Projects with Unequal Lives

In practical life, an enterprise has many options to invest in long term projects. These projects have different life span. For financial analyst to evaluate various projects with unequal lives, the solution is not easy. He cannot compare NPV or IRR of the projects with unequal life to suggest the best possible option. Here the concept of Equivalent Annual Net Present Value comes into focus. It is also called Equivalent annuity cash flow (EAC). The project that yields the highest annual net present value is selected to be undertaken.

Formula

Annual Net Present Value = NPV / Annuity factor

Example

ABC is engaged in the publishing of books for different level of classes. It is considering investing in either one of the two under consideration projects:

Option 1 – Invest in Project A

Investing in new world class printing set up that will give boost in its production by 35 {1bb28fb76c3d282be6cfd0391ccf1d9529baae691cd895e2d45215811b51644c}. The initial investment requires for this project is $ 200 million. The expected cash flows are $ 300 million per year for the next 06 years.

Option 2 – Invest in Project B

The 2ndoption is to acquire the same setup as Project A but the machinery will be of China manufactured. This will require initial investment of $ 500 million and $ 600 million cash inflows for the next 03 years.

Required

You are the financial analyst of ABC. Suggest ABC whether it should go for project A or B. For calculation purpose, consider discount rate equals to 10 {1bb28fb76c3d282be6cfd0391ccf1d9529baae691cd895e2d45215811b51644c}.

Solution

Project 1

Year0123456
Cash Flow-500600600600600600600
Discount factor10.90910.82640.75130.68300.62090.5645
PV-500545.46495.84450.78409.8372.54338.7
NPV$ 2113.12

Annuity Factor =4.3553

Equivalent annuity cash flow (EAC) = NPV / Annuity factor = 2113.12 / 4.3553 = $ 485.18

Project 2

Year0123
Cash Flow-500600600600
Discount factor10.90910.82640.7513
PV-500545.46495.84450.78
NPV$ 992.08

Annuity Factor =2.4869

Equivalent annuity cash flow (EAC) = NPV / Annuity factor = 992.08 / 2.4869 = $ 398.92

Conclusion

When we compare EAC of both projects, project A has higher value than that of project B. So, ABC should undertake project A.