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Thursday, November 15, 2012

MGT201 Assignment 1 Solution Due Date 15-11-2012


Semester Fall 2012
Financial Management (MGT201)
Assignment No. 01


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:



Project
Cash Flows (Rs. ‘000)

FY- 0         FY-1         FY-2         FY-3         FY-4         FY-5         FY-6

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]
Show formulas and complete calculations as they carry marks.


Note:
Only in the case of Assignment, 24 hours extra / grace period after the due date is usually available to overcome uploading difficulties which may be faced by the students on last date. This extra time should only be used to meet the emergencies and above mentioned due dates should always be treated as final to avoid any inconvenience.


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SOLUTION IDEA

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
 http://vustudents.ning.com/
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
 http://vustudents.ning.com/
Everything done according to handouts -  well most of it. Formula’s used from the handouts as well. I didn’t understand the hint formula at the end, so I just used what’s given in the handouts. Pray I pass all my subjects this semester please :(


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Solution Idea

  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 = 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

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 = 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


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