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 Capital Budgeting Techniques for Projects with Unequal Lives

Learning Objectives - The students are expected to understand the application of usual capital budgeting techniques applied particularly to the projects with unequal lives. Learning Outcomes - After going through this activity, the student would be able to apply capital budgeting techniques especially in the case of projects with unequal lives. 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:

projects – Theta and Gamma.The cash flows associated with these projects are: Project Cash Flows (Rs. ‘000) FY- 0 FY-1 FY-2 FY-3 FY-4 FY-5 FY-6 Theta(40,000) 8,00014,00013,0005,00011,000 10,000Gamma(18,000) 9,00015,10012,000--- --- ---

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] Show formulas and complete calculations as they carry marks.

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Replies to This Discussion

kis ki language sakht hai?????

Usman Saheb is right :) Answers are same.

narmi tmari samaj say oper ki cheez a !!!!!!!!!!!!!!!!!

calculations are wrongs on attachment file.... my answers are

Project Theta C.L NPV = +Rs 6634.362396
Project Gamma C.L NPV = + 6002.904254

any one tell me...i m rite?????

yes bhai mere b yehe answers hain

(1 + i)^n / [(1 + i) ^n -1]
Where n = life of project & i=discount rate
Project Theta’s EAA Factor = (1+0.084) ^6 / [(1+0.084) ^6 – 1]
= (1.084) ^6/ [(1.084) ^6 – 1]

is ko koi solve krain agay.... how it solve

Soooo Sorrry Meri thori c values galat hainnn pleaase sare sai krlo

  1. 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:




1st yr =  8,000/(1.084)^1 = 7380.07

2nd yr =11914.32

3rd yr = 10205.99

4th yr =3621.20

5th yr = 7349.30

6th yr =  6163.45

1st yr =  9,000/(1.084)^1 = 8302.58

2nd yr =12765.34

3rd 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 = 12488.84





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:



Cash Flows (Rs. ‘000)


FY- 0


FY- 1


FY- 2


FY- 3


FY- 4


FY- 5


FY- 6










Now we calculate PV’s for the 4th, 5th and 6th year.

PV for 4th = 6518.16

PV for 5th = 10021.77

PV for 6th = 7396.14

Hence the Common Life NPV for Gamma will be = 36424.91



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: 58947.32



  1. 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

 Nadia it's ok ..

yahan discussion ka purpose hi yahi hai ... sirf solution provide karna nai..

ik dusaray say discuss karna or kuch sikhna 

Tqriq sir u all have discussed the formula given in HO about EAA and what about the formula given in the assignment as HINT??

plz let us clear this which formula we should use although we'll find the same conclusion with both formulas but method is different????

plz sort it out soon.



Dear students.

please koi batai ke common life mein Gamma I0 18000 Should be subtracted twice as given in the handout page 57 formula. For calculating Gamma why every one is just using straight formula. like- I0 + CF1+CF2+CF3 ...... IN case of calculating Gamma for common life. Formula in example is - Io +[(CF1-Io)/1.1]+ CF2/(1.1)^2= 156.( you have to subtract 18000 twice)


Because usne 1 year project ko expand kia hva hai over two years. that is why he is subtracting twice. 

See its like for his project he has the initial investment of 100, and 200 cash flow for year one. After that  the project ends.

In this case, the project goes on for at least 3 years, uske pas q k data extend krne k lie 100 aur 200 he thy tu usne usi ko use kia hva hai, according to handouts, and the formula you show, usne assume kia hai k investment 100 ki thi, year1 100 outflow tha, year2 200 outflow that (see CF2/(1.1)^2 - ub to the power 2 indicates this is for the second year.)

hmare pas 9000, 15000, 12000 hai, we can simply reuse it and assume k the cash outflow remained the same over the next three years as well. usne sara aik he formula mein show kia hva hai, according to my solution, har year ki present value (PV) is calculated serperately.

yes masood raza you are right aisa he hoga 

subtract hoga. 6000 aye ga wo bi minus main.

and 22***.** answer hoga.


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