Introduction to DCF Valuation and Cost of Capital Estimation¶
Introduces the discounted cash flow (DCF) valuation of a stock. This lecture series focuses on the cost of capital (WACC) side of the model.
Resources¶
Introduction to Discounted Cash Flow (DCF) Valuation¶
Notes¶
The Discounted Cash Flow (DCF) valuation of a stock is often considered a capstone finance model as incorporates many different concepts and also the technical skills to implement them
I have often heard of job applicants being asked to prepare a DCF model to prove their skills and knowledge
It is also generally considered the valuation approach which can be the most accurate, though there are a lot of assumptions which must be made which could influence the results
There are two main portions of the DCF model: coming up with the weighted average cost of capital (WACC) and estimating future free cash flows. Each of these portions have smaller tasks involved
At the end of the day, the concept of the model is extremely simple: take the present value of future cash flows to determine the value of the company. The difficult part is figuring out those cash flows and the discount rate
In this segment we will be focusing on the cost of capital estimation, and we will come back in the next segment to cover FCF estimation
We will focus on using the Capital Asset Pricing Model (CAPM) to estimate the cost of equity and we will discuss several approaches for estimating the cost and market value of debt depending on the availability of data and amount of time that can be invested into building the model
Transcript¶
- hey everyone this is nick diabetis
- teaching you financial modeling
- today we're going to be doing an
- introduction to the
- discounted cash flow evaluation model
- this is part of our lecture segment on
- the cost of capital in the gcf model
- so this model
- the dcf model is a way that we can
- value a stock and it's certainly not the
- only approach
- that can be used for stock valuation
- there are a number of other common ones
- um some of the other common ones are
- the dividend discount model which we
- have briefly touched on
- as well as comparable based approaches
- which
- uh look at similar companies and try to
- uh base the valuation off of the
- valuation of other companies
- uh but different uh valuation models
- are best applied in different settings
- depending on different
- features of the company the dividend
- discount model
- can be a perfectly valid model but
- it should only be applied when the
- dividends
- are very stable they are growing at a
- fairly constant rate
- there's not really a risk of the
- dividend being cut
- and so this is typically only going to
- be very mature companies
- that have a long history of paying
- dividends
- and have not deviated from just
- kind of constant growth in those
- dividends
- and then the comparable approaches
- the issue there is that it's not going
- to be very specific to this
- company you're always just comparing
- to other companies that are out there
- and the approach is only going to be as
- good as those comparisons can be
- and oftentimes for a company or valuing
- there are not
- really good comparables available
- so the dcf model can be applied to any
- company
- and is completely about the particulars
- of this company
- not having to look at any other
- companies and it works just fine for a
- company that does not pay any dividends
- or their dividends have been irregular
- now it is quite a bit more involved than
- these other approaches
- i discussed um
- and that's why a lot of times these
- other
- types of models are still used because
- they're quite a bit
- easier to apply but the dcf
- is kind of the most detailed evaluation
- approach
- and is going to work for any possible
- company
- and then we're also focusing on this in
- the course because it's often considered
- kind of a capstone
- finance model basically you know anyone
- that
- wants to do financial modeling should
- know how to build a dcf model
- and i've often seen this uh as part of a
- job application
- process that employers about actually
- request that you prepare a dcf
- for the interview and so it's definitely
- something that you want to know how to
- do if you want to work in financial
- modeling
- and it covers a lot of different
- concepts
- and brings them all together into one
- model and so
- there's a lot of value in learning it
- just for trying
- to work through all the component pieces
- so what's involved here in the dcf model
- so there's two main sides of this model
- the cost of capital and the free cash
- flow
- sides of the model so you can broadly
- break it down into those two parts
- there is a little bit outside of that in
- determining the
- enterprise value and stock value but
- that's a very small part of the model
- primarily the work involved is in
- estimating the cost of capital
- and estimating the future free cash
- flows
- so for the cost of capital that's the
- main focus of
- this lecture series and then we'll come
- back in the following lecture series
- to look at free cash flow estimation
- the cost of capital estimation has a few
- different parts
- uh we can break that down into the
- debt and equity side of things and then
- within debt and equity you're going to
- have to evaluate both the cost
- or or rate on the debt or equity
- whatever
- the capital as well as the market value
- of it so that we can see uh the
- proportion of each in the capital
- structure
- ultimately come up with a weighted
- average cost of capital or
- whack that represents the entire
- business
- and on the free cash flow side of the
- model there we will be
- uh calculating the historical free cash
- flows based off the
- financials and we'll be projecting
- the historical financial statements
- into the future and then calculating the
- free cash flows off of those projected
- financial statements and then
- all this gets put together to ultimately
- come up with the enterprise
- value of the company
- so the dcf
- uh as you may have already thought a
- little bit by the name
- discounted cash flow uh it's all about
- just taking the present value of
- future cash flows to determine the value
- of this company
- so i mean you'll see that in a lot of
- financial models that at its core we're
- just taking a present value somewhere
- um but that is a very essential concept
- in finance so it's not surprising
- um because we can
- look at any any apps at any asset that
- pays cash flows
- no matter whether it's a stock it's a
- bond it's a derivative
- uh it's a a crypto security token
- whatever it is if it pays cash flows
- then we can value it
- by taking the present value of the
- future cash flows
- plain and simple anything that pays cash
- flows we can value
- by that approach
- uh when thinking about the dividend
- discount model
- there we're saying well the dividends
- are the cash flows
- to the stockholder and so if we just
- take the present value
- of all the future dividends then we're
- going to get the
- value of the stock so that's
- what the dividend discount model is
- based on so also
- on is just the present value of future
- cash flows
- and so the same thing over here on the
- dcf model as well
- just with the dcf model we're looking at
- the
- free cash flows of the company
- which is representative of the company
- company's operations
- and so it's it's made off of the assets
- debt plus equity and so ultimately we
- get
- uh the value of the entire business by
- doing this discounted cash flow approach
- and then we back out the equity or stock
- value
- based upon that
- so we're going to be digging in this
- lecture series into the cost of capital
- estimation and i just quickly mentioned
- before
- uh that what we're trying to get to is
- the weighted average cost of capital or
- the whack
- and within that we have two components
- the cost of equity and the cost of debt
- for the purpose of this lecture series
- we're going to
- ignore preferred stock it is generally a
- very small
- proportion of any company's capital
- structure
- and so it's not going to make much of a
- difference
- but you could apply similar approaches
- there just if you value
- the market value and the cost of uh
- preferred stock then you could work that
- into this same structure
- we're just going to focus on the equity
- in the debt so we're gonna have to
- figure
- out the costs of each of those
- as well as the market value
- of each of those to be able to put them
- together into the whack
- as far as the um cost of equity
- we're going to look at using the capital
- asset pricing model or
- cap m for that approach
- though there are certainly other valid
- models that we could use
- um and cost of debt we'll look at
- a couple different approaches but the
- most common approach is to look
- at interest payments uh
- on the balance on the income statement
- to determine that
- and getting into free cash flow
- estimation
- so there um we have to start by looking
- at
- historicals calculating historical
- uh free cash flows and then we go
- to project the future cash flows
- uh which is typically done by projecting
- the financial statements themselves
- into the future and then calculating the
- free cash flows
- from those projected financials
- so that's a quick overview of everything
- that we're going to be doing in the dcf
- model and then for the rest of this
- lecture series we're going to focus
- on digging into this whack
- and how we can estimate the cost and
- market values
- of equity and debt and put that together
- into the whack we're also going to look
- at
- this uh remaining uh
- enterprise and stock value portion of
- the model and see what we need to do
- there as well
- so thanks for listening and see you next
- time
Enterprise Value and Equity Value¶
Notes¶
When we take the present value of future cash flows, we will get the enterprise value which is a combination of the value from different sources of capital
Ultimately we are interested in determining the value of the stock which represents only equity value, and so we need to extract the equity value from the enterprise value by removing the other components
Many struggle with the concept that additional cash reduces enterprise value. I think it is useful to think through scenarios with the two interpretations of enterprise value: asset value or cost to acquire the company. In the context of cost to acquire, if an acquirer buys the business, they immediately own that cash on hand, so really the cash on hand offsets the purchase price. In the context of asset value, imagine two companies with identical operations. One decides to issue an additional $10M of stock just to put cash on the balance sheet. Now they have $10M of additional equity value, and if cash also added to enterprise value then all of a sudden they would be worth $20M more than the other company despite the same operations. If the cash comes in the equation negatively, then there is no change in value for the stock issuance, which makes sense as the two companies still have the same operations
Transcript¶
- hi everyone
- this is nick diabetis teaching you
- financial modeling today we're going to
- be talking about enterprise value
- and equity value in the context of the
- dcf model
- this is part of our lecture series on
- the discounted cash flow
- valuation focusing on the cost of
- capital side of the model
- so we already gave a quick introduction
- of the dcf
- and now we are getting into
- the enterprise value and equity value
- portion of the model so
- in that um we have to
- disentangle what is enterprise value
- versus equity value
- so the enterprise value is the
- value of the entire business and so you
- can think of it as
- the value of the assets in terms of
- you know the basic accounting equation
- assets equals liabilities plus equity
