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 negative $ 51 $ 25 $ 22 $ 21 $ 13 B negative $ 99 $ 22 $ 42 $ 50 $ 59

a. What are the IRRs of the two​ projects? b. If your discount rate is 5.1 %​, what are the NPVs of the two​ projects? c. Why do IRR and NPV rank the two projects​ differently?

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

The IRR for project A is 24​%. ​(Round to one decimal​ place.)

The IRR for project B is nothing​%. ​ (Round to one decimal​ place.)

Answer 1

Solution:
a.		IRR
	Project A	24.0%
	Project B	22.7%
Working Notes:
We can get exact IRR by excel method like below
A	B	C	D
1	Year	Project A CF	Project B CF
2	0	-51	-99
3	1	25	22
4	2	22	42
5	3	21	50
6	4	13	59
	IRR	23.97874%	22.6639376%
	Round to one decimal​ place	24.0%	22.7%
	Using Excel formula	=IRR(C2:C6)	=IRR(D2:D6)
	here in formula C is column in which all cash flows are entered.
	Number 2 & 6 shows that data from 2th row   to 6th row of column C   & column D is used for IRR calculation.
b.		NPV (in 2 decimal)	NPV (in 1 decimal)
	Project A	21.45	21.4
	Project B	51.38	51.4
Working Notes:
Project A
	A	B	C=A x B
Year	Project A CF	PVF @ 5.1%	Present value
0	-51	1	-51.00
1	25	0.9514748	23.786870
2	22	0.9053043	19.916694
3	21	0.8613742	18.088858
4	13	0.8195758	10.654486
		NPV	21.44691
		NPV (in 2 decimal)	21.45
		NPV (in 1 decimal)	21.4
Notes: PVF is calculated @ r% = 1/(1+r%)^n     where n is the period for which PVF is calculated. And r is discount rate of calculated above 5.1%
Project B
	A	B	C=A x B
Year	Project B CF	PVF @ 5.1%	Present value
0	-99	1	-99.00
1	22	0.9514748	20.9324
2	42	0.9053043	38.0228
3	50	0.8613742	43.0687
4	59	0.8195758	48.3550
		NPV	51.37891
		NPV (in 2 decimal)	51.38
		NPV (in 1 decimal)	51.4
Notes: PVF is calculated @ r% = 1/(1+r%)^n     where n is the period for which PVF is calculated. And r is discount rate of calculated above 5.1%
c.
	NPV	Ranking based on NPV	IRR	Ranking based on IRR
A	21.4	II	24.0%	I
B	51.4	I	22.7%	II
Since	Only one project can be selected these projects are mutually exclusive projects , it should be based on NPV Ranking having 1st the Project B , Should be selected.
Ranking	Is given 1st to the project Based on NPV to Project A with highest NPV
	Is given 1st to the project Based on IRR to Project B with highest IRR
Reasoning	As only one project can be selected these projects are mutually exclusive projects .
	The NPV & IRR provides Different Rank.
	The calculation of NPV assumes that the intermediate period cash in flows can be reinvested at cost of capital rate(i.e. required rate of return) and it is always possible.
	The calculation of IRR assumes that the intermediate period cash inflows can be reinvested at IRR (i.e. available rate of return) which is not possible every time.
	The NPV provides the result is absolute amount i.e. present value of net surplus. It can be used to find the increase in amount of wealth .
	It is the IRR provides the percentage annual available return on amount invested.
	The absolute figure has better use than percentage, Due to above reasons the project with better NPV is selected.
Please feel free to ask if anything about above solution in comment section of the question.