This master class introduces and explains four key investment appraisal techniques: Accounting Rate of Return (ARR), Payback Period, Net Present Value (NPV), and Internal Rate of Return (IRR). These methods are used by companies to evaluate and select the most profitable investment projects that maximize shareholder wealth.
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hi there welcome along to this kaplan
master class on investment appraisal my
name is andrew moer and i'm a tutor at
so the plan for this short video is to
run through the main types of investment
appraisal now just to remind you what
investment appraisal is about a company
might be looking to choose which project
to do so they might have a range of
different projects that they need to
decide on or different investments that
they need to make a decision on and
we're going to use these techniques to
decide which of those investments are
going to be best for shareholders which
of these are going to really make those
shareholders happy
and maximize their wealth which is often
the aim of financial management to
maximize shareholder wealth
so we've got these four techniques we're
going to look at today the first one is
called the accounting rate of return
otherwise known as the arr
we're then going to move on to this
thing the payback period
we're thirdly going to look at npv's the
net present value and finally we'll look
at the internal rate of return commonly
known as the irr so these are the four techniques
techniques
now for each one what i'm going to do is
just give you a quick overview of what
it's about
i'm then going to do an example so for
each one i'll do a little example just
to give you an idea as to how they work
and then we're going to look at the
advantages and disadvantages of each as
well because in a lot of exams they like
you to then discuss the method that
you've used or to consider the
weaknesses of particular methods so i
thought it'd be worthwhile just
recapping the main advantages and
disadvantages of each as well so you've
got quite a nice little overview of each
of these four types of investment
appraisal by the end of this
session so this first one the accounting
rate of return the arr um just be
careful this is also known as return on
capital employed roce for a particular
project um so they do sometimes mix up
the name but we're going with this thing
the arr and what this is is the average
annual profit before interest and tax so
pbit profit before interest and tax
divided by the investment that you've
made in the project now there are two
ways of dealing with that investment
which we'll explore in my example in
just a minute or two
so all this is doing really is just
giving you a percentage return
on your investment so if the answer
comes out say 15
what we're saying is this is giving us a
15 return
on the investment we made on this
project so it's a nice simple measure um
that's widely used a lot of people will
use this um to compare projects and it
works nicely of projects of different
sizes as well
let's have a quick look at an example
then so i've just made up some some nice
easy numbers here we've got this four
year project we're making the initial
investment of of 150 scrap of 50 and
then we've got p bits so profit before
interest and tax
of 60 50 80 and 30 across the four years
of the project now we're often assuming
in financial management that we're not
going to earn any returns on our project
in year zero so year zero is today
that's when we're buying that machinery
or investing in this in this particular
project um immediately up front we then
assume that we start getting returns
from that a year later so in year one is
where we start getting those returns so
you notice there's not a p bit figure
in that year because like i say we're
not going to buy the machine today and
instantly made loads of money from it so
we assume that they start a year later
so if we think about first of all the
formula says we need the average annual
profit before interest and tax so all
i'm going to need to do is take the average
average
of these four figures here so i'm just
going to need to take the average of
those four figures and hopefully you're
all okay with averages
if i just add them up and divide them by
four and that will give us the average
annual profit before interest and tax
so sure enough if i do that um we end up
with 55 so that's the average
profit before interest in tax is 55 if
you add up the four numbers and divide
them by four
so that's the top bit of the formula
that we need that's the average annual p bit
bit
what we now need to do is divide it by
the investment
as i said there are two ways of doing
that the the simplest way probably is
just to divide it by the initial
investment so firstly what i'm going to
do is just do 55 over 150 what is that
as a percentage and if i do that if we
use the initial investment so 55 over 150
150
we end up with 37
is our average um return so that's the
accounting rate of return that's the
percentage return we're getting on our
investment each year
now what that doesn't factor in is this scrap
scrap
remember we said that we were going to
sell it for 50 after four years
we haven't thought about that yet if we
haven't brought that into it so what you
can do instead of using the initial
investment on the bottom of this formula
you can take the average so what you do
is you take the average of what you paid
for it and what you sell it for
so we buy this thing for 150 but then at
the end we sell it for 50. so it's only
really cost us 100 isn't it if you think
about that it's only really cost us
sort of halfway in between those two
