Question

A firm has a capital budget of $100 which must be spent on 1 pf 2 projects, each requiring a present outlay of $100. Project A yields a return of $120 after 1 year, whereas Project B yields $201.14 after 5 years.

Calculate

1. The NPV of each project using 10% discount rate
2. The IRR of each project

What are the project rankings on the basis of these two investment decision rules? Supposed that you are told that the firms reinvestment rate 12% which project should the firms choose?

Answer 1

Calculation of NPV: [Using discount rate(r)=10%]

Year	Cash flow(A)	Cash Flow(B)	PV factor[1/(1+r)^n]	Discounted CF (A)	Discounted CF (B)
0	-100	-100	1	-100	-100
1	120		0.909090909	109.0909091	0
2			0.826446281	0	0
3			0.751314801	0	0
4			0.683013455	0	0
5		201.14	0.620921323	0	124.8921149
			NPV	9.090909091	24.89211492

Calculation of IRR:

IRR is the rate which equals the present value of cash inflows to be received throughout the life of project to the initial investment.

In our question there is only single cash inflow in both the projects.(in A it is at 1st year end and in project B it at 5th year end.)

So IRR of Project A:

100=120/(1+r)^{^1}

(1+r)^{^1}=120/100

1+r=1.2

r=1.2-1

=.2 or 20%

IRR of Project B:

100=201.14/(1+r)^{^5}

(1+r)^{^5}=201.14/100

1+r=2.0114^{^(1/5)}

r=1.150005-1

=.150005 or 15.0005%

Ranking:

	Project A	Project B
NPV	9.090909091	24.89211492
Ranking	2nd	1st
IRR	20.0000%	15.0005%
Ranking	1st	2nd

If the firms reinvestment rate 12%:

We shall choose the project with higher NPV

Calculation of NPV: [Using reinvestment rate(r)=12%]

Year	Cash flow(A)	Cash Flow(B)	PV factor[1/(1+r)^n]	Discounted CF (A)	Discounted CF (B)
0	-100	-100	1	-100	-100
1	120	0	0.892857143	107.1428571	0
2	0	0	0.797193878	0	0
3	0	0	0.711780248	0	0
4	0	0	0.635518078	0	0
5	0	201.14	0.567426856	0	114.1322378
			NPV	7.142857143	14.13223776

We shall choose the project B even if the reinvestment rate is 12%.

Please do not forget to upvote my solution if you like the same.

Feel free to ask any query via comments.

Good Luck!