IRR
Internal Rate
of Return
The rate of return which equates the
Net Present Value (NPV) of the cash flows to zero.
Remember: the NPV calculation discounts future
cash flows for the time value of money.
To help you remember
this, think of a banana,
just remember there’s
an NB at the end.
N
A
IRR = A + [(B-A) x NA – NB ]
A B A NA NA NB
A = Lower discount rate
B = Higher discount rate
Step 1
NA = NPV at lower discount rate
NB = NPV at higher discount rate
Find out what your investment cash flows are.*
*Remember that cash outflows are
Year
0
1
2
3
negative and that any cashflows
happening today are in year 0.
Step 2
Year
0
1
2
3
Cash flow
(1000)
210
260
720
Take your first discount rate, either given
in the question or an arbitrary one, say 10%,
and discount your cash flows.
Cash flow
(1000)
210
260
720
r=10%
1
0.9091
0.8264
0.7513
Your year 0 discount
factor is 1 – we don’t
discount today’s money.
PV @ 10%
(1000)
191
215
541
(53)
If you are struggling
with this step, revisit your
notes on Net Present Value
(TC Finance module 3).
Note: If you have a NPV = 0 you’re done.
Your discount factor is your IRR.
Step 3
Choose and apply your second discount factor.
Q
How do I know
which rate to use?
A
We use educated
guesswork.
Picture a basic line graph and work out where your first
discount factor and NPV fall:
NPV
We want to find where NPV=0,
i.e., where the line crosses the x
axis.
?
5%
10%
The IRR formula works best with one
negative and one positive NPV* so
in this case to get a bigger, positive
NPV we need a smaller discount
factor, e.g., 5%.
DF
-53
Year
0
1
2
3
Cash flow
(1000)
210
260
720
Step 4
r=10%
1
0.9091
0.8264
0.7513
PV @ 10%
(1000)
191
215
541
(53)
r=5%
1
0.9524
0.9070
0.8638
PV @ 5%
(1000)
200
236
622
58
*At TPS you can get away
with two signs the same,
as long as the choice of
discount rate moves in the
right direction.
Substitute your results into the formula.
N
A
IRR = A + [(B-A) x NA – NB ]
58
= 0.05 + [(0.1-0.05) x
]
58 + 53
= 0.0761
Watch out for a double
negative turning positive
Step 5
Conclude.
Compare the IRR you have calculated to the required
rate of return.
IRR > RRoR
[Equivalent to
a POSITIVE NPV]
ACCEPT THE PROJECT
IRR < RRoR
[Equivalent to
a NEGATIVE NPV]
REJECT THE PROJECT