Internal Rate of Return (IRR)
Ferdous Arfina Osman
What is IRR?
• IRR analyzes the potential return of a new project that a
company/govt considers undertaking
• IRR is a metric used in financial analysis to estimate the profitability of
a future investment
Cntd..
• IRR does two things:
i) estimates cost of capital through discounting
ii) estimates Net Present Value (NPV)
• IRR represents the discount rate at which the NPV of an
investment is zero
• IRR considers what discount rate will be needed to produce
an NPV of 0.
Net Present Value (NPV):
• NPV is a discounted cash flow method that considers time value of money in
evaluating capital investments
• NPV is a method of calculating the present value of cashflows of an
investment proposal using the cost of capital as an appropriate discounting
rate.
• Time Value of Money and Discounting:
• When we estimate receiving money in future we discount (reduce) that to
present value. Value of money falls with time passes by
• Discounting means discounting Future value (FV) to Present value (PV). That is
the value of money.
• Using a discount factor (10/11%) we discount the FV
Computing Present Value (PV)
PV= FV 1
Formula: (1+r)n
• (PV =Present value; FV=Future Value;r=discount rate; n=number of year)
At 10% discount rate PV of 500 crore taka will be:
PV=500x 1
(1.10)1
= 454.5
n
Discounting Factor
Using a discount factor (randomly 10/11%) we discount the FV
PV FV
455 500 in a year
Computing NPV
Year Cash Inflows DF 10% PV
0 1,36000 1 -136,000
1 30,000 0.909 27,270
2 40,000 0.826 33,040
3 60,000 0.751 45,060
4 30,000 0.683 20, 490
5 20000 0.621 12,420
NPV 2,280
Calculation of IRR
• IRR represents the discount rate at which the NPV of an investment is zero
meaning :
the PV of the expected cash inflow=Initial cash outflow (investment)
• IRR considers what discount rate will be needed to produce an NPV of 0.
• Calculate two NPVs for the project at two different discount rates to have one
+NPV and one –NPV
• To get Negative NPV higher discount factor to be chosen than the one used for
positive NPV
Steps of Calculating IRR
To calculate IRR, you need two NPVs : one positive and one negative.
Calculate two NPVs for a single project at two different discount rates to have
one +NPV and one –NPV .
While calculating if you get negative NPV (-) then calculate the second NPV
with lower discount rate to get a positive NPV (+)
If the first one is + NPV then calculate NPV with higher rate to get a negative
NPV (-)
Then positive and negative NPVs are calculated by using a formula to get a rate
at which NPV becomes 0.
Exercise
• Calculate the IRR of an investment of TK1,36,00 crore which yields the following cash inflows:
Year Cash inflow
0 -136,000 (Outflow)
1 30,000
2 40,000
3 60,000
4 30,000
5 20,000
NPV 1
Year Cash Inflows DF 10% PV
0 1,36000 1 -136,000
1 30,000 0.909 27,270
2 40,000 0.826 33,040
3 60,000 0.751 45,060
4 30,000 0.683 20, 490
5 20000 0.621 12,420
NPV 2,280
NPV 2
Year Cash Inflows DF 12% PV
0 1,36000 1 -136,000
1 30,000 .893 26,790
2 40,000 0.797 31,880
3 60,000 0.712 42,720
4 30,000 0.636 19,080
5 20000 0.567 11,340
NPV -4,190
Formula of IRR
IRR= L+ NL x (H-L)
NL-NH
L=Lower Rate; H= Higher Rate;
NL= NPV at Lower Rate
NH=NPV at Higher Rate
IRR= L+ NL x (H-L)
NL-NH
= 10+ 2280 x (12-10)
2280- (-4190)
= 10+ 2280 x 2
2280 +4190
=10+ 4560
6470
=10+ 0.70
=10.70%
IRR= 10.70%
• So, IRR is 10.70%
• At this rate if the PV of all the inflows is calculated it will be equal to
the initial investment and the NPV will be 0.
• Company may also have a certain hurdle rate/ benchmark (11%). If
IRR becomes greater than 11% project is viable. If it is less than 11% it
is not viable.
