Case:
Fiber Limited (FL) is involved in processing of cotton and sale of fiber to the country’s textile sector. On the basis of a recent market research, Fiber has found two mutually exclusive projects – Theta and Gamma. The cash flows associated with these projects are:
Cash Flows (Rs. ‘000)
Project
FY 0 FY1 FY2 FY3 FY4 FY5 FY6
Theta (40,000) 8,000 14,000 13,000 5,000 11,000 10,000
Gamma (18,000) 9,000 15,100 12,000 — — —
Discount rate for both projects is 8.4%. The management of FL wants to undertake only one project.
Required
1. Determine the viability of both projects by applying Common life approach and Equivalent Annuity Approach method (EAA). (11 + 6)
2. Which project would be feasible for Fiber Limited and why? (3)
Hint: Formula for calculating EAA is PV ÷ [{1(1+i)n} ÷ i]
Solution :
 Simple NPV = −Initial Investment + Sum of Net Cash Flows from Each Future Year.
Simple NPV = − Io +PV (CF1) + PV (CF2) + PV (CF3) + PV (CF4) + …+ ∞
PV(CFx) = CFx/ (1+ i)^x
Where x is the year for which you are calculating
Calculate present value (PV) for each year for both projects independently like:
Theta  Gamma 
1^{st} yr = 8,000/(1.084)^1 = 7380.07
2^{nd} yr =11914.32 3^{rd} yr = 10205.99 4^{th} yr =3621.20 5^{th} yr = 7349.30 6^{th} yr = 6163.45 
1^{st} yr = 9,000/(1.084)^1 = 4612.54
2^{nd} yr =12765.34 3^{rd} yr = 9420.92

Then calculate the simple NPV for each project. For that you will need to add all the PV’s you calculated for each project.
Simple NPV for Theta = 6634.32
Simple NPV for Gamma = 8798.8
Now
Common Life Approach:
The NPV formula remains the same:
Simple NPV = − Io +PV (CF1) + PV (CF2) + PV (CF3) + PV (CF4) + …+ ∞
Least common multiple: 6 (Since theta lasts for 6 years, and gamma lasts for 3, the least common multiple will be 6)
Now Common Life NPV for Theta will be the same as Simple NPV = 6634.32
But the Common Life NPV for Gamma will be different:
Since we need to assume that Gamma lasts as long as Theta, we assume that gamma has the same outflow over the next three years as it had the first three years:
Project 










Gamma 
(18,000) 
9,000 
15,000 
12,000 
9000 
15000 
12000 
Now we calculate PV’s for the 4^{th}, 5^{th} and 6^{th} year.
PV for 4^{th} = 6518.16
PV for 5^{th} = 10021.77
PV for 6^{th} = 7396.14
Hence the Common Life NPV for Gamma will be = 32734.87
EAA Approach:
In order to find the EAA value, first calculate the EAA factor:
EAA FACTOR = (1+ i) ^n / [(1+i)^ n – 1] where n = life of project & i=discount rate
EAA Value For Theta = 2.62
EAA Value For Gamma = 4.72
EAA for each project: Simple NPV * EAA Factor
Theta: 17381.91
Gamma: 46250.33
 I think Gamma is better
Advantages of asset with short life
The advantage of a short life asset is that the investor, by making reinvestment in the asset of a
superior quality, lowers down the costs and updates the project to the new technological requirements.
Plus more cash inflow
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