things and so what we do is if you do
150 plus 50 gives you 200 divide that by
two so we're just taking the average of
the two things so halfway between what
we bought bought it for and then what
we're selling it for at the end um so if
you do that using the average investment instead
instead
so that little bit there is just taking
the average
of the two figures so that's a hundred
you end up with there isn't it halfway
between what we bought it for and what
we're selling it for is 100 um and we're
doing 55 over 100 which obviously gives
us 55 so um it's a different way of
doing it and um they in most exams that
i teach this stuff in they tell you
which way they want you to do it either
using the initial investment method or
the average investment method so you've
got a couple of ways of dealing with that
that
and obviously they do give different
answers so they would need to specify
okay so that's the arr a little example
of of the technique nice and
straightforward hopefully
um in terms of good things about this as
i say it is quick and easy to do
it does take into account the whole life
of the project because it's an average
annual p bit
we are thinking about the whole life of
the project which is good um and it's
also a relative measure which is a
percent that means it's a percentage um and
and
that's good in some ways as we'll see in
a minute sometimes it's not but it does
allow you to compare projects and
investments of different sizes so yeah
whether this is a 10 million pound
investment or a 10 000 pound investment
yeah you'll still be able to compare and
you'll get something relative out which
is quite nice for those comparisons um
um
however it does use profits this is one
of the few investment appraisal
techniques we do that uses profit most
of the others will use cash flows now we
don't particularly like using profits
profits are they're just theoretical
aren't they they're just an accounting
thing and it depends on your
depreciation policy and it depends on
and revaluations and all sorts of
different things
whereas cash flows are much more factual
you can spend cash you can pay out as a
dividend so we prefer using cash flows
and the fact that this uses profit is a weakness
weakness
um it ignores the time value of money
which is that idea of discounting cash
flows we're saying that
80 000 in in five years time or whatever
is still worth 80 000 today
it's not we aren't discounting things
yet so it's ignoring the time value of
money and also these percentages can be
misleading um so these relative measures
although they're good for comparisons
yeah if we're just looking at the
percentage um saying oh this this
project's got an arr of 75 you go wow
that's incredible um but it might be
that that's because it returns 75 pounds
on an investment of 100 pounds
and they think oh actually this is a
really really small
low-key project whereas one might have a
an arr of 60
which is 60 million on 100 million yeah
we don't we can't tell the scale of
things so sometimes these percentages
don't give the the full story um which
isn't necessarily the best thing
so that's your arr the second technique
i want to look at today is the payback
period and which again is hopefully a
nice concept is how long it's going to
take to pay back the initial investment
and the answer for this will be in years
so how many years is it going to take us
to pay back the initial investment
which is which again is hopefully a nice
simple concept
again gonna do a few numbers um here
you'll notice this one uses cash flows
instead of profits so we are looking at
cash flows rather than profits in when
we're doing payback period which is um
which is preferable
what i've done here is given you the
investment of 650 i then made up some
cash flows here 200 250 175 and 300
across the four years
i've then added this cumulative row and
all that is is just keeping track
of where we're at with this project so
we spend 6.50 so at year 0 we're
immediately 650 down
we then end up with 450 and if what i've
done there is you start with your 650
investment if i know then add back 200
because we're earning 200 in year one
all i've done is just add
six the minus 650 i've added on um 200
and then we've ended up with our our
450. so i've just added those together
we're just keeping track of how much
we've got
equally even earned back 250 in year two
so now we're 200 under um in year three
uh we earned that 175 so now we're 25
under we're pretty close to breaking
even there remember we're looking at the
point at which we get to zero when do we
break even and then in year 4 we make
300 so now we're on 275. so hopefully
you can see that the breakeven point or
the payback period
is going to be somewhere between these
two isn't it because we've gone from
being under um zero to suddenly we're
over zero so at some point in between those
those
now if we were doing this to the nearest
whole year you'd just say four years um
it's taken four years to pay back i know
we've nearly paid it back after three
years we're on -25 we're really close
but we technically we haven't yet so
we'd have to wait until year four to say
it's fully paid back
some questions and and some exams want
you to go into that little bit more
detail then and actually say specifically
specifically
how many months has it taken us to pay
it back and if you assume that we earned
this this 300 back evenly throughout
year four so it's spread out nice and
evenly across the year we can guess
roughly how many months through the year
we need to get to now we only need 25 to
break even don't we um so we only need
25 more to get back to zero so what you
