Computation of Cost of Capital, Accountancy and Financial management Video Lecture | Accountancy and Financial Management - B Com

so cost of debt is the cost of debt
financing to a company when it issues a
bond or takes out a loan there are two
methods of estimating cost of debt one
is the yield to maturity approach and
other is the debt rating approach so
let's talk about the yield to maturity
approach first
the yield to maturity is the annual
return that an investor earns on a bond
today assuming that he holds the bond
till maturity so let's take a simple
example let's say that a company issues
a bond and this is a tie in both with
quant as well as material that you saw
in afar a in the reading on non current
liabilities so essentially we are
figuring out what is the return that a
company needs to provide its bondholders
so if a company issues are born let's
say that a company issues a five-year
ten percent semi-annual bond and let's
say that the par value is equal to
thousand let's say that the issue price
was equal to nine hundred and fifty so
this is a discount bond because the
issue price is less than part and so if
you if you recall your Fr a lesser the
the interest rate of ITM is going to be
more than ten percent
to figure out the exact number you need
to pull out your calculators and let's
just quickly see the cash flow here so
at time zero the company
let's let's look at it from an investor
perspective so investor pays up 950 and
now what will the investor get so in
this case since we have five years and
semi-annual we will have twenty six
months periods so one two all the way -
I'm sorry so five year semiannual so we
actually have ten periods and what is
the coupon payment that the investor
will get every six months remember this
period is six months so the interest
payment that he will get every six
months is 5% of thousands so 5% of
thousand is equal to fifty so he will
get 50 50 and so on and as at maturity
the investor will get 50 plus he will
get par value that hopefully this should
be very familiar and to calculate the
YTM we first calculate the six-month
yield so that six-month yield you
basically calculate using your your
calculator so plug in n is equal to 10
your T V is equal to minus 950 your
payment is equal to 50 FV is equal to
thousand and you have to compute the
interest rate this interest rate that
you compute will be the six-month
interest rate and then you simply
multiply it by two to come up with the
annual rd so you can you can do the
calculation I am pulling up my
calculator and doing the same right now
so let's get into
DVM mode so you should get an interest
rate of five point six seven and to come
up with your cost of debt you need to do
five point six seven multiplied by two
which is eleven point three four percent
so as you can expect since this is a
discount bond the interest rate is going
to be higher than the coupon rate and if
you get this answer that is what you use
as the pre-tax rate for your vac formula
okay another approach is called the debt
rating approach when a reliable current
market price for a company's debt is not
available so that's the nine fifty
figure in a previous slide then the debt
rating approach can be used to estimate
the before tax cost of debt so what the
analyst can do is use the rating and
maturity of the firm's existing debt to
estimate the before tax cost of debt so
what you can say is let's say that the
rating on your company's debt is
currently double a B and you can see
that in the market other bonds with the
similar rating and similar maturity have
a cost of debt equal to 15% then as a
proxy you can use 15% for your cost of
debt
now let's talk about the cost of
preferred stock generally speaking with
preferred stock there is a common
dividend that stays or there is a
dividend preferred dividend that remains
constant and let's say that you have a
situation where you have preferred stock
with par value equal to 50 which pays
dividend of
10% so what this is saying is that the
actual dividend value so the preferred
dividend is 10% of par value which is
equal to 5
so this is our cash flow let's say that
our preferred stock is trading at 45 so
the dividend is 5 every year and let's
say that the preferred stock is
currently trading at 45 then the way we
come up with the cost of preferred
dividend it's equal to the annual
payment which is 5 divided by 45 which
is equal to
eleven point so this is equal to eleven
point so 11.11% so it's a simple
calculation and if you recall this is
based on the annual T formula where you
have a very simple cash flow of five
five five forever so this is an annuity
and the way you figure out the present
value of an annuity so in this case the
present value of this annuity would be
the market price or the stock so the
present value is equal to the the
annuity cash flow which is five divided
by the the rate that we are using or the
interest rate from this formula you can
simply derive that r is equal to five
over P if P is given as it was in our
case this was fortified that's how we
come up with this formula so very
straightforward okay
cost of common equity and this is
extremely significant because you will
see this concept again in portfolio
management and then you will see it
again in equity so if you understand
this well now then you are in good shape
so cost of equity we generally denote
this as R II so cost of equity is the
rate of return required by a company's
common shareholders a company may
increase equity through the reinvestment
of earnings so that's retained earnings
or through the issuance of new shares of
stock the estimation of common equity is
challenging because of the uncertain
nature of future cash flows in terms of
amount and timing so this is just a good
to know even though at CFA level one we
are
given the data so we don't encounter
this challenge but in the real world
obviously we have issues now how do we
calculate our e there are three methods
number one Kapaun capital asset pricing
model so the next one is the dividend
discount model this is yeah and the
third is the bond yield plus risk
premium method you need to know all
three very well so let's get into it one
of the most important formulas and
Finance is given right here and this is
your capital asset pricing model so
essentially the four steps here are as
follows the cost of equity is equal to
the risk-free rate
so obviously step one is to figure out
what the risk-free rate is in your
economy let's take the Pakistan example
so risk-free rate here is about 13
percent and remember the risk-free rate
has inflation built in so whenever we
quote a risk-free rate it is the nominal
rate which is the rate on government
bonds and in Pakistan that's roughly 13
percent right now plus beta this beta
represents the riskiness of common
equity and we'll talk about this in a