- so it's the whole asset side and so that
- means it's also
- liabilities plus equity or you can think
- of it as
- the acquisition cost so if you are
- someone that wants to purchase
- this entire company and own it outright
- this
- is how much it would cost you to
- purchase that
- so in terms of the formula that we can
- use
- to define the enterprise value and
- related to the equity value
- we have that the enterprise value equals
- equity value
- plus that value minus cash um
- and then what is the equity and debt
- value in here so this the equity value
- is just the value from the stock
- side of the company
- so going back to assets equals
- liabilities plus equity
- you got to finance your assets with
- either borrowing money the liabilities
- or issuing stock uh the equity side
- so um a company that only issues stock
- and never issues
- debt their uh all their
- assets are going to be financed by
- equity and so all of that is going to be
- an equity value
- but if company has
- a lot of money to finance their assets
- then the debt on the balance sheet
- is representing the debt value
- in the company it's the value of
- the bonds and loans whatever
- instruments they use
- to finance their assets
- so we can use this same formula
- to back into the equity value
- we just do a little bit of algebra flip
- this and we would have
- equity value is equal to enterprise
- value minus debt value
- plus cash um and that's what you can use
- in the dcf model
- to back out the equity value
- uh where where a lot of students
- struggle
- with this definition is the fact that
- we're
- subtracting cash here um
- you might think well cash is a good
- thing so shouldn't it add to the value
- of a company
- and in order to help understand this
- i like to think about these two possible
- ways that we can conceptualize the
- enterprise value
- asset value or the acquisition cost and
- within each one
- there's a way we can understand why
- cash is actually being subtracted to
- determine the enterprise value
- so under the asset value kind of
- interpretation
- that the you know enterprise value is
- representing
- the stockholders uh value as well as
- the value of the loans so
- for that we can think about two
- hypothetical companies which
- have the exact same operations
- they produce the same cash flows they
- everything is the same about these
- companies uh
- even their capital structure and
- everything
- and so they have the same exact
- enterprise value right now
- now say that one of them uh says
- that i'm gonna go issue uh
- 10 million dollars worth of stock and
- so they issue the stock and then get
- cash in return for that stock
- so now they have uh 10 million
- additional dollars of equity and also
- 10 million additional dollars of cash
- the asset side and so the balance sheet
- still balances right
- but if we said that cash should be
- adding to the enterprise value
- well then we would be adding 10 million
- for the equity value and we would again
- be adding another 10 million
- for the cash on the balance sheet so now
- even though these two companies are
- still exactly the same in terms of their
- operations
- one just decided to raise money and just
- hold it
- all of a sudden it's worth 20 million
- dollars more that doesn't make sense
- uh but if the cash actually offsets
- the value of the equity they just raised
- they get 10 million dollars of equity
- but they also have 10 million dollars
- more of cash
- then it washes out and the two companies
- still have the same value
- so that makes more sense now if the
- company
- took that cash and deployed it into
- assets that are going to create value
- for the company
- then it can come back into the
- enterprise value but they have to
- actually use that cash for something
- useful
- in order to increase their enterprise
- value
- and then the other way we can think
- about this is in terms of the
- acquisition
- price how much someone would have to pay
- to own the company outright
- so in that you can think well uh in
- order to
- uh own the company outright they have to
- buy out all the stockholders
- but they also have to buy out all the
- debt as well and so that's why these two
- are both getting added in
- but then after they bought the company
- they have the cash
- uh from the company now in their
- possession
- and so that actually reduces the cost of
- acquiring the company because they have
- that cash coming back to them
- um so either of these ways that we can
- conceptualize the enterprise value
- in both ways it makes sense for cache to
- come negatively
- into the equation
- so that's how we can um
- disentangle the enterprise and equity
- value
- and basically as you complete the dcf
- model
- uh you'll take the present value of all
- the free cash flows
- at the discount rate of the whack and
- you'll be left with an enterprise value
- from that
- so then you can just reverse that
- formula
- to back out the equity or stock value
- in order to get to the stock price
- so that's enterprise value and equity
- value and then the
- lab exercise on this um
- there are two different exercises
- involved here
- so this first one
- you have some cash flows here
- and you're basically trying to figure
- out what is the
- enterprise value you have cash flows and
- you also have a weighted average cost of
- capital
- um and you want to get ultimately to
- both the
- enterprise value as well as the stock
- value
- so you can reverse
- this formula to get to the equity value
- from the enterprise value
- and then if you divide the equity value
- by the number of shares outstanding
- you'll be left with the stock price
- so that's the uh
- first exercise here and the second one
- um
- is similar we're also trying to give the
- enterprise value
- as well as the stock value um
- with a slightly different situation
- so that covers enterprise value and
- equity value
- in the dcf model thanks for listening
- i'll see you next time
Introduction to Cost of Equity¶
Notes¶
We are using the Capital Asset Pricing Model (CAPM) to estimate the cost of equity for the company
There are many other possible models which could be used such as one of the many factor models including Fama-French factors, but CAPM is the most basic and once you understand the approach it is not difficult to switch for a more complex model
In the general approach, we estimate the model on historical data and assume that the resulting estimated parameters will hold in the future to predict the future cost of capital
Transcript¶
- hey everyone
- this is nick dear burtis teaching you
- financial modeling today
- we're going to be doing an introduction
- to cost of equity estimation
- this is part of our lecture segment on
- the dcf model
- focusing on the cost of capital side of
- the model
- so we already gave a quick introduction
- to the dcf model
- and its various parts and then we talked
- through
- enterprise and equity value now we're
- getting
- to the cost of equity estimation
- so we're going to focus here on using
- the
- capital asset pricing model or cap m
- as our model for estimating the cost of
- equity
- now it's definitely not the only model
- we could have used
- uh it does tend to be the most basic
- model that can be applied
- and we're just focusing on the basic
- approach here
- because once we learn the general
- way that we can go about this then
- it is not too difficult to expand into
- using more complex models
- so the cap-m was kind of the dominant
- asset stock pricing model
- from the 60s uh and going into the 70s
- and then in 1976
- we had the arbitrage pricing theory
- come along and that really spawned a
- whole new era
- of models being used to
- look at the returns in stocks
- so that's where you'll have models like
- the pharma french factor models
- and many many other factor-based models
- are coming out of this
- arbitrage pricing theory um
- and so you can definitely expand into
- using those other models
- like palma fringe three five factor or
- whatever other factor models
- you would just need to have data on
- those factors and otherwise you would be
- following
- a similar approach to what we're going
- to do here with the cap
- out but with the kappa
- the general idea is
- that here we have an equation
- where the return on the
- stock is being explained by
- the risk-free rate plus
- a beta coefficient which represents the
- covariance
- of stock this stocks returns with
- the market risk premium
- we multiply that beta by the market risk
- premium
- which is the average return on the
- market
- minus the risk-free rate
- and then we also have an error component
- in here in the model representing that
- this is not going to be exact we're
- never
- going to be able to predict stock
- returns exactly
- if i could do that then i would be very
- rich
- but no one can predict stock returns
- there's always randomness
- involved in them and that is picked up
- by this last
- term here
- um and because it's random
- sometimes it'll be positive sometimes
- it'll be negative and so we just assume
- that on average
- this term is actually zero
- so the approach we're going to use here
- is to estimate the model on historical
- data
- and then assume that that
- the the parameters we fit from the model
- are going to apply in the future as well
- and ultimately uh this ri
- after we use our our parameter we
- estimated from historical and now we're
- calculating the future the ri is going
- to be
- the return on the stock or the cost of
- equity for the company
- those two are actually one of the same
- the return on the stock and the cost of
- equity
- for the company you can think of
- them as just being on opposite sides but
- they're the same thing
- um every uh
- bit of money that the investor earns is
- a cost
- for the company and so those rates are
- going to be the same
- so um getting more specifically
- into the estimation of this
- so looking at historical data we're
- going to have
- historical stock prices and from those
- we'll calculate historical returns
- and we'll have that for our stock as
- well as
- for some security which represents the
- market
- typically the s p 500 is a common
- security that people use for that
- so we have historical prices on each of
- those then we get historical returns
- on each of those and so
- uh we're gonna have the historical stock
- returns coming over here
- uh on the left and then uh we'll have to
- use
- an estimate of the risk-free rate that
- can either be
- uh using the historical risk-free rate
- getting data on treasuries in order to
- estimate that
- or you can just put a static single
- risk-free rate in there that you think
- is representative of the time period
- and then the historical market returns
- uh the s p
- 500 or whatever security you're using
- are going to come in as this rm
- so then the things that we don't know
- are this veda
- and this epsilon the epsilon
- we said sometimes it's it's going to be
- positive sometimes it's going to be
- negative on average it should be zero
- and so we're just going to ignore this
- um
- and just deal with this part of the
- model
- so then we have just one parameter here
- that we're going to estimate and that's
- our goal of
- fitting this model on historical data is
- then to estimate
- this beta um
- so we estimate that beta based off the
- historical data
- and then in order to predict the cost of
- capital
- going forward we have to make an
- assumption
- and that's that the beta that was there
- and the historical data
- is going to be the beta going forward
- so if you have very strong opinions
- about this you could adjust
- the beta in your model if you think that
- the future is going to be substantially
- different than the past
- data is typically thought of as a
- measure
- of systematic risk
- because it's measuring how much this
- company moves
- with the overall market
