Question

Project Year 0 Year 1 Year 2 Year 3 Year 4

A    -$ 49 $ 25 $ 22 $ 22 $ 15

B -$ 101 $ 19 $ 39 $ 51 $ 61

a. What are the IRRs of the two​ projects?

b. If your discount rate is 4.8%​, what are the NPVs of the two​ projects?

c. Why do IRR and NPV rank the two projects​ differently?

Answer 1

a)Calculation of IRR(Internal rate of return)

IRR is the discounting rate at which Net present value of project is equal to zero.We can find the IRR of the projects by trial and error method as follows;

let assume the discount rate of 15% and 30%

NPV of both projects at 15% is as follows

Year	Cash Flow($)	Discounting factor@15%	Present Value
	Project A	Project B	Project A	Project A	Project B
0	-49	-101	1	-49	-101
1	25	19	.870	21.75	16.53
2	22	39	.756	16.63	29.48
3	22	51	.658	14.48	33.56
4	15	61	.572	8.58	34.89
NPV	12.44	13.46

NPV of both projects at 30% is as follows

Year	Cash Flow($)	Discounting factor@30%	Present Value
	Project A	Project B	Project A	Project A	Project B
0	-49	-101	1	-49	-101
1	25	19	.769	19.23	14.61
2	22	39	.592	13.02	23.09
3	22	51	.455	10.01	23.21
4	15	61	.350	5.25	21.35
NPV	-1.49	-18.74

Now,IRR is;

=Lower Discount rate+(NPV at lower discount rate/Present value of cash inflows at lower discount rate-Present value of cash inflows at higher discount rate)*Difference between higher rate and lower rate)

Project A's IRR=15%+(12.44/61.44-47.51)*15

=15%+13.40

=28.40%

Thus IRR for project A is 28.40%(approx)

Project B's IRR=15%+(13.46/114.46-82.26)*15

=15%+6.27

=21.27%

Thus IRR for project B is 21.27%

b)Calculation of NPV

Statement showing calculation of NPV

Year	Cash flow(a)	Discounting Factor @4.8%(b)	Present Value(a*b)
	Project A	Project B		Project A	Project B
0	-49	-101	1	-49	-101
1	25	19	.954	23.85	18.126
2	22	39	.910	20.02	35.49
3	22	51	.869	19.12	44.319
4	15	61	.830	12.45	50.63
NPV($)	26.44	47.57

c)NPV and IRR are similar in sense that both are discounted cash flow models.But they also differ in their main approach.NPV is abosolute measure i.e . it is the dollar amount of value added or lost by undertaking a project.IRR is a relative measure i.e it is the rate of return that a project offers over its life span.

The underlying cause of NPV and IRR conflict is the nature of projects(mutually exclusive or independent) and size of the project.