Question

Under what circumstances will the IRR and NPV rules lead to the same decision (accept/reject)? When might they conflict? (It is important to explain your answers with details or demonstrate your understanding by applying examples.) please this answer should not be from text book.

Answer 1

NPV and IRR rules lead to the same decision in those cases in which the projects which are being analyzed have conventional cash flows. Also when projects have similar cash flow patterns then NPV and IRR rule will yield similar results. Let me explain with an example of two mutually exclusive projects – X and Y.

Year	Project X's cash flow	Project Y's cash flow	1+r	PVIF	PV of X	PV of Y
0	-                        50,000.00	-                      100,000.00	1.10	1.0000	- 50,000.00	- 100,000.00
1	2,000.00	10,000.00		0.9091	1,818.18	9,090.91
2	3,000.00	120,000.00		0.8264	2,479.34	99,173.55
3	4,000.00	12,000.00		0.7513	3,005.26	9,015.78
4	5,000.00	13,000.00		0.6830	3,415.07	8,879.17
5	150,000.00	55,000.00		0.6209	93,138.20	34,150.67
				NPV	53,856.05	60,310.09
				IRR	28.44%	31.82%

We can see that both X and Y have conventional cash flows and similar patterns of cash flow. Under both NPV and IRR rule project Y will be selected.

The NPV and IRR rules conflict when the cash flows are unconventional or when the cash flows do not have similar patterns for the projects. Take another hypothetical example of projects X and Y:

Year	Project X's cash flow	Project Y's cash flow	1+r	PVIF	PV of X	PV of Y
0	-                           5,000.00	-                           5,000.00	1.10	1.0000	-   5,000.00	-      5,000.00
1	2,000.00	-		0.9091	1,818.18	-
2	2,000.00	-		0.8264	1,652.89	-
3	2,000.00	-		0.7513	1,502.63	-
4	2,000.00	-		0.6830	1,366.03	-
5	2,000.00	15,000.00		0.6209	1,241.84	9,313.82
				NPV	2,581.57	4,313.82
				IRR	29%	25%

In the above case Y has a different cash flow pattern from X. NPV rule suggests that Y is better while IRR rule suggests that X is better.