Corporate Finance

Free Cash Flow Valuation 
 197

Project Investment NPV Life

A 5m 6.0 7 years

B 3m 4.0 4 years

Based on NPV if we were to choose A, we would be ignoring the project lives.

Under the replacement chain method, both the projects are replicated till their lives become equal. If, for

example, two projects have lives of 2 years and 3 years, the first project is replicated thrice and the second

project is replicated twice so that their lives become six years. Consider two projects given below:

Project 1 Project 2

Year Cash flow Cash flow

0 –1,000 –1,500

1 750 800

2 750 800

3 800

NPV 337 489

Discount rate 8 percent 10 percent

The NPV after replicating the projects are 875 and 857 respectively. Based on RC NPV, we would choose

Project 1.

Under the equivalent annuity method, the NPV of the projects are converted into their annual equivalent

and then compared.

The equivalent annuity is the annuity that produces the same NPV as that of the project.

Equivalent Annuity = NPV/Annuity factor (r,n)

where r= discount rate and n is the project life.

Consider the following projects:

Project Investment NPV Life

A 50 lac 6.0 7 years

B 30 lac 4.0 4 years

If the discount rate is 15 percent, equivalent annuity for the two projects would be:

6.0/PVIFA (15,7) = 1.44

and 4.0/PVIFA (15,4) = 1.40

Based on the equivalent annuity, we would choose project A. Note that this technique can be applied only
if the projects can have the same risk complexion and, hence, discount rate. What if the risk complexion is
different? The correct way to implement the equivalent annuity method is to find the annuity over the replicated
life of the project, 12 years in the given example.
Consider the example given under the RC method. The EA for the two projects are:

337/PVIFA (8 percent, 2 years) = Rs 189 p.a.

489/PVIFA (10 percent, 3 years) = Rs 197 p.a.