1. I t lR t fR t
Internal Rate of Return
f f j
Internal rate of return of a project is that discount rate
which equates the aggregate present value of the cash
inflows (CFAT) of the project with the aggregate
present value of cash outflows of the project
 The decision rule is :
 Accept project only if IRR > required return
 Steps to computing IRR –
1. Determine the project cash outflow and inflows
2. Take initial guestimate of the probable IRR rate
3. Compute NPV for such initial rates
4. Use intrapolation whenever needed
narain@fms.edu

2. Ill t ti
Illustration
A firm is considering following two projects for the
purpose of adoption in the next budget year. Their
f d i i h b d Th i
cash flow estimates are given below:
Year 0 1 2 3 4
Project A (45,555) 15,000 15,000 15,000 15,000
Project B (64,320) 20,000 25,000 28,000 24,000
Calculate the internal rate of return of both the projects
if required rate of return on the projects are 10%.
narain@fms.edu

3. Illustration 1.9
Determine the acceptability of the project using IRR method
with following cash flows if the minimum required rate of
return is 20%.
return is 20%
Cash outflow: 35,750
Year
Y 1 2 3 4 5 6
CFAT 10,000 12,000 14,000 16,000 18,000 20,000
narain@fms.edu

4. Illustration
A firm is considering two projects, with a capital outlay
of Rs. 1,00,000 each and the following cash inflows.
Compute their internal rates of returns
returns.
Year 1 2 3 4
Project A 33,620 33,620 33,620 33,620
Project B - - - 1,36,050
narain@fms.edu

5. Exercise
You are required to analyse following two projects, each
with a cost of Rs. 10,000 and cost of capital is 5 The
p 5%.
projects’ expected net cash flows are as follows:
Year 1 2 3 4
Project X 6,500 3,000 3,000 1,000
Project Y 3,500 3,500 3,500 3,500
What is their Internal rate of return?
Which project should be accepted if they are
p j p y
independent?
Which project should be accepted if they are mutually
exclusive?
narain@fms.edu

6. Evaluating IRR method
 It has intuitive appeal to those who want to analyse the
project in terms of rate of return
DDetermination of IRR does not depend on the
i i f IRR d d d h
required rate of return
 It is consistent with NPV method for a single project
 IRR method is based on the reinvestment assumption
by which cash flows of the project are reinvested at the
IRR itself: use MIRR
narain@fms.edu

7. Pitfalls of IRR
1. It is a relative measure of evaluation, not the absolute
one.
Projects Outflow Inflow IRR NPV @ 10%
A ‐1,000 +1,500 50% +364
B +1,000
+1 000 ‐1,500
1 500 50% ‐364
364
 We need to modify the acceptance criterion for
borrowing and lending Projects
 What to do in case project is both borrowing & lending?
Period 0 1 2 3
Cash Flows +1,000 ‐3,600 +4,320 ‐1,728
Min.
Min return 10% IRR=20% NPV=‐0.75
NPV= 0 75
narain@fms.edu

8. Pitf ll 2 C t ti lH d
Pitfall 2: Computational Hazards
 Multiple rate of IRR
Period 0 1 2
Cash
‐1,600 1,000 ‐1,000
flow
IRR= 25% and 400% NPV at 10% = ‐1,517
 No IRR
Period 0 1 2
Cash flows 1,000 3
‐3,000 2,500
5
narain@fms.edu

9. Pitfall 3: Mutually exclusive projects
Pitf ll 3 M t ll l i j t
 Mutually exclusive projects are those projects from
which only one of them is to be chosen
 T h i ll Fi
Technically or Financially
i ll
 Inconsistent ranking of projects based on the IRR
criterion and other evaluation criterion
 Size‐disparity
 Time‐disparity
 Life‐disparity
narain@fms.edu

10. Size Disparity Problem
Size Disparity Problem
 Try this:
Printer
P i Outlay
O l CFAT IRR NPV @ 10%
NPV %
Inkjet 10,000 20,000 100% 8,182
LaserJet 20,000
20 000 35,000
35 000 75% 11,818
11 818
 Which project will you prefer?
 The difference lies in the implicit compounding rate of
interest
 IRR – funds are compounded at the project IRR
 NPV – funds are compounded at the discount rate
 Use incremental project analysis if IRR has to be computed
narain@fms.edu