- so uh you know a beta of two basically
- means that if the market's going up one
- percent then the stock is going up two
- percent
- and if the market goes down one percent
- then the stock is going down two percent
- um and so it's kind of a multiplier on
- the market's returns
- making it into a piece of our overall
- stocks return
- now when the market goes up one percent
- this stock's return even if it has a
- beta two is not necessarily going to be
- two percent
- and that's because of this epsilon term
- it could be higher or lower than that in
- any given time period
- but on average basically uh it's
- governed by the data
- that it should be moving around a
- multiple
- of the markets returns
- um so if you
- think that the company has just taken on
- new opera they just started a new
- business line which is going to be
- substantially more risky
- than their existing business you might
- estimate a historical beta of one but
- you might
- adjust it upwards to 1.1 or 1.2 or
- something like that in order to reflect
- that well there's going to be additional
- risk in the company going forward
- compared to before
- and so you don't just have to take the
- historical one and use it directly but
- that's
- that's the most common is that you don't
- have any new information on whether the
- risk is going to be higher or lower
- and so you just use the historical beta
- um and
- the way that we're going to estimate
- that beta is
- through a regression approach
- um so you know the regression
- is a classic y equals mx plus b
- um and so
- uh the risk-free here is the b the
- intercept
- um and the uh
- b here is the m in the mx and the market
- risk premium
- is the x so this is the exact format
- of a regression equation and so we can
- fit
- a regression on these data in order to
- determine the beta so that's
- what we're going to look at in the next
- two videos
- accomplishing that in both python
- and excel so thanks for listening and
- i'll see you next time
Cost of Equity in Python¶
Notes¶
The process to estimating cost of capital using prior stock prices is straightforward: calculate returns, run the CAPM regression, then take the coefficient on the market risk premium (MRP) as the Beta, then plug the beta in the CAPM to estimate the future cost of equity based on an expected market return and risk free rate
Once you calculate returns, the first row will have missing data as there is no prior price. Statsmodels cannot handle missing data, so we will need to add a Pandas command to remove those rows
Resources¶
Transcript¶
- hey everyone this is nick diabetis
- teaching you financial modeling
- today we're going to be talking about
- estimating the cost of equity
- in python using historical stock returns
- this is part of our lecture segment on
- the dcf model focusing on the cost of
- capital
- side of the model so we've already
- given a general introduction of the dcf
- model
- and its various parts we talked through
- the enterprise value and stock value
- portion
- and we also gave an introduction on
- estimating the cost of equity in general
- kind of the conceptual framework behind
- it
- so make sure that at least you've seen
- that
- general cost of equity introduction
- before coming into
- estimating this cost of equity in python
- so we can go ahead and go over to
- the example jupiter notebook for this
- all of these
- uh materials are there on the course
- site as well
- so uh here's the
- duper notebook focused on estimating
- the cost of equity so here as explained
- in the prior video
- we are using the cap model to
- [Music]
- estimate this future cost of equity
- and to do that we're going to fit the
- model with historical data
- and then use the fitted model to then
- predict the future
- so the first thing that we're going to
- do
- is read in the data that we need to use
- so
- i provided this price data file
- which has the price on the market
- portfolio that could be something like
- an s p 500
- or russell 2000 or
- some kind of index which captures a
- large portion
- of the market and then we have the price
- of the asset or stock that we're
- interested
- in determining the cost for
- and we have a 100
- uh and one different prices here
- for each of the two assets
- so now that we've loaded in this data
- into the data frame
- now we can go about calculating the
- returns because we have prices
- but we need to work with returns in the
- model
- and so the return on a stock or any
- asset
- is just the percentage change in its
- price new minus old overall
- um and thankfully in pandas we don't
- even need to know that
- the formula for percentage change so
- hopefully
- you do know that um but we have this
- percent change method
- on the data frame so you just do dot
- percent change and that's going to
- do that calculation for you on every row
- of every column so that's
- really nice when you just have a data
- frame full of prices you can convert it
- into a data frame
- full of returns with just a single
- command
- and you'll notice that the first row
- here has these
- nans so nan means not a number
- it is the representation for a missing
- value
- in penis this is just saying that there
- was no way to calculate
- the these values because the percentage
- change is new minus
- old over old and for the first row we
- don't have any old we only
- we don't have any prior price to look at
- to calculate the return and so there's
- no
- return for the first period
- um but we do get the returns going all
- the way
- to the end of the data set just fine
- so in the cap model
- we have this market risk premium portion
- here the return
- on the market minus the risk-free rate
- and so we're going to need to calculate
- that in order to
- run the regression because we can think
- of
- a simple linear regression in this
- format
- and so here the uh rate on the market
- minus the risk free is becoming the x
- and this equation so we need to just
- calculate that first
- so that we can use that as the x
- so we're just gonna assume here that the
- risk-free rate is three percent
- uh another approach here is to actually
- collect data on
- treasuries and use historical treasury
- rates
- as the risk free rates and then it could
- vary in each period
- uh but for simplicity here i'm just
- going to use three percent
- which is quite high in 2020 but
- more have more normal rate in normal
- times
- um so to
- come up with that uh market returns
- minus first free well we just take the
- the market market portfolio return
- column
- and subtract the risk free and we can
- save that into a new column
- in the data frame and now we have this
- market risk premium
- column which is just the
- market return minus the risk free and be
- careful about your units here this
- is a percentage and so it should be in
- decimal format
- so now we have the setup that we need in
- order to go
- and run the capem on the historical data
- through an ols regression
- so to run a regression in python we can
- use the stats models package
- so here is kind of the standard
- convention
- for the import so most code samples you
- see online are doing this
- import sas models dot api as sm and then
- we use
- sm dot for everything
- um and it's very important that you
- uh include the constant in this
- regression
- with stats models you do have to
- explicitly tell it to include the
- constant
- um because if you look
- at the format of the cap-m the risk-free
- rate here
- is the interceptor constant and so if we
- estimated it without
- then we would not be appropriately
- estimating the cap
- m and so we need to have that intercept
- um and so we add that here to the market
- risk premium
- and the y is going to be the price of
- the returns on the stock
- and then we can estimate the model um
- but lotus as was already there
- uh we have this missing data error
- coming up that
- exogenous which means the x variables
- contains either infinity or missing
- values which of course we do have
- missing values we saw that before
- the first row has missing values
- and stats models cannot directly just
- work
- with those missing values so what we
- have to do
- is drop those missing values so this
- drop n a command
- on a data frame is going to remove
- any rows which have missing values
- and there are options on it you can say
- uh
- default is if there's anything missing
- in the row it will drop it
- you can also do how equals all and then
- it's
- uh only if everything is missing will it
- drop it
- but here we do want any because which is
- the default
- because uh any missing value
- is going to mess up the estimation so
- after dropping and you can see that the
- first row here
- is what the second row was before
- we have just eliminated this first row
- because it was all just
- missing values so and then we saved that
- back
- into the returns data frame you do have
- to
- assign it back otherwise it's not going
- to take effect
- in the original data um
- so now that we have removed those
- missings let's go ahead and try
- this regression again and this time it
- works just fine
- so we see all the standard uh regression
- summary output all the fit statistics
- and then here is what we're really
- interested in
- the coefficient on the market risk
- premium
- is the beta which was that main
- parameter that we're trying to estimate
- through this approach
- and we see here that the beta is 0.8338
- so this is uh generally less risky
- than the overall market in terms of
- systematic risk
- um so we're going to want to use that
- beta in a calculation
- and in stats models we have this uh
- results.params which is a series
- and a series of the coefficients so
- we've got
- a constant and you'll notice that this
- estimated to be
- uh very close to our three percent
- risk-free rate so that's a really good
- sign that it came up
- as three percent it should not be too
- far from
- uh your risk-free rate and then
- uh we've got the beta here as well so we
- can pull the mrp
- uh coefficient out of that which is the
- beta
- so then just saving that into a variable
- now we've got beta into a variable and
- can use it
- to estimate the future
- market return very sorry to estimate the
- uh cost of equity going forward
- um so again the capital formula now
- we've estimated it and gotten the
- historical
- beta and we're going to assume that beta
- applies in the future as
- well and so now we want to plug that
- beta end
- along with the projected risk-free rate
- going forward and the projected market
- return
- going forward to ultimately come up with
- the cost
- or rate of return on this stock
- so we know the beta and we can just
- assume that the risk free is going to be
- the same as it was
- so then what we do still need to get is
- the market return to plug in here
- so we can just take an average of all
- the historical
- returns and use that as an estimate for
- the future
- now you can definitely adjust this that
- would be kind of like the baseline case
- to just
- take it as it was but then if you think
- a recession is coming up or we've just
- entered a recession
- then it could be lower than this you
- could adjust it downward
- if we're an expansion economy uh then
- you could adjust it upward
- and certainly with uh some kind of uh
- sensitivity analysis or scenario
- analysis or monte carlo simulation you
- can vary
- these kinds of things to understand
- what's going to happen to the cost of
- equity cost of capital ultimate value of
- the stock
- when we change our assumptions about
- what's going to happen in the future
- but here we're just going to use the
- historical assume that that is going to
- apply in the future
- so then we can go ahead and estimate the
- model to get the cost of equity
- going forward so all we do is just plug
- everything into the left hand
- or right hand side of the model again
