- Remember to apply EAA only to repeatable, not one-off, investments.