Semester “Spring 2011”
“Corporate Finance (Fin622)”
This is to inform that Graded Discussion Board (GDB) will be opened according to the following schedule
Schedule
Opening Date and Time
April 19 , 2011 At 12:01 A.M. (Mid-Night)
Closing Date and Time
April 22 , 2011 At 11:59 P.M. (Mid-Night)
Topic/Area for Discussion
“ Capital budgeting”
Note: The discussion question will be from the area/topic mentioned above. So start learning about the topic now.
Discussion Question
Usually NPV and IRR techniques of project evaluation leads to the same ranking for given projects and make the decision to undertake project relatively simple. But sometimes it does happen that a ranking conflict arises by using both techniques i.e. both techniques provide contradictory ranking of given projects.
You are required to discuss the circumstances when NPV and IRR lead to a ranking conflict for two projects?
Your answer should be relevant and should not exceed 4 to 5 lines.
:::::::::::::::::::::::::
Solution:
NPV and IRR Conflict
Conflicts between NPV and IRR can arise in numerous circumstances: different lives, different sizes, different risk factors, or different timing of cash flows. The underlying cause of the conflict resides in the assumption of cash flow reinvestment. The process of discounting and time value of money is predicated on interest compounding and discounting is predicated on what discount rate is chosen. In IRR calculation, the implied interest rate of reinvestment of cash flows is IRR itself. In NPV calculation, it is the discount rate. Which of the two methods is correct depends on the choice of what is a more realistic rate of reinvestment of cash flows: IRR or discount rate. Most often the reinvestment opportunities that a company has are those that can earn its weighted average cost of capital, because it is what its projects earn on average. Relying on an assumption of weight average cost of capital as the reinvestment opportunity is also more conservative. Thus, NPV is most often the safest basis for decision.
But that may not be always the case. For instance, choosing projects that have positive NPV implies that they earn a higher return than risk adjusted cost of capital. This implies that we expect opportunities for reinvestment of cash flows at higher rates. Higher rates of return can also be required when future inflation is anticipated. To investigate the impact of cash flow reinvestment opportunity, advanced textbooks in financial management recommend calculating an adjusted NPV and an adjusted IRR. These are obtained by first calculating a terminal value which is the future value of cash flows compounded at the opportunity rate of reinvestment calculation of future value). Then the terminal value is discounted to the present using the weighted average cost of capital. Thus the adjusted NPV is given by
Adjusted NPV = - I0 + (Ct(1+k0)t ) * ((1 + kc )n – 1) / kc
where I0 = initial outlay
Ct = cash flows
k0 = opportunity rate of reinvestment
kc = weighted average cost of capital
t = time period
n = length of project
Likewise, the adjusted IRR is given by
Adjusted IRR = x where I0 = (Ct(1+k0)t ) * ((1 + x )n – 1) / x
By using the same rate of reinvestment of cash flows for NPV and IRR removes the conflict between NPV and IRR. The additional steps required in the calculation of adjusted NPV and IRR are not intuitively appealing. The complexity of the procedure makes it rather unpopular, and as long as conservative rates of reinvestment are used the results merely confirm the conclusion reached with the unadjusted NPV. This gives even more reason to rely on ordinary NPV. Also keep in mind the rough estimates often used in cash flow projections: the theoretical complexity seems somewhat remote from reality.
:::::::::::::::::::::::::::::::::::
Assuming these projects are mutually exclusive, the circumstances that lead to conflict include this: project a generating less cash flow in the first couple of years and then generating most of total cash flow in the last years of the project. project b is the opposite; it is generating most of its cash flow in the first couple of years and then generating the least in the last years of the project.
When everything is summed up for the two projects, project a has generated more cash flow than project b. However, the IRR is greater for project b. how is this so? remember that we are discounting the cash flows. So, project a having most of its cash flow in the last years meant it had to be discounted back more years, resulting in less present value. project b having most of its cash flow in the first years led to a greater return when NPV is zero.
What you see is that when the discount rate is zero, the NPV is greater for project a since it generated more total cash flow. As you increase the required return, you then see that at some point, there will be a crossover, and the NPV of project b will be greater than project a. This is how NPV and IRR leads to ranking conflict.
To sum up, if you have two projects in which project x has greater cash flows and most of those cash flows happen at the end of the project's cycle, it is more attractive if the discount rate is lower since the NPV will be higher than project y. for project y which has lower cash flows and most of those cash flows happen at the start of the project, it is more attractive if the discount rate is high since the NPV will be higher than project x.