- assuming this
- epsilon is zero uh so we're going to
- plug the risk free
- plus the beta that we estimated times
- the market return
- that we estimated as the average of
- historical minus that risk-free again
- and then we calculate that and we get
- the overall cost of equity that we can
- go
- and then use in calculating the whack
- which will ultimately let us do the
- discounted cash flow
- valuation of a stock
- so that's what's involved and estimating
- the cost of equity
- and python using the cap m and then if
- you wanted to use a different model
- other than the cap
- m such as maybe like a power fringe
- three factor model the only thing that
- would change here
- is when you uh you would have to collect
- data on whatever factors you want to use
- and then you would uh include those
- in the regression as well as other x
- variables
- and you would also estimate the
- coefficients on those
- and then you would also have estimates
- of those factors
- going forward which would probably be
- based off of
- um averages of the factors historically
- and you could adjust those and
- then you would just plug everything in
- here at the end so the
- approach is going to apply no matter
- which
- type of model you're using you just need
- to change a couple of steps a little bit
- to apply it
- with different stock pricing models
- so that's everything involved here and
- estimating this in python
- in the next video we're going to come
- back and cover handling it in
- excel so thanks for listening and see
- you next time
Cost of Equity in Excel¶
Notes¶
The process to estimating cost of capital using historical prices in Excel is similar to doing it in Python
The main difference is just how we run the regression with the Data Analysis Tookpack GUI rather than through statsmodels
A disappointing aspect of doing this in Excel is it cannot automatically update if you add new data
Resources¶
Transcript¶
- hey everyone
- this is nick diabetis teaching you
- financial modeling today we're going to
- be talking about
- estimating the cost of equity in excel
- this is part of our lecture segment on
- the dcf model focusing on the cost of
- capital
- side of the model so
- we went through this uh intro on the dcf
- model and talked about its various parts
- we discussed enterprise and equity value
- we discussed the general approach to
- cost of
- equity estimation and we also looked at
- how to carry that out in python
- as well so now we're coming to now
- estimating that in excel
- so we can jump over to the
- excel workbook
- so here we have the prices
- on the market portfolio as well as the
- prices on the asset
- and we have the risk free rate as well
- so the first thing that we want to do is
- in order to fit the cap model we need to
- be using returns
- and not prices so we want to calculate
- the returns
- on the market and on the asset so
- um add the market return
- and asset return columns
- and i'm going to start from the second
- row because you can't
- calculate a return on a single value
- it has to be using this value and the
- prior value
- so a return is simply just percentage
- change
- in the stock price and so it's going to
- be
- new minus
- old over old
- i messed up my parentheses there make
- sure you have parentheses around this
- hop
- um so that the order of operations is
- maintained
- and then this should work to calculate
- the return we should get like
- 17 or sorry 11
- 17 yep um
- then should be able to just uh complete
- that down
- that is still working properly and also
- drag that over
- that it's also working properly so now
- we have the returns on both the market
- and the asset
- so then uh in the cap m formula
- we have this return on the market minus
- the risk-free rate the market risk
- premium
- that we need to use to estimate it so we
- can calculate the market risk premium
- as the return on the market
- minus the risk-free rate and fix that
- risk-free rate so that it can go all the
- way down and still reference the same
- rate
- and there now we see this is working
- appropriately
- so now we have the market risk premium
- so now we can go ahead and
- estimate the regression which is going
- to fit the
- historical cap m model so
- we can go to the data tab and
- over to data analysis that is going to
- be the area
- um where we can find the regression
- if you don't see this over here if
- there's no analysis section at all
- you need to enable the data analysis
- tool pack
- in order to do that it's just file
- options
- add-ins manage excel add-ins
- and then you want to check this analysis
- tool pack
- and then it should show up over here
- it's included on all excel
- it just only shows up if you enable it
- so then we can use this data analysis
- and we want to pick regression
- out of this list the regression
- and the y is going to be
- the market risk premium
- or sorry the y is going to be the asset
- prices
- and the x is going to be the market risk
- premium
- and we can put this on a new worksheet
- and here i do not have any labels
- because we had this gap i started from
- here
- um so now we're ready to estimate it
- then we see this uh new sheet open up
- uh we can call this the cap m regression
- and
- we see the beta here as the coefficient
- on the x
- variable so we can see that it's the
- same
- as the one that we had estimated in
- python as well
- and i'm just going to bring that back
- over to this sheet
- for our calculation of
- the cost of capital going forward
- so now we have the beta
- now in order to estimate the future
- cost of capital we also need to know the
- market return
- that we're going to plug into the model
- so
- we can
- calculate the market return as the
- average
- of the historical market returns
- so simply just taking an average
- of the market return column
- will be enough to give a good estimate
- for the market return
- uh now you can always adjust this as
- well as the beta
- based on your expectations about the
- future
- and i spoke about this concept more in
- the prior two videos going over the
- overview of cost of equity and on the
- python side
- um but taking the historical average
- uh is basically our baseline kind of
- estimate for the future and it can be
- adjusted if you think that the future
- is going to be substantially different
- from the past
- so now we have all the component pieces
- that we need to be able to estimate the
- cost of equity
- going forward
- so in order to get the cost of equity
- remember that in the capital formula
- it's the
- first free rate plus the
- beta times the
- market risk premium and the market risk
- premium is the market return
- minus the risk free rate
- so that's all that we have to do to get
- an estimate
- of the cost of equity in
- excel calculate the returns calculate
- the markers premium
- run the regression of the asset returns
- on
- the market risk premium take the beta
- from that
- calculate the historical market returns
- and put it all together
- into the cost of equity estimate for the
- future
- so then in order to wrap up
- this portion of the lecture on cost of
- equity
- uh we also have a lab exercise here and
- so there's some price data on the course
- site you can go ahead and download that
- consumer history rate of two percent you
- want to come up with the beta
- and cost of equity um
- and then i'm also getting into this uh
- you should be thinking about adjusting
- these things if necessary
- so imagine that it's going to recession
- in the future and so the market returns
- gonna be three percent lower
- what would be the new cost of equity
- um and for this exercise feel free to
- use
- either excel or python whatever you
- would prefer
- and the answers are provided for you
- here as well
- so that's everything involved in excel
- cost of equity estimation and the lab
- exercise on this material
- so thanks for listening and i'll see you
- next time
Market Value of Equity¶
Notes¶
If you are dealing with a publicly traded company, the calculation of market value of equity is simply number of shares multiplied price per share
With a private company, this is much more difficult. You can look at public comparables to help with this. If a public competitor has a $10B valuation, and this company has 10% of its market share and similar profit margins, a $1B valuation might be a reasonable estimate
With early stage companies, you might not even have financials or a reasonable public comparable. But often these companies do not have debt and so it is not necessary to estimate the market value as you know it will be 100% of the capitalization
Transcript¶
- hey everyone
- this is nick dear burtis teaching you
- financial modeling
- today we're going to be learning about
- how to calculate the market value of
- equity and this is part of our lecture
- series
- on the discounted cash flow valuation
- model focusing
- on the cost of capital portion of the
- model
- so we have already discussed
- the overview of the dcf model and
- how to work with enterprise value and
- equity value
- and then we also estimated the cost of
- equity so now we're coming to
- estimating the market value of equity
- because ultimately to
- create the whack we're going to need the
- cost and market values
- of both equity and debt
- so coming to the market value of equity
- we are going to need this basically in
- order to
- create the weights and the whack formula
- so the weights are taking
- the market value of equity and dividing
- it by the total capital that would be
- the equity weight
- and the debt weight would be the market
- value of debt divided by the total
- capital
- and the total capital is just the sum of
- the market values of equity and debt
- as long as we're ignoring preferred
- stock which
- for the purposes of this lecture we are
- and it tends to be a very minor portion
- of the capital structure
- so if your company is publicly traded
- it is very straightforward to calculate
- the market cap or market value
- of the company because it's already
- publicly available information you just
- look in the market since it's publicly
- traded
- and there you'll be able to see the
- number of shares outstanding
- as well as the current share price and
- when you multiply these two things
- together you get the market
- capitalization
- which is the same as the market value of
- equity
- so that's all it takes for a publicly
- traded company
- now if your company is not publicly
- traded
- that's where this can become a
- challenging exercise
- so if your company
- is not publicly traded but they are
- well established and have
- competitors which are fairly comparable
- a lot of people will use comparable
- based approaches
- to calculate the market value of equity
- basically look at the competitors which
- uh you would find one that is publicly
- traded or
- hopefully multiple that are publicly
- traded and look at the market value of
- those companies
- and then compare the company that you
- ultimately want to get the market value
- for
- to these companies along different
- dimensions
- to try and back into the market value of
- this company
- for example if a competitor has 10
- billion dollars of market value
- and they have a 10 market share
- and the structure of this company is
- very similar to the one that you're
- trying to value
- and the one that you're trying to value
- has a five percent market share
- and you see that the profit margins are
- similar across the two companies
- then it might be reasonable to conclude
- that the value of
- the company that you're trying to value
- the market value of equity is half
- of the market value of this other
- company so 5 billion
- so these are the kinds of thought
- exercises that
- people go through to be able to come up
- with the market value for
- non-public companies uh by looking at
- comparables
