An analyst assesses two alternatives: (1) a ring levee with a 20-year life and (

Question

An analyst assesses two alternatives: (1) a ring levee with a 20-year life and (2) floodwalls with a 60-year life, both designed to prevent river flood damage                    to neighboring residential properties. Suppose the NPV for the 20-year ring levee is $3 million and the NPV for the 60-year floodwall is $5 million, both                    discounted at 5%. Calculate the EANB for each project. Then, use the replication method to determine which project                    should be adopted.
Note: EANB is (net present value) / (annuity factor).

Explanation / Answer

First determine the annuity factors:

AF20 = (1/.05)-1/(.05(1.05^20)) = 12.46

And

AF60 = (1/.05)-1/(.05(1.05^60)) = 18.93

Thus:

EANBrl = $3 million / 12.46 = $240,770.5

And

EANBfw = $5 million / 18.93 = $264,140.9

For part b, note that the shorter project might be preferred if there is a chance new technology would be

developed that could be implemented if society is not locked into the longer project.

For part c, the AF is given by the present value of a $3 perpetuity minus the present value of a $3

perpetuity, discounted T years in the future. The intuition is that getting a $3 annuity for T years is

equally valuable to getting a $3 perpetuity today, and having it taken away T years in the future.

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