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# MGT201 Assignment No 1 solution & Discussion Due Date: 15-11-2012

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

Final values gamma ki ziada hain, gaur se daikho.

yaa i know.........many bhi to yehi kaha hy
in final Gma is Better

kya koi bata skta ha k 4thn , 5th or 6th year ki value ksy i 9000,15000 or 12000 wali

Project
Cash Flows (Rs. ‘000)

FY- 0

FY- 1

FY- 2

FY- 3

FY- 4

FY- 5

FY- 6

Gamma (18,000) 9,000 15,000 12,000 9000 15000 12000

MGT201_Assignmnt_no_1_solution_13_november_2012

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least common multiple tu 18 anay chahiye....... because 6*3=18.... 6 for theta and 3 for gamma..... handout main multiple kiya gya hy both year ko.... koi bataye ga i m rite....page 56 handout

6*3 nai krna bhai. least common multiple is LCM, apne ye matric k zmane mein para hoga, LCM HCF. LCM nkalo agr 6 aur 3 ka tu 6 ata hai, ksi chote behn bhai ya cousin ko bolo wo nkal de ga. aur handouts mein 1 and 2 ka LCM nikala hva hai, wo 2 hota hai.

Agr ap common sense b use kro, tu common life approach kehta hai k donoun projects ka lifespan aik jtna krdo, since aik ka lifespan 6 saal hai, durse ka 3 saal, tu ap ne simple 3 saal wale ko 6 saal ka bnana hai. hence, the common factor amongst the two is 6

least common multiple is 3: it's the least of the two which is multiple of both.

You're not right. Its about the Lowest common multiple not just the multiplication.

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:

 Theta Gamma 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 = 4612.54 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 = 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

 Cash Flows (Rs. ‘000)

 FY- 0

 FY- 1

 FY- 2

 FY- 3

 FY- 4

 FY- 5

 FY- 6

Gamma

(18,000)

9,000

15,000

12,000

9000

15000

12000

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 = 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

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

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:

 Theta Gamma 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 = 4612.54 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 = 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

 Cash Flows (Rs. ‘000)

 FY- 0

 FY- 1

 FY- 2

 FY- 3

 FY- 4

 FY- 5

 FY- 6

Gamma

(18,000)

9,000

15,000

12,000

9000

15000

12000

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 = 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

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

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:

 Theta Gamma 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 = 4612.54 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 = 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

 Cash Flows (Rs. ‘000)

 FY- 0

 FY- 1

 FY- 2

 FY- 3

 FY- 4

 FY- 5

 FY- 6

Gamma

(18,000)

9,000

15,000

12,000

9000

15000

12000

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 = 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

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

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