- sometimes you're not even gonna have
- comparables
- especially for very early stage
- companies
- they might be coming up with some new
- technology
- that nobody else has created before how
- do you come up with a comparable for
- that you can't
- and so for those companies
- luckily most of the time those early
- stage companies are not even going to
- have
- debt in the capital structure they're
- going to be 100
- equity uh financed and so to come up
- with their whack it's 100
- equity you only need to consider the
- cost of equity you don't even
- need the market value of equity to
- calculate the whack
- so hopefully that's the case but if your
- company
- is private has no comparables
- and also has debt in the capital
- structure
- then all you can really go off of is
- trying to look at the
- the business and trying to estimate
- the value based on the present value of
- future cash flows
- which of course is quite a bit more
- involved than these other approaches
- but again it's pretty rare that you need
- to do that because these early stage
- companies where you don't have
- comparables
- typically do not carry debt and so you
- don't need to go through this exercise
- but as far as this class is concerned
- and probably most of the time that
- you're going to be
- calculating the whack for a company it's
- going to be a public company
- and in that case just use the market cap
- as
- the market value of equity and you're
- done
- so that covers market value of equity in
- the context of calculating rack
- so thanks for listening and see you next
- time
Cost of Debt¶
Notes¶
If your company is very mature and stable, the financial statements approach to cost of debt may be a reasonable approach
If your company does not have market bonds outstanding or you do not have access to data on these bonds, you are stuck with the financial statement approach regardless
If you can find information on even one market bond, it may be better to use the market rate of bonds approach, though this approach is even better when you can take a weighted average of multiple bonds
The handling of taxes is crucial in dealing with the cost of debt considering that debt is tax-advantaged in the US and many countries
The tax rate can be estimated from historical financial statements
Transcript¶
- hey everyone
- this is nick dear burtis teaching you
- financial modeling
- today i'm going to be talking about
- estimating the cost of debt
- and this is part of our lecture series
- on the discounted cash flow valuation
- model focusing
- on the cost of capital side of the model
- so we have just finished talking about
- the equity
- side of the cost of capital um and now
- we're headed
- into the debt side starting with the
- cost of debt
- and in the following video we'll talk
- about the market value of debt
- so for estimating the cost of debt
- what we're trying to do is determine
- what is the uh percentage
- uh interest rate basically that would
- have to be
- offered on one dollar of additional debt
- issued right now so this
- is the marginal cost of debt that we're
- trying to estimate
- not the historical because we're
- concerned
- about how things are currently the risk
- with the company
- could have changed that changed the cost
- of debt
- and we're considered about the current
- state of the company and so that's why
- we're looking at the marginal
- or cost of raising one additional dollar
- instead of just thinking about the
- historical
- and in estimating this we will discuss
- here two general approaches the
- financial statements approach
- and the market rate of bonds approach
- and each the two approaches require
- different information and so you may be
- forced into one or the other
- but we'll look at both of the approaches
- and
- uh generally the market rate of bonds
- approach
- would be a better approach to take
- because
- that is more directly targeting the
- marginal
- or forward-looking rate of interest
- rather than the financial statements
- approach which
- is only considering the historical
- so the market rate of bonds approach
- basically
- we're going to look at bonds which are
- currently outstanding for the company
- and use the rate on those to determine
- the cost of debt
- whereas with the financial statements
- approach we're going to look at the
- balance sheet
- and so that's always going to be a
- historical look
- at the cost of debt which is not going
- to be able to adjust
- for any recent changes in the cost of
- debt
- since the last balance sheet period so
- if this is a very stable company
- the cost of debt is not changing much at
- all
- over time then the financial statements
- approach
- can get very close to the marginal cost
- of debt
- but in general the market rate of bonds
- approach
- is going to be a better approach but it
- does
- require that information on currently
- outstanding
- bonds for the company and their prices
- so looking more specifically at the
- financial statements
- approach so again we're using the
- balance sheet data
- in order to calculate the cost of debt
- based on the historical information
- and here more specifically
- we are going to take uh well
- interest expense from the income
- statement so it's income statement and
- balance sheet
- so interest expense from the income
- statement and total debt
- from the balance sheet and
- we just have a simple formula then to
- estimate the cost of debt
- which is just that interest expense
- divided by
- the total debt just saying that well if
- you borrowed a thousand dollars
- and you paid a hundred dollars in
- interest
- 100 over a thousand you paid 10 interest
- on the debt that you hold
- now um there's definitely flexibility
- in this measure as far as
- what you count in the total debt
- most commonly people uh just take
- short-term debt and long-term debt and
- add them together to get the total debt
- and often a total debt line item will be
- provided
- on the balance sheet and you can use
- that
- but it's it's you know up for debate and
- discussion whether
- other other sources of debt such as
- trade credit or operating leases
- or things like that should be considered
- in here
- as well but generally most people
- consider uh just the short-term and
- long-term debt
- as the total debt for this calculation
- and you would do this for the most
- recent data available
- and use that as the cost because
- the most recent should be the most uh
- appropriate to estimate the future
- now if you calculate it over time
- and this most recent period is very
- different than the prior periods
- uh then you're gonna have to investigate
- further into the company as to why
- that's the case
- and make a call on is this relevant to
- the future or should i use uh some of
- the older historical periods in order to
- estimate that so
- this can take additional research to
- understand
- which you know how you should
- extrapolate into the future based on
- that historical information
- but as the general approach you would
- just take the most recent data
- available and use that
- so then moving on to the market rates of
- bonds approach
- so again we're trying to get at what is
- the marginal cost of debt or the cost
- to raise new debt and so if we're
- looking at
- what's currently out there in the market
- and how
- those market bonds prices have adjusted
- in response to the changing risk of the
- company
- that's going to give us a good picture
- of the cost of debt today
- for the company
- so the way that we look at that with the
- currently outstanding bonds
- is that we look at the yield of maturity
- on those bonds
- so the yield of maturity is a measure
- of the rate of return on investing in a
- bond
- and it can also be thought as of
- as the company's uh cost to issue a new
- bond
- if they would issue a new bond uh it is
- very typical for companies to issue
- bonds at par
- which means that the coupon rate
- on the bond is equal to the yield
- to maturity and so the interest rate
- that the company is paying
- is equal to that yield current yield of
- maturity
- um now when we look at the historical
- bonds
- the company is going to pay whatever the
- original interest rate was on that bond
- that's not going to change throughout
- the life of the bond
- but the yield does change because the
- price of the bond changes
- and that yield tells us currently what
- is the cost of debt
- for the company
- so we can think of
- the sealed maturity as both
- the rate of return required rate of
- return
- for the investor in the bond as well as
- the cost
- of that bond for the company now again
- looking at a historical basis they're
- actually going to pay the contracted
- rate of
- interest on the bond the coupon rate um
- but the yield to maturity is going to
- adjust as risk on the company changes
- and when the company issues a new bond
- they're going to have to
- issue the coupon rate matching with that
- yield of maturity
- so that's why we can think of it as the
- cost for the company
- as well as the required rate of return
- for the investor
- and to calculate the yield of maturity
- it's simply just the internal rate of
- return or irr
- of the bond um
- and considering that uh
- bonds have very defined payment
- structures with regular payments
- you can use the
- like you know five keys on the financial
- calculator kind of approach
- uh which you have uh also the
- rate function in excel and numpy's
- rate function in python so if you just
- pass
- uh the appropriate other inputs
- uh you know the the time remaining on
- the bond
- the coupon payment uh the price of the
- bond
- the part value put all these things into
- the rate function
- in either excel or python and you'll be
- able to get the yield of maturity
- on the bond and then you can use that
- yield of maturity
- as the cost of debt now
- in the following video we'll talk a
- little bit about seniority and how
- a company can actually have multiple
- different costs of debt
- but as far as we're focusing on this
- course we'll just kind of simplify that
- away
- and just talk about it generally but not
- handle it in the models
- for this class and just use a single
- cost of debt
- for our models to keep them relatively
- simple
- one other thing that we have to consider
- with the
- cost of debt is that
- in our tax system and in many tax
- systems around the world
- debt is tax deductible
- that means that the company is
- going to pay income tax
- on the earnings before tax
- and the interest has already been taken
- out
- or we get to that line item so
- by paying interest you actually reduce
- your income as it's being considered for
- taxes
- and so that reduces your tax payment as
- well
- so uh the way that we can
- kind of think through this think about
- two companies
- which are exactly the same in terms of
- their
- operations and they bring in the same
- revenues
- same cost structure everything
- one of these companies is
- completely equity finance they issued
- stock
- in order to fund their operations
- and then have just kept it growing by
- the retained earnings in the business
- and then the other one has 50
- debt in its capital structure so it took
- out
- bank loans or bonds or
- lines of credit or whatever in order to
- finance half of their assets
- and the other half is that same stock
- issuance as the other company
- so going down the income statement
- they're both going to have the exact
- same ebit so that's
- uh basically the operating income
- after we take the revenues take out all
- the costs of operations
- we're left with the ebit and so those
- two numbers are going to be exactly the
- same
- across the two companies but then
- uh for this 50 debt company
- now they have an interest payment coming
- out to service that debt
- and so that uh ebt which is the next
- line item we just subtract interest and
- then get to ebt
