Download IRR = 12.3%

Internal Rate of Return
Andrew Jain and Ravinder Saidha
What We Will Cover
• What is Internal Rate of Return?
• Formula to calculate IRR for:
•
•
•
•
•
•
•
•
Projects / Common Stocks
Zero-Growth Models
Constant Growth Models
Multiple Growth Models
Crossover Rate
Independent & Mutually Exclusive Projects
Advantages and Disadvantages of IRR
Conclusion
What is Internal Rate of Return?
• Another way of making a capital budgeting decision
• Is calculated when the Net Present Value is set equal
to Zero
• There are four model types we will cover:
•
•
•
•
Projects / Common Stocks
Zero Growth
Constant Growth
Multiple Growth
IRR for Common Stocks
• Formula
CFN
CF1
CF2
NPV  CF0 

 ... 
0
1
2
N
(1  IRR ) (1  IRR )
(1  IRR )
N
CFt

0
t
t 0 (1  IRR )
Sample Question
Time Period:
0
Cash Flows:
PV of the
inflows
discounted
at IRR
-1,000
-1,000
NPV = 0
1
2
500
400
3
300
4
100
Sample Question Continued
• Can only find IRR by trial and error
CFN
CF1
CF2
NPV  CF0 

 ... 
0
1
2
N
(1  IRR ) (1  IRR )
(1  IRR )
500
400
300
100
0  1000 



1
2
3
(1  IRR ) (1  IRR )
(1  IRR )
(1  IRR ) 4
• IRR = 14.49%
Practice Question
Professor Stephen D'Arcy is planning to invest $500,000 in to his own
insurance company, but is unsure about the return he will gain on this
investment. He produces estimated cash flows for the following years:
•
Year 1: $200,000
•
Year 2: $250,000
•
Year 3: $300,000
How do you find his internal rate of return for this investment?
200,000
250,000
300,000


(1  IRR )1 (1  IRR ) 2 (1  IRR )3
• A
500,000 
• B
 500,000 
200,000
250,000
300,000


(1  IRR )1 (1  IRR ) 2 (1  IRR )3
• C
 500,000 
200,000
250,000
300,000


(1  IRR )3 (1  IRR ) 2 (1  IRR )1
• D
500,000 
• E
This is a trick question
200,000
250,000
300,000


(1  IRR )1 (1  IRR ) 2 (1  IRR )3
IRR for Zero Growth Models
• A zero growth model is when dividends per
share remain the same for every year
• Formula:
D1
IRR 
P
• Where:
• D1 = Dividend paid
• P = Current price of stock
Sample Question
• Andrew is prepared to pay his stockholders $8 for
every share held. The current price
that his stock is currently held for is $65.
What is his internal rate of return?
$8
IRR 
$65
• IRR = 12.3%
IRR for Constant Growth Models
• A constant growth model is when the
dividend per share grows at the same rate
every year
• Formula is similar to zero growth, except
you have to add growth:
D1
IRR 
g
P
Sample Question
• Rav paid $1.80 in dividends last year. He
has forecasted that his growth will be 5%
per year in the future. The current share
price for his company is $40.
What is his IRR?
 What is D1?
 Do * (1 + Growth Rate)
 $1.80 * (1+5%) = $1.89
$1.89
IRR 
 0.05
$40
 IRR = 9.72%
IRR for Multiple Growth Model
•
•
•
•
A multiple growth model is when dividends growth
rate varies over time
The focus is now on a time in the future after which
dividends are expected to grow at a constant rate g
Unfortunately, a convenient expression similar to the previous
equations is not available for multiple-growth models.
You need to know what the current price
of the stock is to find IRR
N
Formula:
D
D
P
t 1
•
t
(1  IRR ) t

t 1
( IRR  g )(1  IRR )T
Where:
•
•
•
•
•
Dt = Dividend payments before dividends are made constant
Dt+1 = Dividend payment after dividends are set to a constant rate
t = time dividends are paid at
T = time that dividends are made constant
P = Current price of stock
Sample Question
•
•
The University of Illinois paid dividends in the first and
second year amounting to $2 and $3 respectively. It then
announced that dividends would be paid at a constant rate of 10%. The
current price of the stock is $55.
We know:
•
•
•
•
•
D1 = $2
D2 = $3
P = 55
T = 2 (as after second year, dividends become constant)
We need to find D3:
• $3 * (1+10%) = $3.30
55 
•
$2
$3
$3.30


(1  IRR )1 (1  IRR ) 2 ( IRR  0.1)(1  IRR ) 2
IRR = 14.9%
Practice Question
•
Professor Stephen D'Arcy is the CEO of a large insurance
firm, AIG. He is prepared to pay $10 in dividends for the first three years, in
which after the third year, the growth rate in dividends will be 10%. If the
stock currently sells for $100,
how do you find his internal rate of return?
• A
100 
$10
$10
$10
$11



(1  IRR )1 (1  IRR ) 2 (1  IRR )3 ( IRR  0.1)(1  IRR ) 4
• B
100 
$10
$11
$12.1
$13.31



(1  IRR )1 (1  IRR ) 2 (1  IRR )3 ( IRR  0.1)(1  IRR ) 4
• C
100 
$10
$10
$10
$11



(1  IRR )1 (1  IRR ) 2 (1  IRR )3 ( IRR  0.1)(1  IRR )3
• D
100 
$10
$10
$10
$10



(1  IRR )1 (1  IRR ) 2 (1  IRR )3 ( IRR  0.1)(1  IRR )3
• E
I have no idea what you want me to do
Crossover Rate
• The crossover rate is defined as the rate at which the
NPV’s of two projects are equal.
Source: http://people.sauder.ubc.ca/phd/barnea/documents/lecture%202%20-%202004.pdf
Internal Rate of Return
• Advantages
• Doesn’t require a discount rate to calculate
like NPV calculations
• Disadvantages
• Lending vs. Borrowing
• Multiple IRRs
• Mutually Exclusive projects.
Disadvantages
• Lending vs. Borrowing
• Example: Suppose you have the choice between projects A
and B. Project A requires an investment of $1,000 and pays
you $1,500 one year later. Project B pays you $1,000 up front
but requires you to pay $1,500 one year later.
Project
C_0
C_1
IRR
NPV at 10%
A
-1,000
+1,500
+50%
+364
B
+1,000
-1,500
+50%
-364
Disadvantages Continued
• Multiple IRR’s
• In certain situations, various rates will cause
NPV to equal zero, yielding multiple IRR’s.
• This occurs because of sign changes in the
associated cash flows.
• In a case where there are multiple IRR’s,
you should choose the IRR that provides
the highest NPV at the appropriate discount
rate.
Disadvantages Continued
• Mutually exclusive projects can be misrepresented by the
IRR rule.
• Example: Project C requires an initial investment of $10,000
and yields a inflow of $20,000 one year later. Project D
requires an initial investment of $20,000 and yields an inflow
of $35,000 one year later. It would appear that we should
choose project C due to its higher IRR. Project D, however,
has the higher NPV.
Project
C_0
C_1
IRR (%)
NPV at 10%
C
-10,000
+20,000
100
+8,182
D
-20,000
+35,000
75
+11,818
Conclusion
• There are various types of models for calculating IRR
including common stock, zero growth, constant
growth, and multiple growth.
• Despite the disadvantages covered, IRR is still a much
better measure than the payback method or even
return on book.
• When applied correctly, IRR calculations yield the
same decisions that NPV calculations would.
• In cases where IRR causes conflicts in
decision-making, it is more useful to use NPV.
Questions?