Question

You are choosing between two projects. The cash flows for the projects are given in the following table​ ($ million):

Project	Year 0	Year 1	Year 2	Year 3	Year 4
A	−$51	$24	$21	$22	$12
B	−$102	$20	$38	$50	$58

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

b. If your discount rate is 5.4 %, what are the NPVs of the two​ projects?

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

Answer 1

Answer to the question:

a) Calculation of the IRR of two projects :

IRR = Lower rate + PV of cash flow @ lower interest rate - Initial investment * (higher rate –lower rate

                        PV of cash flow @ (lower interest rate – Higher interest rate)

Rate	PV of cash Flow Project A	Rate	PV of cash Flow Project B
20%	53.1019	18%	104.5875
23%	50.4580	20%	99.9614

IRR of project A = 20% + 53.1019- 51 * (23-20)

                                            53.1019-50.4580

Hence IRR of project A = 22.3850%

IRR of project B = 18% + 104.5875- 102 * (20-18)

                                            104.5875-99.9614

Hence IRR of project A = 19.1187%

b) Calculation of the NPV of two projects

Year	Project A	Project B
	Cash Flow in $	PV of cash Flow @5.40%	Cash Flow in $	PV of cash Flow @5.40%
1	24	22.7704	20	18.9753
2	21	18.9033	38	34.2060
3	22	18.7888	50	42.7020
4	12	9.7234	58	46.9965
PV of Inflow		70.1859		142.8798
Less: Initial Outflow		51		102
NPV of the project		19.1859		40.8798

c) NPV And IRR Rank The Two Projects Differently Because They Are Measuring Different Things. NPV is measuring value​ creation , while IRR Is Measuring Return On Investment.