- uh that's going to be low for the debt
- firm
- and higher or the equity firm
- and so now the equity firm is going to
- pay a larger tax bill
- than the debt firm
- and therefore the
- equity firm is going to have a lower
- value than
- the debt finance firm because the
- operations are 100
- the same but one of them had to pay more
- taxes
- and so that company is less valuable
- and what this means going into our cost
- of debt calculations is that
- we can factor in this tax savings
- into the cost of debt we can instead of
- just taking
- whatever the rate of interest is then
- considering that the cost of debt
- we can say well we know we're going to
- get this tax credit because of the debt
- and so we can take that out within the
- cost of debt
- in order to work that into the weighted
- average cost of capital
- so all we have to do there is multiply
- the pre-tax cost of debt whatever rate
- of
- interest there is on the debt securities
- and just multiply that by one minus the
- tax rate
- and that's going to tell us what the
- after-tax cost of debt
- is for the company
- and that way we'll be taking into
- account the fact that
- companies with more debt all else equal
- are going to be more valuable because
- they actually have a lower cost
- of capital due to the tax savings
- so just make sure that when you go to
- include the cost of debt
- into the wac that you multiply that
- pre-tax cost
- by one minus the tax rate to adjust it
- for that tax effect
- so that covers cost of debt
- and in the lab exercise on it we have
- two different levels here
- so the first level um
- we just have some chemical manufacturer
- and we have
- details about a market bond
- that they have outstanding and
- we're trying to get the pre and post tax
- cost of debt for this company
- and then in level two i'm trying to get
- you towards
- uh doing more and more on your own
- so for level two i'm gonna have you go
- to
- stockrow.com that is a good source
- for uh financial statement information
- go there and get walmart's financials
- and then calculate the cost of debt
- actually using those financial
- statements in the financial statement
- approach
- and you're not going to just have a tax
- rate there you're going to also have to
- calculate
- the effective tax rate uh using
- the uh the income taxes that were paid
- and the earnings before taxes
- so and then you can feel free to
- complete
- either of these exercises in either
- python or excel
- so that covers cost of debt and
- we will look in a future video about how
- that works into
- the weighted average cost of capital and
- into the dcf model so thanks for
- listening
- and see you next time
Introduction to Market Value of Debt¶
Notes¶
Simple models often just assume the market value of debt is equal to the book value of debt. While this makes the calculation simple and is sometimes all you can do due to data availability, this can be quite inaccurate for most companies
The market value of individual instruments approach can be the most accurate but requires the most data and takes more effort to implement
We are still keeping things a bit simple for both MV and cost of debt. In a more detailed model you would also consider seniority of the debt when doing these calculations
Transcript¶
- hey everyone
- nick dear burtis here teaching you
- financial modeling
- today we're going to be doing an
- introduction to
- the market value of debt how to think
- about it
- and how to calculate it and this is part
- of
- our lecture segment on the discounted
- cash flow valuation model
- focusing on the cost of capital portion
- of the model
- so we already talked about
- the cost of debt in prior video
- and now we are getting into the market
- value
- of debt because we need the costs and
- market values
- of each of equity and debt to ultimately
- be able to calculate
- the weighted average cost of capital or
- whack
- so
- after a bond is issued its value can
- change
- over time and it almost certainly will
- change over time
- um and this is not a debt course
- and so i'm not going to go into a ton of
- detail here
- um so definitely reference some
- additional debt materials
- if you haven't learned about any of
- these concepts before
- uh when we think about the value of
- debt be it bond bank loan
- whatever else we can determine its value
- just like any other financial asset any
- asset that pays cash flows
- we can always just take the present
- value of
- those future cash flows and that will
- get us the value of the asset
- so for a bond it's going to be the
- regular interest or coupon payments and
- then the final
- uh principal plus coupon payment in the
- last period
- that we use to determine the value of
- the bond
- but remember that when we take the
- present value of something
- it's both the cash flows as well as the
- discount rate
- that affect the value
- and with bonds the
- payments the interest coupon payments
- are contracted at beginning
- of the life of the asset and remain in
- place
- for the entire life of the asset a bond
- is just a contract
- which says that the company is going to
- pay
- a certain amount of interest in return
- for a loan
- and then they're going to return the
- money at the end
- um and so
- the value of the bonds can change over
- time
- but the interest payments cannot change
- and so that means that what must be
- changing is the discount rate
- because those are the only two
- components of the present value equation
- so why would the discount rate change
- for a company
- well a discount rate or a company
- is supposed to be reflecting the amount
- of risk
- in that company and specifically
- we're looking at the rate on the debt so
- specifically the riskiness
- of the company's debt
- so a lot of things can affect that and
- for most companies it does fluctuate
- quite a bit
- over time um
- some things that could affect that
- include taking on additional debt
- if you have a lot of debt already in
- your capital structure you've got to be
- making
- all these interest payments it becomes
- more risky to issue additional debt and
- have an even higher interest payment
- could be starting a new project
- if this project especially if it's
- something
- new that the company is trying to
- innovate
- that is not comparable to their existing
- operations
- it could be substantially more risky or
- less risky
- than the existing operations and that's
- going to change the overall
- mix of risk in the company and therefore
- the cost of debt
- or even just having a bad year can
- change
- the cost of debt or discount rate for
- the company
- because they have to make those payments
- on their interest
- and that's what debt investors are
- concerned about
- if all of a sudden they're less
- profitable this year and they're only
- barely able to make that interest
- payment that's
- a very negative signal or going forward
- in their ability to pay the future
- interest payments and so that raises the
- discount rate
- so why should we care about all of this
- let's walk through an example
- so a company issues a bond it's a
- three-year bond
- 10 coupon and
- as is typical for essentially every bond
- the bond is going to be issued at par
- and that means
- that uh the principal the value of the
- principal
- is equal to
- the price at which the bond is being
- issued
- um companies always just set it up this
- way that's kind of the standard
- in the industry is to do this so that
- the price of the bond when it's issued
- is a thousand
- the same as the
- face value par value principal value
- a thousand dollars
- and when we have a stream of cash flows
- like this
- uh 10 per year and then getting the
- interest
- plus the principal back at the end
- uh then there must the discount rate
- must also be equal to the interest rate
- in order for the bond to be priced at
- par
- so when it's issued everything is in
- sync the coupon rate
- is equal to the discount rate
- and the price of the bond is equal to
- the face value of the bond
- so a year passes by and now
- the company becomes substantially more
- risky they had a bad financial year
- maybe one of the one of the other
- situations we talked about they issued
- additional debt
- et cetera but now
- in order to issue new bonds investors
- are requiring that the company offer 15
- in order for people to be interested in
- buying these bonds
- so because of that now we see that the
- existing bond
- that they had outstanding the three year
- which was originally priced at a
- thousand
- is now priced at 9 18.71
- and that's reflecting that if someone
- buys a new bond that the company issues
- they would earn a 15 rate of interest
- but if they buy this existing bond they
- would only earn a 10
- rate of interest less than the rate
- which would now be offered by the
- company
- and so they should not be willing to pay
- as much for that
- when a new bond would cost a thousand
- dollars
- and we calculate the irr on that bond
- which is the yield of maturity
- and that would be 15
- so the 15
- yield that we have on this existing bond
- with its new market price matches up
- with the cost of debt for the company
- what it would cost to issue a new bond
- but if we look at the book value of the
- debt
- the book value would still be at a
- thousand the book value just stays
- at whatever it was issued at
- and so if you were to
- try to calculate the um
- yield of maturity or cost of debt based
- on that thinking about it
- as being priced at a thousand then you
- would get 10 which is
- far away from the actual new
- cost of debt for the company
- you would also say that
- debt has a greater proportion in this
- capital structure
- than is actually the case because it has
- actually decreased
- in value so we can end up with quite
- interact
- inaccurate estimates if we
- focus completely on the historical
- rather than
- looking at the market
- so how do you go about calculating this
- market value of debt so we'll discuss
- three different approaches here
- and similarly to the cost of debt it's
- going to depend on what data you have
- available
- which approach that you can use and some
- are going to be more accurate than
- others
- so first approach
- we're discussing here is the pure
- financial
- statement approach um and for that
- you're just taking the book value of
- debt and using that as the market value
- of debt
- and sometimes that's all you have enough
- data to do
- and so you just kind of have to settle
- with that
- but it's always preferable to be able to
- look at
- what's going on in the market currently
- to be able to
- come up with the market value of debt
- rather than just
- looking at the historical because of the
- issues that we just talked through
- so then um
- if you have the cost of debt
- and it's actually a market cost of debt
- from the market uh bond approach
- and if you know on average
- the maturity of the company's debt
- then you can basically model
- all of the company's debt as one big
- hypothetical bond
- and use that kind of evaluation approach
- to come up
- with the market value of debt
- and that's going to be more accurate
- than the financial statement approach
- because it does
- consider what's going on in the market
- currently
- but there are a number of assumptions we
- have to make here and
- so um it's not as accurate as the last
- possible approach
- which is you have information on all of
- the debt that the company
- has and the current uh
- details of all of those
- you can calculate the market value of
- each individual debt instrument
- and sum them up to get the total market
- value of debt
- so this is going to be the most accurate
- assuming that
- you can collect all of the data on this
- um if you are missing substantial
- portions of
- the instruments or if you can't get it
- at all
- then it's not going to be an accurate or
- feasible approach
