Question

Furthermore, the client has mentioned that they are reviewing two mutually exclusive projects, each costing $100 thousands. Your team has already analysed these projects and expected the following cash flows for each project:

Cash Flow	Project Alpha	Project Beta
Year 0	-100,000	-100,000
Year 1	32,000	0
Year 2	32,000	0
Year 3	32,000	0
Year 4	32,000	0
Year 5	32,000	200,000

The client’s required rate of return was 11%. The client was using payback method to decide which project to choose. However, you have explained that NPV or IRR methods might suit the client better.

1. If the required rate of return changes, how does such change affect the project’s internal rate of return?
2. What are assumptions of reinvestments implicitly made by NPV and IRR? Which one is better?
3. If there is a ranking conflict, what is the reason for that?
4. Which project should client accept and why?

I NEED TYPED VERSION ,NOT EXEL.CAN YOU HELP PLEASE. IT SHOILD BE WITH FORMULAS AND EXPLANATIONS.THANK YOU IN ADVANCE

Answer 1

1]	CALCULATION OF NPV:
	Project Alpha NPV = -100000+32000*(1.11^5-1)/(0.11*1.11^5) =	$          18,269
	Project Beta NPV = -100000+200000/1.11^5 =	$          18,690
2]	CALCULATION OF IRR:
	IRR is that discount rate for which NPV = 0.
	Project Alpha:
	The equation for IRR is:
	0 = -100000+32000*PVIFA(irr,5)
	PVIFA(irr,5) = 100000/32000 = 3.125
	The PV of $1 for 18% and 19% for n = 5 are	18%	19%
	IRR lies between 18% and 19%	3.1272	3.0576
	By simple interpolation IRR = 18%+1%*(3.1272-3.125)/(3.1272-3.0576) =	18.03%
	Project Beta:
	IRR = (200000/100000)^(1/5)-1 =	14.87%
3]	Both the projects have positive NPVs and hence are acceptable
	under the NPV rule.
	Both have IRRs greater than requred rate of return and hence
	are acceptable under the IRR rule.
	But, as the projects are mutually exclusive, the project with the
	higher ranking shoule be selected.
	However, the two methods give different rankings to the two
	projects.
	While the NPV ranks Beta [with higher NPV] as 1, the IRR ranks Alpha [with higher IRR] as 1.
	Hence, there is conflict in ranking.
4]	Change in required return does not affect IRR. Only NPVs are
	affected.
5]	The reason for conflicting ranking between NPV and IRR methods
	is the assumption as to the rate at which the intermediary cash
	flows are reinvested.
	While the NPV assumes the same required rate of return [here
	11%] as the rate of reinvestment of intermediary cash flows for
	all the projects, the IRR assumes the IRR of each project as the
	rate of reinvestment for their intermediary cash flows. Such a
	difference magnifies the difference in PVs of the cash flows when
	the rate changes.
6]	The better assumption is that of NPV, as the discount rate used by
	NPV is the cost of capital, which is what the firm can earn on its
	cash flows. In contrast the IRR uses as many rates as there are
	projects, which is not going to happen, especially where the IRR
	is much higher than the cost of capital.
7]	If there is a conflict, the NPV verdict should be accepted. That is
	Project Beta should be accepted. This is because, the projects
	have equal lives.
	If the projects do not have equal lives, then the equivalent annual
	NPV should be calculated, and the one with the higher value
	should be accepted.
8]	The MIRR can also be used to resolve the conflict.
	For MIRR it is assumed that the intermediary cash flows are
	reinvested at the cost of capital and then IRR is worked out.
	Project Alpha:
	FV of cash inflows = 32000*(1.11^5-1)/0.11 =	$       1,99,290
	MIRR = (199290/100000)^(1/5)-1 =	14.79%
	Project Beta:
	MIRR = (200000/100000)^(1/5)-1 =	14.87%
	As Beta has higher MIRR, it should be selected.