Internal rate of return

SHAH ABDUL LATIF UNIVERSITY,
GHOTKI CAMPUS
Course Title: Project Evaluation
Instructor: Nadia Memon
Lecture topic: Different investment criteria
Batch: BBA-Part IV, 7th Semester
DEPARTMENT OF BUSINESS
ADMINISTRATION

Topics of discussion
 Internal Rate of Return
• The IRR rule
• Qualities of IRR
• Problems with IRR
• Modified Internal Rate of Return
 The Profitability Index

The Internal Rate of Return
 The internal rate of return universally known as IRR is the discounted rate that
equates the present value of a project’s expected cash inflows to the present value of
the project’s costs(initial investment).
 IRR is the way to find out a single rate that summarizes the merits of project by
providing the exact figure of return rate that is expected by firm to break-even and to
evaluate related project with same investment options.
 As this technique is closely related to NPV but in NPV we consider the discounted rate
that we can get elsewhere on the same investment unlike in IRR we calculate the
discounted rate that is internally based on projects own estimated cash flows rather
than any opportunity cost or rate we get elsewhere.
 Apparently NPV and IRR provide identical result, but it is only possible when cash
flows are conventional (normal) and projects are independent( not mutually
exclusive).

The IRR Rule
 More generally it is said that the discounted rate that makes NPV of an
investment equals to zero that is IRR.
 When NPV is equal to zero means no value is created neither destroyed,
economically it is break-even of investment and so firm is indifferent between
taking and not taking the project.
 Based on IRR rule, an investment(project) is acceptable if the internal rate of
return exceeds the required return(hurdle rate). It should be rejected
otherwise.
 when the IRR is determined, companies compare it with their hurdle rate or
minimum acceptance rate of return (MARR) generally known as cost of capital
calculated through comparing interest on debts, risk and other factors. If the IRR
is higher then hurdle rate, the project will be considered otherwise rejected.

 The Internal Rate of Return with NPV profile
 NPV profile
 With NPV on Y axis
and discount rate
(IRR) on X axis.
 Graph can be
developed by using
investment and
estimated cash
flows with different
discounting rates.

 The Internal Rate of Return with single period investment
 Internal rate of return enable us to calculate the return of simple as well as for complicated
investments. Finding IRR for single period investment is relatively easy.
 Fore example:
 We have invested 500,000 in a project, after one year we have cash flow of 525000. what is
the return on this investment?
 With the help of NPV formula, setting NPV= 0
 NPV = 0 = -500,000 + (
525000
(1+𝑅)
)
 500,000 = 525000/(1+R)
 1+R = 525000/500,000 = 1.05
 R = 1.05 – 1
 R = 0.05 or 5%

 The Internal Rate of Return for annuity cash flow
 Finding IRR for annuity or with constant cash flows is more complicated, unfortunately the only way
to calculate it is trial and error until we find a solution (rate ) that brings 0 NPV value.
 A project that provides annual cash ﬂows of $24,000 for nine years costs $110,000 today. At what
discount rate would you be indifferent between accepting the project and rejecting it?
 NPV = −I + C 𝟏 −
𝟏
𝟏+𝐑 𝐧
𝐑
 Lets, place 15% as IRR
 NPV= - 110,000 + 24000 𝟏 −
𝟏
𝟏+𝟎.𝟏𝟓 𝟗
𝟎.𝟏𝟓
 NPV = - 110,000 + 24000 (4.771586667)
 NPV = 4518
 NPV is still positive so we must try some higher value like 15.5%, 16%, 16.05% till we get 0 NPV.

• A project has a total up-front cost of $435.44. The cash ﬂows are $100 in the
ﬁrst year, $200 in the second year, and $300 in the third year. What’s the IRR?
If we require an 18 percent return, should we take this investment?
• Let's start with 0% rate , 10% and 15% .
• NPV = -435.44+ 100 + 200 + 300 = 164.56
• NPV = -435.44 +
100
1+0.1
+
200
1+0.12 +
300
1+0.13 = 76.26
• NPV = -435.44 +
100
1+0.15
+
200
1+0.152 +
300
1+0.153 = -0.02
• The IRR for this project is almost 15%.
 The Internal Rate of Return with multiple cash flow

 The Internal Rate of Return using spread sheet
 Because finding IRR with trial and error is a tedious process so we can use
spread sheet or financial calculator to minimize time and efforts.
 In the next slide the spread sheet is given.
 You have to insert values in cells, like mentioned in sheet.
 Then select (formulas).
 Then select IRR from formula table.
 Place values in argument table, by selecting values at once.
 You can place 0 or any value as guess for IRR.
 Note if you calculate IRR, then must calculate NPV with same data to prove
the answer with 0 NPV value.