- but if you have that information it's
- going to be the most accurate
- so those are the three approaches we're
- discussing in this course and we're
- going to
- look at how to implement each of them in
- the following video
- but before we wrap up i do want to just
- talk a little bit about the seniority
- of debt
- and we're not going to handle it
- within the examples in this class
- but it is something that you want to
- think about
- if you go to build a more serious
- debt side of a dcf model for wind
- you need to be really accurate in the
- model
- so seniority is the
- concept that uh
- when the company goes bankrupt or if the
- company goes bankrupt
- and they're liquidating the assets
- there is an order in which the different
- debt holders
- get paid off during this process
- so debt holders get paid before
- equity holders uh essentially always
- you pay off all the debt holders and
- then if there's anything left it will go
- to the stockholders but
- uh oftentimes there's not even enough
- money after liquidating the assets to
- pay all of the debt holders
- and so some debt holders are going to
- get paid and others are not and the
- seniority
- is what determines that so seniority
- is just about this payoff order
- a senior loan is going to get paid off
- first
- and then if there's still money left
- over then the junior
- loans are going to get paid off
- and uh there are different levels of
- seniority uh it's often just referred to
- as just
- senior or junior but a company can have
- as many different levels
- of seniority as they want it's just
- however they write the
- bond contracts
- so the seniority is important
- because
- lenders have to consider this bankruptcy
- recovery scenario
- when they are setting the rates that
- they would be willing to lend at
- and if you have a senior loan then in
- this recovery process
- there's a higher chance that you're
- going to get more money out of the
- process
- and with the junior loan there's a lower
- chance that you're going to get money
- or how much or you might not even get
- paid at all
- so the junior loans have to command a
- higher interest rate
- in order to compensate for the fact that
- they're not going to get paid
- at all or as much in the
- recovery bankruptcy process
- um and when
- thinking about the cost and market value
- of debt in this class
- we're not we're not working with the
- seniority we're just assuming
- everything has the same seniority
- but in a more detailed model you would
- want to find the different levels of
- seniority
- in this specific company's debt
- structure
- and treat them separately so here you
- know say there's three levels a senior a
- junior
- and and kind of a medium level of
- seniority
- then you would just take these as three
- categories and you would find the costs
- of debt within each of these categories
- and keep them separate in
- the analysis so it's not going to be a
- big change
- beyond what we're doing in this class
- but it does complicate matters a little
- bit and so that's why we're not
- handling that here but it will be easy
- to extend into that
- after you understand the basic process
- so that's how we can think about
- calculating
- the market value of debt and we'll come
- back in the following video
- to look at examples of calculating this
- so thanks for listening and see you next
- time
Calculating the Market Value of Debt in Python¶
Notes¶
The value of a hypothetical bond approach just uses traditional bond valuation techniques
For the market value of individual bonds approach, again we are just applying traditional bond valuation, but we can use Pandas to apply the single calculation across all the bonds at once
We are also covering some material here on working with dates as you will usually have a maturity date to work with and need to convert it into a number of years
Resources¶
Transcript¶
- hey everyone
- nick dear burtis here teaching you
- financial modeling
- today we're going to be looking at how
- to calculate the market value of debt
- in python using three different
- approaches
- this is part of our lecture segment on
- the discounted cash flow
- valuation model focusing on the cost of
- capital portion
- of the model so
- we in the last video talked through the
- uh three different approaches for
- calculating the market value of debt
- the financial statement approach
- assuming the book value is equal to the
- market value
- the hypothetical bond approach and the
- market value of individual instruments
- approach
- so we'll look at each of these
- and take a look at that last video if
- you want additional detail on all of
- these
- but for here we are going into the
- python example
- of how to do this um and
- the completed example is here on the
- course site
- as well so let's jump over to the
- jupiter notebook
- and again this is split up into three
- sections based on the three different
- approaches so i'll start here by just
- defining some inputs that we're going to
- use throughout
- the total book debt interest expense and
- cost of that
- so you can assume that
- these would be loaded in from financial
- statements
- and um the cost of debt
- was calculated previously in some other
- exercise using the
- financial statement approach or the
- market
- value of a bond approach so we already
- have the cost of debt
- and we got this other info from the
- financial statements
- so now going into the first approach
- which is if all you have is the
- financial statements
- you don't have anything on market
- currently outstanding market debt
- this is all you can do and that's just
- that
- we just assume the uh book value of debt
- the total
- book debt from the balance sheet is
- equal to the market value
- and so we're done so it's really okay
- it's not even a calculation we're just
- using
- the historical as uh the market
- and sometimes that's all you can do
- but we can definitely do better than
- that if we have the data available
- so next is going to
- the hypothetical bond approach
- um so there for the hypothetical bond
- approach we need to also know what is
- the average maturity
- of outstanding bonds and that may be
- difficult to determine
- so that can be a reason that
- you may not be able to go to this
- approach
- but if you do have that then we can
- basically model
- all the company's debt as a single bond
- and
- find the value that way so let's just
- say
- we were able to determine that the
- average maturity on
- the outstanding bonds is uh
- five years and this would be a weighted
- average maturity by the way uh looking
- at the different
- uh values of each of the bonds
- so we want to create a hypothetical bond
- that represents all the company's debt
- so the first thing that we need to do
- is come up with the coupon rate
- that would be paid on this hypothetical
- bond
- which we can get that from the financial
- statements
- we can take the interest expense divided
- by the total book debt
- and take that as the coupon rate on the
- bond
- so with our existing numbers that puts
- the coupon rate at six percent
- so now that we have the coupon rate we
- can create
- the cash flows of the bond and just take
- the present value of those cash flows
- so the coupon raymond the principal
- uh of this hypothetical bond is
- the uh entire debt for the company the
- booked at
- um and the
- coupon payment is just that rate we just
- calculated multiplied by the principal
- and the cash flows are going to be
- that coupon payment um
- for as many periods
- up until the final period
- which then we have uh the principal
- plus the coupon payment
- so calculating that uh with this
- five-year hypothetical bond then we have
- 60 000
- cash flows for the coupon payments
- followed by
- a 1 million 60 000 payment on the end
- so now that we have the cash flows and
- we can use the
- cost of debt which we have calculated
- separately
- as the discount rate then we can
- determine the market value of debt
- and make sure with numpy that you
- include a zero at the beginning of the
- cash flows because
- it always assumes that it's getting
- period zero first and this would be
- period one
- um and through that we get the market
- value of debt
- so here we're getting 920
- 000 as the estimate of the cost or
- market value of debt
- and you don't necessarily have to go
- through this
- approach of creating uh
- the cash flows directly um
- and also if the
- maturity is not a whole number which it
- almost certainly won't be then this
- direct approach won't work this was more
- uh to just kind of emphasize that
- uh theoretically this is what's going on
- here we're just lining up the
- hypothetical bond payments and taking
- the press
- value but there is a formula which
- allows us to do that in one step
- so it's given here
- and then you could you know copy paste
- this formula into your model
- to complete the calculation
- um and that is basically using the
- annuity formula and then adding on
- the final payment as a separate term
- so then with that approach we get the
- exact same
- market value as we did with lining up
- the cash flows
- but this will also work for maturities
- that are not whole numbers
- and we can create a function which
- does all of that so you can definitely
- feel free to
- uh copy paste this function into your
- model
- um and that is going to be taking the
- average maturity cost of that
- total book debt and interest expense and
- giving you
- the market value of the debt by this
- approach
- so then once we have the function we can
- pass in
- whatever numbers different uh average
- maturities
- we could do a sensitivity analysis or
- other extensions etc
- so then coming to the
- last approach here valuing the
- individual
- debt instruments so it's basically the
- same as what we just did but instead of
- creating one hypothetical bond that
- represents the entire company's debt
- we just do this uh value bond valuation
- process with each of the individual
- bonds that the company holds
- and then sum up the values of each of
- those to get the total market value
- so let me load in
- some data and this is just some
- example data of just three different
- bonds
- um with some
- maturities and coupons principle
- so um in order to
- use this approach we do
- have to make sure that we are getting a
- good sample
- of the company's uh bonds we should have
- nearly all of the company's debt
- instruments
- for this approach to be valid
- so the way we can check that is we can
- sum up the principal
- on all the debt instruments that we have
- and that should be close to the
- company's total book debt
- the one that you get from the balance
- sheet
- so these two things are close and they
- don't have to line up exactly they
- almost
- never will line up exactly because there
- you know could have been additional
- bonds issued or retired since the last
- balance sheet period
- um but as long as they're close i would
- say within
- a few percent of each other then
- this approach is going to be valid and
- if you're further than fro then rather
- than a couple percent
- you could do some kind of adjustment
- approach if you have 10 percent
- if you have 90 of the bonds uh
- outstanding then you could just you know
- multiply the ending market value that
- you get by
- 1.11 repeating to uh
- to kind of normalize that but in general
- i would say just
- use this approach if you have data on
- nearly all of the bonds
- outstanding
- so in this case they match up exactly
- because it's a simple example and so
- we're going to move forward
- so then it's going to be the same
- approach that we just looked at
- lining up the cash flows and taking the
- present value of those cash flows
- and then we can
- get the market value of any bond
- and you may want to use the function we
- looked at earlier
- instead because that will be able to