Thus, in a situation where you could only choose one project and not both, you first would calculate the crossover point, the point in which both projects have the same NPV and required return. You would then check where the investors' expectations are concerning their required rate of return. If it is lower than the crossover discount rate, then project x is a better choice than project y.
Discussion Question
Usually NPV and IRR techniques of project evaluation leads to the same ranking for given projects and make the decision to undertake project relatively simple. But sometimes it does happen that a ranking conflict arises by using both techniques i.e. both techniques provide contradictory ranking of given projects.
You are required to discuss the circumstances when NPV and IRR lead to a ranking conflict for two projects?
Your answer should be relevant and should not exceed 4 to 5 lines.
:::::::::::::::::::::::::
Solution:
NPV and IRR Conflict
Conflicts between NPV and IRR can arise in numerous circumstances: different lives, different sizes, different risk factors, or different timing of cash flows. The underlying cause of the conflict resides in the assumption of cash flow reinvestment. The process of discounting and time value of money is predicated on interest compounding and discounting is predicated on what discount rate is chosen. In IRR calculation, the implied interest rate of reinvestment of cash flows is IRR itself. In NPV calculation, it is the discount rate. Which of the two methods is correct depends on the choice of what is a more realistic rate of reinvestment of cash flows: IRR or discount rate. Most often the reinvestment opportunities that a company has are those that can earn its weighted average cost of capital, because it is what its projects earn on average. Relying on an assumption of weight average cost of capital as the reinvestment opportunity is also more conservative. Thus, NPV is most often the safest basis for decision.
But that may not be always the case. For instance, choosing projects that have positive NPV implies that they earn a higher return than risk adjusted cost of capital. This implies that we expect opportunities for reinvestment of cash flows at higher rates. Higher rates of return can also be required when future inflation is anticipated. To investigate the impact of cash flow reinvestment opportunity, advanced textbooks in financial management recommend calculating an adjusted NPV and an adjusted IRR. These are obtained by first calculating a terminal value which is the future value of cash flows compounded at the opportunity rate of reinvestment calculation of future value). Then the terminal value is discounted to the present using the weighted average cost of capital. Thus the adjusted NPV is given by
Adjusted NPV = - I0 + (Ct(1+k0)t ) * ((1 + kc )n – 1) / kc
where I0 = initial outlay
Ct = cash flows
k0 = opportunity rate of reinvestment
kc = weighted average cost of capital
t = time period
n = length of project
Likewise, the adjusted IRR is given by
Adjusted IRR = x where I0 = (Ct(1+k0)t ) * ((1 + x )n – 1) / x
By using the same rate of reinvestment of cash flows for NPV and IRR removes the conflict between NPV and IRR. The additional steps required in the calculation of adjusted NPV and IRR are not intuitively appealing. The complexity of the procedure makes it rather unpopular, and as long as conservative rates of reinvestment are used the results merely confirm the conclusion reached with the unadjusted NPV. This gives even more reason to rely on ordinary NPV. Also keep in mind the rough estimates often used in cash flow projections: the theoretical complexity seems somewhat remote from reality.
:::::::::::::::::::::::::::::::::::
Assuming these projects are mutually exclusive, the circumstances that lead to conflict include this: project a generating less cash flow in the first couple of years and then generating most of total cash flow in the last years of the project. project b is the opposite; it is generating most of its cash flow in the first couple of years and then generating the least in the last years of the project.
When everything is summed up for the two projects, project a has generated more cash flow than project b. However, the IRR is greater for project b. how is this so? remember that we are discounting the cash flows. So, project a having most of its cash flow in the last years meant it had to be discounted back more years, resulting in less present value. project b having most of its cash flow in the first years led to a greater return when NPV is zero.
What you see is that when the discount rate is zero, the NPV is greater for project a since it generated more total cash flow. As you increase the required return, you then see that at some point, there will be a crossover, and the NPV of project b will be greater than project a. This is how NPV and IRR leads to ranking conflict.
To sum up, if you have two projects in which project x has greater cash flows and most of those cash flows happen at the end of the project's cycle, it is more attractive if the discount rate is lower since the NPV will be higher than project y. for project y which has lower cash flows and most of those cash flows happen at the start of the project, it is more attractive if the discount rate is high since the NPV will be higher than project x.
Thus, in a situation where you could only choose one project and not both, you first would calculate the crossover point, the point in which both projects have the same NPV and required return. You would then check where the investors' expectations are concerning their required rate of return. If it is lower than the crossover discount rate, then project x is a better choice than project y.
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