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(15 of 20) Ch.9 - IRR approach issues: comparing mutually exclusive projects - YouTube
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And now, let's look at the last issue, issue
number three, mutually exclusive projects.
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So here we are comparing two projects.
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So, we have $100 million and that's all we
can invest, we cannot invest into two projects,
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A and B, right.
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That's what mutually exclusive means.
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We have to pick one.
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So, what do we know about each project?
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So, let me first read what the problem says.
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The real estate company has $100 million that
it would like to invest into a new real estate
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market.
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So maybe buys, you know, a few buildings in
some geographic region, is choosing between
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two mutually exclusive properties.
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Market A would generate $50 million in one
year, $40 million in two years, another $40
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million-- sorry, 40 million in two years,
40 million in three years and $30 million
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in four years.
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If $100 million is instead invested into market
B, then in one year the real estate company
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would generate a $20 million profit.
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In two years, it would generate a $40 million
profit, in three years $50 million, in four
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years $60 million.
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So, these are our cash flows.
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This is a conventional type project because
we invest money today and receive money in
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all future years.
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OK.
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Because these are mutually exclusive project,
we cannot invest money into both, even if
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both look good.
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So which market should the company invest
$100 million into?
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And we want to use the internal rate of return
approach.
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So, let's try a couple of different discount
rates and complete the net present value for
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those separately for each project.
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If you try let's say 5% and use that as the
discount rate for project A, then the net
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present value will be 43, it's all in million
dollars, right?
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Instead, if you try a 50% discount rate for
project A and compute the net present value,
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again using the cash flow keys then we get
a negative $31 million net present value.
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So, we can connect these two points again
with a smooth curve, it slopes down into the
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right, that's the net present value profile
for project A. When we do the same thing for
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project B, add a 5% discount rate, the project
base net present value is $48 million.
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At 50% discount rate, project B's net present
value is negative $42 million.
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We connect the result in two points on our
graph and get the net present value profile
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for B. So, the NPV profile for A is the blue
line, the NPV profile for B is the purple
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line.
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And of course, in one step you can calculate
the internal rate of return for each project.
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For project A that we plotted first, the internal
rate of return is 24%, for project B that
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we plotted second, the internal rate of return
is 21%.
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Now let's see how we would be making our investment
decision.
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Here, things are pretty complicated.
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What does the traditional IRR rule say?
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The traditional IRR rule would tell us that
project A should be accepted if the required
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return, a number that's given to us, is less
than the IRR for project A which is 24%, right?
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So, in this range between 0% and 24%, project
A should be accepted.
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And that makes sense because the NPV line
for project A lies above the horizontal axis,
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which means the net present value is positive.
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But the traditional IRR rule would also tell
us that project B should be accepted if the
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required return is less than 21% which is
the IRR for project B. But the problem is,
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you know, this implies that both projects
should be accepted when the required return
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is less than 21%, right.
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We have this sort of overlap for the acceptance
regions but we cannot do that because we know
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that A and B are mutually exclusive.
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So, we can't use this traditional IRR rule.
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We need to figure out something else.
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And now let's look at this graph more carefully,
let's see what's going on.
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See how the two NPV lines, just based on how
they were plotted, they're crossing.
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And the crossing point means that this is
where the switch occurs between accepting
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one project and accepting the other project.
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So you may realize that if the discount rate
is less than this crossing point, you know
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at the level of the crossing point, then in
this range of discount rates, the NPV line
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for project B is higher than the NPV line
for project A, which means you make more profit
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if you choose project B than if you choose
project A. So, for any required return below
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the discount rate at which the two NPV lines
cross, we should accept project B for which
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the NPV line is higher and reject project
A. Now what happens at higher levels of the
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required return?
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So now we are moving further to the right
from the crossing point, right?
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We are increasing our discount rate.
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When we reach the 21% IRR for project B, until
here, the NPV is higher for A than for B.
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So, A will be accepted, B will be rejected.
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If you keep moving further to the right, right?
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The discount rate is increased again.
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We are still going to be doing the same thing.
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We are going to be looking at the net present
value being higher for A and actually negative
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for B. So, we are still going to accept A
and reject B. But once we exceed the IRR for
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project A, the 24% rate, that's when both
NPV lines are below the horizontal axis.
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So, neither one of the two projects are good,
they're both going to, you know, force us
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to lose our money.
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So, in other words, both projects would be
rejected if the net present value-- sorry,
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if the discount rate, the required return
that is given is greater than the IRR for
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project A, the 24% rate.
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So, see how we have three sort of ranges of
the required return.
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And depending on where the required return
is, in which range it falls, we're going to
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be accepting either project B or project A
only or neither.
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Now, a tricky question I like ask in my class,
in which case are we going to accept both
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projects?
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And usually the class says, oh, that where's
the two lines cross, right?
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And my answer is always you're forgetting
that the two projects are mutually exclusive.
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We cannot accept both.
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So, we can never accept both projects.
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Now, what's going on in the point-- in the
crossover point?
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What's going on here is the two net present
values are the same for the two projects.
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So, what's true is that if the discount rate
is exactly at this crossover point, we are
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indifferent between which project to invest
our money into, whether project A or project
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B. But we are not going to invest into both
because they're mutually exclusive.
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Long story short, with mutually exclusive
projects we can never accept both projects.
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If both are worth it, we need to only pick
one.
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So, things got really complicated when we
are looking at two cross and NPV profiles
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on our graph.
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So, what should be the correct IRR decision
rule in something complicated like this?
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Just like we saw on the graph, to summarize,
we're only accepting project A if the crossover
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rate is less than the required return and
if the required return is also less than the
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IRR for project A. We would accept only project
B if the required return is in the range that's
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below the crossover rate.
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We reject both A and B if the required return
is in the range that's above the internal
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rate of return for project A. And we can never
accept both projects because they're mutually
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exclusive.
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Now, a natural question here would be, so what
is the crossover rate?
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Can we calculate it?
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And the answer is in fact we can.
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