could say is throughout year four we
only need to go 25
over 300 of the way through the year
to get back to zero so that's a very
small amount
so we're going to say the payback period
will be three years plus 25 over 300 of
a year
and if we want to sort of talk in in
more plain english if we want to turn
that into months what we'll do is 25
over 300 times 12
so that ends up being exactly one month
now with that you'd always want to round
up so if it came out as just under a
month we'd want to call it a month but
equally if it came out say is 1.2 months
you'd want to be saying actually we're
going to round that up to two months
because if we said one month it wouldn't
quite have paid itself off yet so you're
always going to round up with payback
period always go just beyond where you
need to be
just to make sure it's paid off so in
this situation the payback period ends
up being three years and one month so
that's how long it will take to get back
so let's think about some advantages and
disadvantages and we're using cash flows
as we said which we prefer
nice easy concept to explain to people
this is how long it's going to take you
to pay back what you invested in it
really nice concept so even for
non-financial managers or people you
know maybe not even financially minded
this is a nice one to be able to explain
and it also links to liquidity now
liquidity is is all about cash so
the shorter the payback period
the better for the company the shorter
your payback period is the quicker
you're breaking even
the better and so it does link to
getting that cash back into the business
which um a lot of investors will like um
because they'll think right we want our
cash back quickly from this investment please
please
now one of the big disadvantages is the
fact it doesn't consider the whole
project um because anything beyond that
payback period once you've got to that
payback period
we're done uh with payback period
there might be cash flows beyond that
there might be year five year six year
seven all these cash flows coming in
it doesn't think about those once you
get to your break-even point once you
get to zero
it is it's it's finished so you might be
turning away some amazing projects that
have really big cash flows in the later years
years
because you're just looking at the the
payback period so it's not great from
that it's not looking at the overall
profitability of the project it's just
looking at how long it takes to pay
itself back um which is yeah maybe not
the best
um this method that we've looked at here
ignores the time value of money as well
and so that idea of discounting things
back to their present value um again
we haven't done that yet there is a
technique called the discounted payback
period which does do that um so you just
have to look out for that which is a
slight improvement on this method
and also there's not a clear decision
yeah the answer is coming out in in
years isn't it it's saying
all right your payback period is three
years and one month in that question we
just looked at
well is that should we do the project then
then
i don't know um is that a good project i
don't know i'm not sure so it's not a
clear decisive yes or no or this is
risky this isn't it's it's still then up
to you know to managers and so on to
decide whether it's worthwhile so it's
not a really clear-cut black-and-white
now of all the investment appraisal
methods we look at um
um
mpvs are the best and they are the they
are all singing all dancing they they
tick all the boxes a lot of these
weaknesses we've been discussing get
fixed using npv's um so they are the
most thorough most detailed most widely
used they're brilliant they're really
good for investment appraisal and
there's a simple concept it's just the
present value of all the money you're
getting in from a project less the
present value of all the money you're
spending on the project
and just to remind you if that ends up
being positive
and if it ends up being negative
you should reject it
if it's exactly zero by the way that is
at the break-even point which we'll look
at shortly but um
so if it's zero that's the break-even
point but in simple terms if it's
positive what that means is your inflows
are greater than your outflows so yeah
let's do it it's going to make us money
whereas if it's negative it's the other
way around the outflows are greater than
the inflows it's not worth it and at the
break-even point your inflows and your
outflows are the same so it doesn't
really matter um so that's the decision
criteria so that's a really nice
like we said with um payback period not
a clear decision npvs give you an answer
at the end it says yes or no shall we do it
it
shall we not it's a really really
clear-cut decision
so let's have a look at a little example
um so i'll just get rid of that and
bring up some numbers so we've got our
initial investment and we've got our
cash flows just the same as the payback
example then um
um
what i've then done is discount those
cash flows using a discount rate of 10
um so these are what we call the
discount factors one 0.909 826 751 and 683
683
you can get those often in most exams
you'll get given some tables that give
you your discount factors so how to turn
those cash flows into their present
values so just to remind you for example
what this is doing is it's saying right
if we're getting 300 in four years time
that's not worth 300 today because of
this time value of money so what i'm
going to do is discount it using this
rate of 0.683
and in today's terms
that's worth about 205 and so 300
like pounds or whatever in four years time
time
is worth about the same as 205 today so