little more detail later but the basic
idea is this beta is a measure of how a
given stock moves with the market so for
example for if the market is going up by
two percent and let's say that this
common equity then also generally goes
up by two percent and if the market is
down by two percent
then the stock generally also goes down
by two percent so if essentially this
talk has the same roughly the same as
and moves up and down with the market
then we say that beta is equal to one so
in other words market beta is one and if
a given stock moves up and down with the
market then that stock has a beta of one
a risky stock which has say a beta of
two means the following this means that
if the market generally is going up by
two percent then the stock goes up by
four percent and the risk comes in on
the downside where if the market goes
down by two percent then the stock goes
down by four percent so this is the
general idea behind behind beta so let's
take a simple case where we have a stock
with a beta of two so this is relatively
risky stock as depicted here so that's
step number two wriggling out the beta
and then step three is figuring out the
risk premium or sometimes called the
market risk premium the market risk
premium is equal to the expected return
on the market so in pakistan's context
this would be the expected return that
you would get if you invested in the
Karachi stock exchange let's say that
you bought a index fund based on the KS
e100 let's say that the expected return
there is 19% minus the risk-free rate
which is 13 percent so in pakistan's
context the approximate
market risk premium is 6% so if you are
discounting a stock which has a beta of
two then the required return on equity
would be 13% plus 2 times 6 which is 12%
so this would be equal to 25% a high
number but that is expected given that
we have a high discount rate high risk
period and relatively high market risk
premium another interpretation of this
market risk premium so the market risk
premium of 6% this is the additional
return that equity investors demand for
taking the risk of investing in the
stock market in other words in by
misting in risk free government bonds an
investor could get 13% by taking the
additional risk of investing in the
stock market investors require an
additional return of 6% ok in your final
in your in your exam you might have
questions that either give you the
expected return of the market and the
risk-free rate or at times you are
simply given the risk premium which in
this case is 6% so read the words very
carefully the second model that you need
to know is the dividend discount model
and this again is based on present value
of cash flows so I will first give you a
simple scenario which ties in with
material that you saw in quant so let's
say that you have a cash flow which is a
growing perpetual
so what's the growing perpetuity a
growing perpetuity means that let's say
that you have a cash flow of one that
you get at the end of period one and
let's say that this is growing at a rate
of two percent and let's say that our
required rate of return is ten percent
then the present value of a growing
perpetuity is equal to cash flow watt so
cash flow one divided by discount rate
minus G which is the growth rate so in
my simple example cash flow 1 which is
the cash flow at the end of period 1 is
1 divided by the discount rate which is
10% so that is 0.1 minus the growth rate
which is 2% so that is 0.02 so the
present value will be 1 divided by 0.8
so this is actually 1 divided by 0.08 so
1 divided by point zero 8 is equal to 2
so this is equal to 12.5 so we are
saying that the present value is equal
to 12.5 for this cash flow now in the
context of a dividend paying stock the
the formula changes essentially the same
formula instead of CF 1 we simply write
this as d 1 or dividend 1 so the present
value for a dividend paying stock is the
dividend that you expect at the end of
period 1 divided by R minus G notice
that we do not use the dividend at time
0 in many questions you'll see this
referred to as the dividend that was
just paid out so you need to figure out
what's D 1 which
either be given to you or if you are
given D not then you increase it by 10%
to get d1 so the price of a share at
time zero then is this formula d1 over
the cost of equity minus G but if you
are if you know the price of the share
and you want to find R then you simply
rewrite this equation in terms of art so
using some simple algebra you can see
that the cost of equity is equal to d1
over the current market price plus the
growth rate so given the expected
dividend at the end of period 1 given
the current price and given the expected
growth rate you can find the cost of
equity now how do you find the growth
rate the approximate formula for growth
rate is the retention rate retention
rate is the percentage of earnings that
are retained so let's say that a given
company retains 60 percent of its
earnings so the retention rate would be
0.6 multiplied by return on equity so
remember return on equity is your net
income divided by equity so let's say
that the return on equity for a given
company is 20% then in this case the
growth rate is going to be 0.6 into 20
which is 12% so so you need to know
these formulas given a problem where you
are shown the payout ratio a payout
ratio is the percentage of earnings that
appeared out so to calculate the
retention ratio you simply do the 1
minus payout ratio multiply that by our
o.e the logic for this formula is
straightforward as you can imagine if
you have two companies that are equal in
all respects one company retains more of
its
and invest those earnings in the company
clearly that company will grow faster so
that's why there is a positive
relationship between growth and
retention rate also a company that has a
higher return on equity will grow faster
and there again you see a positive
relationship between growth and return
on equity so make sure you understand
this formula for growth and make sure
you understand this formula for
calculating our e given dividend price
per share and growth rate and there are
several practice questions in the
curriculum as well as in I'm sure in
your study notes make sure you do those
because this is a guaranteed question on
your exam bond yield + risk premium
approach so this is the third approach
and it's very simple you simply add a
risk premium to the market yield on the
farms long term did suppose company DS
interest rate on long-term debt is 10%
the risk premium is estimated to be 5%
then the cost of equity is simply 10%
plus 5% now notice this 5% is different
from the market risk premium that we
talked about earlier this is the risk
premium for a given company over for a
given company's common stock over that
company's bond so here you simply add
these two and come up with 15%