 Undoubtedly, Internal rate of return fills a requirement by providing exact
number because financial analyst particularly interested in return for some
projects rather then value addition, generally people prefer to talk about rates
rather then rupee values.
 In capital budgeting, the internal rate of return is one method that allow senior
professionals to compare and rank projects based on their projected yield, the
investment with the highest internal rate of return is usually preferred.
 Internal Rate of Return is widely used in analyzing investments for private
equity and venture capital, which involves multiple cash investments over the
life of a business and a cash flow at the end through an Initial Public Offering
or sale of the business.
 Redeeming qualities of IRR

 It’s possible for a very small investment to have a very high rate of return and
large investment have low return rate, investors and managers sometimes choose
a lower percentage return but higher absolute dollar value opportunity.
 Mutually exclusive projects
 Problems arises with IRR when we are trying to compare mutually exclusive
projects which are identical and we have to select one over other, the internal rate
of return in this case IRR can be misleading because relatively higher rates can not
provide higher dollar values.
 Suppose you have two investments. One has a 10 percent return and makes you
$100 richer immediately, the other has a 20 percent return and makes you $50
richer immediately. Which one do you like better? We would rather have $100
than $50, regardless of the returns, so we like the ﬁrst one better. Analyst in this
case find NPV a better measure for evaluation.
 P𝐫𝐨𝐛𝐥𝐞𝐦𝐬 𝐰𝐢𝐭𝐡 𝐈𝐑𝐑

 Non-conventional cash flows
 Conventional cash flows are usually series of positive cash flows with one initial negative cash
flow that is investment.
 In this case of non-conventional cash flows, positive cash flows followed by negative ones and
then by positive ones, because sometimes we have to make more investments over the life of
project.
 In this case the IRR may have multiple values, because more then one discounted rates can
bring NPV equals to 0.
 Fore Example: in this project we have non-conventional cashflows,
year 0 1 2
-60 +155 -100
P𝐫𝐨𝐛𝐥𝐞𝐦𝐬 𝐰𝐢𝐭𝐡 𝐈𝐑𝐑

Problems with IRR
 In this example we can see that
NPV of project becomes equal
to zero at two different rates,
that’s why it will be hard to
determine which IRR rate we
should consider as for
evaluation.
 At 26% rate NPV is almost
equal to zero, where as 33.1%
discounting rate also brings
NPV to zero.

Problems with IRR (NPV Profile)
0.01 0.02
0
-0.2
-0.5
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
26% 32.50% 33.10%
NPV
IRR
NPV
Multiple discounting rates brings 0 NPV

 The Modified internal rate of return (MIRR)
 Modified internal rate of return is a modification of the internal rate of return
(IRR) formula, which resolves some issues associated with that measure as
multiple rates.
 There are several ways to calculate (MIRR), but the basic idea is to modify the
cash flows first and then calculate an IRR using the modified cash flows.
 The rediscounting approach
 The idea is to discount all negative cash flows back to the present at the
required return( cost of capital or rate offered on same investment) and add
them to the initial cost. Then, calculate the IRR.
 Let's get back to our previous example:

If required return is 20%
−100
1+0⋅2 2 = 69.444 + 60 (initial cost) = 129.444
IRR = -129.444 +
155
1+𝐼𝑅𝑅 1 with excel we can try to solve with NPV using
different rates until NPV equals to zero. The modified IRR then is 19.7%


• The reinvestment approach
• In this case all the positive cash flows are compounded and reinvested with
negative cash flows at some required return and then calculate IRR.
• Lets revise our example:
• 155 1 + 0.2 1+ (-100) = 86
• IRR = -60+
86
1+𝐼𝑅𝑅2 with trail and error on excel
• The modified internal rate is exactly 19.72%

 The combination approach
 This approach is the blend of both rediscounting and reinvestment approaches, as negative cash
flows will be discounted and positive will be compounded to get MIRR.
 If required return is 20%
−100
1+0⋅2 2 = 69.444 + 60 (initial cost) = 129.444
 155 1 + 0.2 1
= 186
 The MIRR with zero NPV is : 19.9%
 Note: IRR is only calculated through trial
And error with NPV formula, by trying
Trying out different rates to bring NPV at 0.

 Profitability index is an other useful tool to evaluate investment opportunities, it
is also known as benefit-cost ratio.
 PI is calculated by dividing present value of future cash flows with its initial
investment.
 PI is closely related with NPV, when PV of cash flows is greater than initial
investment it implies positive NPV for project and vise versa.
 The rule of thumb for profitability index is if its value is greater then 1 which
indicate positive NPV, the investment is desirable and if value is less then 1
which indicate negative NPV, it should be left out.
 The profitability index

 Fore example: What is the proﬁtability index for the following set of cash flows
if the relevant discount rate is 10 percent?
 PI = PV of cash flows/initial cost
 PI =
6,200
1+0.11 +
5,600
1+0.12 +
3,900
1+0.13 ÷ 12000
 PI = 5636.36+4628.09+2930/12000
 PI = 1.099 0r 1.1
 According to PI rule the investment is desirable as it has PI value greater then 1.
 The profitability index
year Cash flow
0 -12000
1 6,200
2 5,600
3 3,900

 Closely related to NPV, generally leading to identical decisions
 Easy to understand and communicate.
 May be useful when available investment funds are limited
 May lead to incorrect decisions in comparisons of mutually exclusive
investments.
 At the end all the capital budgeting techniques are closely related and
interchangeable but are used in different scenarios on the basis of available
information and time to evaluate the investment opportunities, these all
techniques can be fruitful when used in their specific context.
 The profitability index at a glance

Doctors Don’t make you healthy
Teachers Don’t make you learn
Trainers Don’t make you fit
Coaches Don’t make you rich
At some point you have To realize
Your Growth is
Your responsibility
Thank you
Have A Great Day

Internal rate of return

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Internal rate of return