we're getting all these things back into
their present values now as a quick um
you can use your tables to get those
discount rates something i like doing
especially if you're using software in
this exam which again a lot of
qualifications are now
what you can do is you can do a little
trick which is equals one plus the rate
uh to the power of which is this little
shift six
and so if you do one plus the rate um
and then that that's the little top hat
shift six on your keyboard and then do
minus the year that will work out the
discount rate for you so for example here
that would be
equals one plus ten percent
to the power of
minus and then i click on that cell there
there
and so that would be minus zero in this
situation and that would give you one um
and then if we do year one um it will be
you'll do it to the power of minus one
so that'll give you 0.909 etcetera um so
that's a nice little shortcut and what
you can do then is just drag that
formula across and it will just fill in
your discount rates for you i'm so much
quicker and that also helps if the
discount rate isn't in your tables so if
it's an odd you know if it's 12.3 or
something um if this will still work you
can still use it um so that's a nice
little way to get those discount rates
right once you've done all that and
you've got all your present values we
just need to add them up
so if you just add up all of these
present values so the mpv is just the
sum of those
which comes out as plus 75. so in this question
question
the inflows all those positive numbers
in year one two three and four
add those up they are exceeding the
investment of 650 by 75 and therefore
it's worth it and that's a really nice
little way to do it and you should
always comment on your mpvs um if it's a
if you can i would say accept the
project as a positive mpv will increase
shareholder wealth so that's a nice
little phrase to
to use there because it's positive we
now in terms of good things it's an
absolute measure and what that means is
the answer will be in uh pounds or
dollars or whatever currency you're
doing your mpv in
but it tells you
how much this product is going to make
you it's quite factual an absolute
measure is nice this is how much money
it's going to make us this is by how
much it will increase shareholder wealth
rather than a percentage or years which
are all relative and open to
interpretation it's much more factual
which is which is great
it does take into account every single
cash flow the whole life of the project
is taken into account um it does also
consider the time value of money that's
another one that's not here on the list
but it does think about discounting
things which is good and as we said
there's that clear accept or reject
decisions remember if it's positive you
accept it if it's negative you reject it
but at the end there's an answer yes we
now these
mpvs are really dependent on that cost
of capital now i just used a discount
rate of 10 which would be the company's
cost of capital when you're doing this
that's that's a whole other masterclass
now i'm uh recording a a class on the
cost of capital so that will be
available as well if you if you need to
look at that
that cost of capital is
based on a lot of assumptions there are
a lot of things that go into that that
mean it's a little bit approximate um
and if you change that in an mpv
it massively
can cause the the mpv to change so i use
10 in the last example if i use 12
instead for example the mpv would be
much lower um so there is that reliance
on that very sensitive to changes in the
cost of capital
um it's also quite complex to explain
especially to people who aren't
financial managers
so whereas with payback period you say
oh yeah it's the time it takes to pay
back the initial investment great we'll
get that yeah nice easy concept with
this you're saying right what i've done
is i've taken the present value of all
the forecast cash flows for the next
four years um i've deducted the present
value of the outflows forecast for the
next four years um discounting them
using the company's cost of capital
and because the inflows exceeded the
outflows i think we should go ahead and
do this project and you can just imagine
a non-financial manager going what have
you just said to me um i've got no idea
what you're on about
whereas with payback period it's going
to take three years to pay yourself off
great i get that um so it's going to be
quite hard to explain potentially to
people who who aren't in this
don't work in this area
um it does rely on forecasts um
so yeah we're predicting what sales are
going to be in four or five years time
which is which is almost impossible to do
do
that's true of all of the investment
appraisal techniques to be fair um that
we are there is an element of
forecasting and guessing what we expect
to happen but um it feels with mpvs
we're quite we're a lot more detailed
with mpv's um so yeah there are a lot of
forecasts going on in there which which
again are based on on estimates
so that's it for mpvs overall brilliant
method really widely used heavily
examined in all financial management
papers um so yeah very very common
so you need to be all over that and
again i am actually going to do a
master class on exam technique of the
bigger mpvs as well so there is going to be
be
more content available from kaplan on
doing mpvs and a few tips for the bigger
ones of those
the fourth and final one i wanted to
look at in this session though was the irr
irr
and that is the discount rate at which
your mpv is zero
now in that last question um we with the
mpvs we i did it at 10 didn't i and the
mpv came out as plus 75.
