Title: Internal Rate of Return
1Internal Rate of Return
- Andrew Jain and Ravinder Saidha
2What 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
3What 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
4IRR for Common Stocks
5Sample 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
6Sample Question Continued
- Can only find IRR by trial and error
- IRR 14.49
7Practice 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
8IRR 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
9Sample 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
10IRR 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
11Sample 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
12IRR 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
13Sample 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
14Practice 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
15Crossover 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
16Internal Rate of Return
- Advantages
- Doesnt require a discount rate to calculate
- like NPV calculations
- Disadvantages
- Lending vs. Borrowing
- Multiple IRRs
- Mutually Exclusive projects.
17Disadvantages
- 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.
18Disadvantages 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.
19Disadvantages 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.
20Conclusion
- 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.
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