Internal Rate of Return

1 / 21
About This Presentation
Title:

Internal Rate of Return

Description:

Practice Question. Professor Stephen D'Arcy is planning to ... E This is a trick question. IRR for Zero Growth Models. A zero growth model is when dividends per ... – PowerPoint PPT presentation

Number of Views:658
Avg rating:3.0/5.0
Slides: 22
Provided by: art8198

less

Transcript and Presenter's Notes

Title: Internal Rate of Return


1
Internal Rate of Return
  • Andrew Jain and Ravinder Saidha

2
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

3
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

4
IRR for Common Stocks
  • Formula

5
Sample Question
  • Time Period 0 1 2 3 4
  • Cash Flows -1,000 500
    400 300 100

PV of the inflows discounted at IRR
-1,000
NPV 0
6
Sample Question Continued
  • Can only find IRR by trial and error
  • IRR 14.49

7
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?
  • A
  • B
  • C
  • D
  • E This is a trick question

8
IRR for Zero Growth Models
  • A zero growth model is when dividends per
  • share remain the same for every year
  • Formula
  • Where
  • D1 Dividend paid
  • P Current price of stock

9
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?
  • IRR 12.3

10
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

11
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 (15) 1.89
  • IRR 9.72

12
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
  • Formula
  • Where
  • Dt Dividend payments before dividends are made
    constant
  • Dt1 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

13
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 (110) 3.30
  • IRR 14.9

14
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
  • B
  • C
  • D
  • E I have no idea what you want me to do

15
Crossover Rate
  • The crossover rate is defined as the rate at
    which the
  • NPVs of two projects are equal.

Source http//people.sauder.ubc.ca/phd/barnea/doc
uments/lecture20220-202004.pdf
16
Internal Rate of Return
  • Advantages
  • Doesnt require a discount rate to calculate
  • like NPV calculations
  • Disadvantages
  • Lending vs. Borrowing
  • Multiple IRRs
  • Mutually Exclusive projects.

17
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.

18
Disadvantages Continued
  • Multiple IRRs
  • In certain situations, various rates will cause
    NPV to equal zero, yielding multiple IRRs.
  • This occurs because of sign changes in the
    associated cash flows.
  • In a case where there are multiple IRRs,
  • you should choose the IRR that provides
  • the highest NPV at the appropriate discount
  • rate.

19
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.

20
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.

21
  • Questions?
Write a Comment
User Comments (0)