what we're looking at now is what what
rate would have meant that the npv is
zero so what i often call this is is is
so it i think that's actually a nicer
name for apologies for my
dodgy writing but the break-even
discount rate is what i actually prefer
to to call this um it's the discount
rate at which your mpv um comes out as a
zero rather than it being actually a
so if we look at um this example with
some cash flows again so it's the same thing
thing um
um
what you can do in
excel and in a lot of the exam software
now as well is to use this irr function
um so if you highlight these cells
don't worry about the years just just
those and it's the cash flows it's not
the discounted cash flows it's the ones
before you've discounted anything if i
do equals irr
uh of
and click on the left one and drag it
across that will tell me what the irr is
and you can try that again try it in
your exam software but it will work um
and that comes out as 15
so if you do it again you can do it in
excel if you want it does work so equals
irr just highlight those cells and it
will tell you what the rr is now there
is another way of finding the irr which
is this linear interpolation which involves
involves
doing two mpvs so you use a higher rate
and a lower rate um and there's a
formula you can use to do that that's a
lot more approximate it's a lot more
guesswork and it's a bit it's a bit of a
faff um so
so
again i much prefer if you are able to
use this in your exam then then i would
recommend doing it
so just to prove to you that this is
right um so we've said right 15
if we discount this using 15 percent now
we should get an mpv of zero so just to
prove it to you um i've done that so
i've done my 15 discount factors um
again you could use that little formula
i showed you earlier or you could use
tables if you get them um to get those
15 discount um discount rates
and if you discount at a 15
add it all up the npv sure enough comes
out as zero
now that's really nice for this company
to know because they know right at the
moment their discount rate what was it
10 we used earlier um we've got a little
bit of leeway then it can go up all the
way up to 15 before we break even
if the company's rate is 16 or 17
this is going to go into negative
territory at the mpv and therefore it
shouldn't be worth doing so 15 is like
the turning point from it being a good
project to a bad project
so it's a really nice point to know
now in terms of the irr
it does use cash flows as well which is
great the whole life of the projects
taken into account
and you don't need to know the cost of
capital this is working out that
break-even point so it doesn't need a
cost of capital to be able to calculate it
it
so we're not reliant on that which is
which is quite useful
unfortunately it can produce either zero
or multiple answers if you've got
irregular cash flows so if you've got a
project where you invest at the
beginning earn a bit of money then you
have to invest a bit more then you earn
a bit more invest and invest earn
it can
that can give you
several different answers for the irr
which which obviously isn't ideal and
quite confusing or if it's an amazing
project it might not have an ir at all
there might not be one
so it's not necessarily the clearest cut
and there is there is something called
the modified irr which um you may come
across in later studies which which is
an improvement on that
i also think the name is a little bit
misleading it says
it's a rate of return it's not really a
rate of return it's a it's the discount
rate at which your mpv is zero so if you
said the irr is
is is 10 to someone or 15 percent it was
wasn't it in this one
all right the internal rate of return of
uh is 15 on this project they'll think
okay right that means it's returning us
15 a year
that's the accounting rate of return
really isn't it and that's that's
something different what this is is
we're saying if you use 15 as a discount rate
rate
then it will break even so it's it's a
little bit misleading and also again
it's a relative measure it's a
percentage um which as we've talked
about um has its advantages and
disadvantages but
means that you don't know exactly how
much money it's going to make you so
this should really be used in
conjunction with the mpv rather than
instead of so it's a nice thing to do
side by side so do an mpv and work out
right that's it for those four
investment appraisal techniques
hopefully that's been useful as a quick
overview of the the main methods that we see
see
as i said there are further master
classes going to be available in terms of
of mpvs
mpvs
and also the cost of capital um as well
so plenty of other things to help you
but hopefully that's given you a little
a bit of a start on investment appraisal
and i wish you good luck with the studies
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