Question

Consider the following alternatives for a Beta company investment project:

Net cash flow

n	Proyect A	Proyect B
0	-10,000	-20,000
1	5,500	0
2	5,500	0
3	5,500	40,000
IRR	30%	?
PW(15%)	?	6,300

 The company's MARR for this type of project is 15%.
(a) Determine the IRR of project B.

(b) Calculate the PW of project A.

(c) Suppose alternatives A and B are mutually exclusive, determine which of them is more attractive using the rate of return as a criterion.

please provide process

Answer 1

a).

IRR is the discount rate at which NPV is 0.
Let IRR be r, then C+C1/(1+r)+C2/(1+r)^2+....Cn/(1+r)^n= 0; where C is the initial investment, C1 to Cn are cash inflows and r is the IRR.

So, -20000+0/(1+r)+0/(1+r)^2+40000/(1+r)^3=0

-20000+40000/(1+r)^3= 0

40000/(1+r)^3= 20000

(1+r)^3= 2

r= 25.99%

IRR of project B is 25.99%

b).

PW for a time period of n can be calculated using the formula: -C+C1/(1+r)+C2/(1+r)^2+....Cn/(1+r)^n; where C is the initial investment, C1 to Cn are cash inflows and r is the required rate of return

So, -10000+5500/1.15+5500/1.15^2+5500/1.15^3

= -10000+4782.61+4158.79+3616.34

= 2557.74

PW of Project A is $2557.74

c).

Given that alternatives A and B are mutually exclusive. Based on rate of return criterion, Project A is more attractive. Because IRR of Project A which is 30% is greater than IRR of Project B which is 25.99%

IRR is the rate at which the cashinflows can be reinvested at that particular rate. So, the project with higher rate of return is more attractive, as cashflows can be reinvested at higher rate. It can also be used as a decision taking criterion, where a project with IRR greater than that of cost of capital neess to be invested into and the ones with lesser IRR than cost of capital should not be taken up.