- handle the
- decimal maturities as well but this is
- just kind of
- for sake of example i think this is
- easier to conceptualize
- what's going on
- so now we have a function
- which can get us the market value of a
- bond
- and we have a data frame full of bonds
- how do we put these two things together
- apply this a function to each of the
- rows in the data frame
- to get the market value of each of the
- bonds that we have information on
- so dot apply on the data frame
- is what's going to be able to do that
- for us
- so i'm just going to briefly here
- introduce dot apply
- and dot apply is just letting you
- take a function which works on
- one row or one piece or one cell
- one part of the data frame and you want
- to apply it across the data frame so
- that's why it's called apply
- um and to help understand
- what's going on when we call apply
- um so here i'm doing df.apply
- and i'm passing this understand apply
- function
- um and
- what we will see here um is we see a
- print statement for each time the
- function is called
- then uh we will see what is being passed
- into this function got values
- and we can see it's a series which is
- there
- which represents the entire row of data
- we can see how this these numbers match
- up with the first row
- in the data frame
- um and you can see that it's a
- series and then
- with a series we can pull out elements
- just like with a data frame
- we put the name of the
- value that we're trying to pull out and
- it will be able to pull it out so then
- the next
- is value of principal and you can see it
- is getting this
- uh 30 000 or you know whatever is
- corresponding to the row
- and this is just bring some extra lines
- to separate so we can see
- that this function got called three
- times it got called once
- for each row
- and so this is exactly what we need to
- be able to
- apply this market value calculation
- across
- all of the different rows in the data
- frame which represent different bonds
- so if we give it a function which is
- able to
- take this series of data
- and return back the market value of the
- bond based on that data
- then we can pass that function to apply
- and get the market value of all the
- bonds at once
- so um and then the one other thing that
- you'll see
- in here is that i have axis equals one
- that means we want to work on the rows
- of the data frame
- uh if we put access equal to zero or
- that's the default
- same thing will happen when i don't put
- any axis
- it works on the columns of the data
- frame
- and so that's why you see um
- got values series of things that's being
- passed to the function this time we got
- the entire principal column rather than
- the first row of the data frame
- so this axis equals one is important to
- be able to work on each row
- at once but if you wanted to do some
- kind of calculation that worked on each
- column at once then you wouldn't want to
- pass this axis equals one
- so now that we understand dot apply
- on the data frame now we can use that
- in the context of calculating the market
- value of these bonds
- so um
- we already have the md bond function as
- we saw previously which can
- get us the market value of the bond
- based on these details
- so now in order to use it with applying
- remember that apply has to be able to
- take the series
- as its first argument and so we
- we wrap this mv bond function call
- inside another function which is
- constructed specifically for using with
- apply on the data frame and so that
- function is going to take the series as
- the first argument
- and in order to do this calculation
- we don't see anywhere in this data frame
- the cost of debt
- and we just have a single cost of data
- that we're going to want to use in all
- the calculations
- so we're going to add that here as an
- additional argument
- and that can be passed when we call
- apply
- bypassing it by the keyword name
- so any additional arguments of the
- function can be passed this way and then
- it's going to get the same cost of debt
- for each row in the data frame
- so the only other thing that we're doing
- here is we're just pulling out
- each of those individual values from the
- series so just like we had seen back
- here
- where we were able to pull the principle
- out of the series
- and use it uh we're just doing the same
- thing here
- with the principle the coupon rate and
- the maturity
- um and then now that we have all those
- individual numbers
- we call the mv bond function passing
- those numbers
- as well as the cost of debt which is
- separately passed to the function
- and then it's able to return the market
- value of the bond
- so we call this and we see the market
- value of the bond
- of each bond and so that lines up
- with the values in the data frame you
- can see the ones with higher principal
- i also have higher market values um
- and so this is staying aligned with each
- row and data frame
- so to kind of wrap this up we can assign
- that back
- into the data frame so i'm just doing
- the same
- apply call over here but assigning that
- back into the value
- column of the data frame so then when we
- look at it
- then we have value come here as an
- additional column
- which now we have the market value of
- each one of these bonds
- and it doesn't matter how many roads are
- in this data frame
- here it was three could have been three
- thousand everything would have been
- exactly the same as far as the code that
- you're writing
- so this is a really powerful approach to
- be able to
- calculate the market value of as many
- bonds
- as you would like
- and then we
- ultimately want to take the sum of
- all these values to get the total market
- value of debt
- for the company and that wraps up
- the individual bonds approach
- to calculating the market value of debt
- but there is one additional thing to
- consider here which is often you're
- going to have a maturity date
- and not a number of years
- of maturity and even if you did have a
- number of years of maturity
- um you know usually it's going to be
- decimal and so we're not going to want
- to use this
- um you know lining up the cash flows
- kind of approach
- so um here i'm
- i'm showing the same function that we
- had from before the annuity
- approach function which uses this long
- formula
- and i created another apply function
- which uses that
- so um in general i would recommend to go
- with this
- uh rather than the prior approach where
- the prior approach was
- really just trying to help you
- understand the calculation that we're
- just
- lining up with cash flows and taking the
- present value but this just does that
- same thing with a simple formula
- um so we'll see when we
- apply that this new function which uses
- the annuity approach
- on the same data frame we get the exact
- same uh
- values that we got with the other
- calculation
- but this approach will be able to work
- for decimal maturities as well
- which once you're just working with
- material maturity dates
- you're almost always going to have a
- decimal
- uh maturity uh something other than a
- whole
- integer
- so let's drop um the
- maturity years and the value
- from this data frame um so now we're
- left with just working with the date
- um and we can check the data types
- of the uh columns in the data frame
- through this dot d types
- because we need to make sure that pandas
- has correctly classified this
- as a date column before we can do any
- date operations with it
- so we see that maturity date has the
- date time
- type and so it has correctly classified
- it
- whereas the coupon is a floating point
- number and the principal
- is an integer now
- um where this usually goes wrong is if
- you have
- uh some rows which are not dates like
- maybe it's a dash or
- a blank or you know
- a year instead of a date or these kinds
- of things
- are going to mess it up and it won't be
- able to detect that as dates
- but if everything is a date it will
- probably load in fine but you should
- definitely
- check regardless but presume that it
- didn't come in as a date
- and then we did whatever cleanup was
- necessary to remove these
- values which are not dates uh
- then we can convert it to a date with
- this
- uh pandas two daytime method
- so we just assign back into that same
- column
- converting that column into a date time
- and after you do this then you'll
- definitely be left with
- daytime now it could error out
- if there's something in the column which
- can't be converted to date time
- which there probably is if it wasn't
- loaded as a date time automatically
- so you would want to add code which
- cleans that up and then
- do the state time conversion
- so then we want to
- uh basically calculate that
- number of years of maturity using the
- date
- um so if we look at
- what happens when we pull out a single
- date we have this time stamp
- so that is the way that panus represents
- dates is with this timestamp data type
- so we ultimately want to say well
- how long is remaining on this bond so
- that's the difference between the
- maturity date
- and today's date so how do we get
- today's date
- in the code without hard coding it such
- that we'd have to update it every time
- we ran the code
- well we have the date time module built
- into python
- this is there in every python
- installation
- and within that you can do
- datetime.datetime.today
- and that is going to give you today's
- date
- and time so
- you can see the date and time here it
- all
- matches up with my system date and time
- and then we can do math but those dates
- just fine
- so if we just subtract uh
- the date uh which we got from the data
- frame
- we subtract today from that date we get
- 360 days as the resulting
- time difference or time delta so this is
- another
- data type in the date time library built
- into python
- which represents the difference between
- two dates
- but we need to convert this
- time delta into a number of years
- now there are some packages out there uh
- which make this process really easy
- uh like date you tell is one of those
- packages
- and then you'll just have like a dot
- seconds or dot
- years kind of attribute
- um takes a little bit extra effort with
- the uh just built-in libraries
- but it's not too bad what we have to do
- is
- convert it to a number of seconds so the
- dot total seconds method
- will convert this time delta into a
- floating point number
- of how many seconds are in the
- difference
- and then you can calculate how many
- seconds are in a year or whatever
- time or whatever length of period you're
- using in your analysis
- so here this is 31 million
- seconds in a year and then you just
- divide the seconds
- by the number of seconds per year to get
- the years elapsed
- so and then even you don't necessarily
- have to do that all yourself you can
- just grab
- this function from the example which
- does all it for you
- so it takes whatever date and it's going
- to grab today's date
- take the difference take the total
- seconds of that difference and turn that
- into years
- so you just call this function on a date
- and it's going to tell you how many
- years
- until that date
- and remember that when we use a function
- with apply
- that it needs to be able to take the
- series the row
- series as the first argument so we just
- make one more function for the purposes
- of apply which
- just wraps calling this
- function which converts the date into a
- number of years from today
- and all this function does is it takes
- the series it gets the date out of the
- series
- and returns the number of years
- and here i made it an optional argument
- of the name of this date column
- so that if your column is called
- maturity space parentheses date
- then it will just work otherwise you can
- pass whatever the date column is
- and it will work with whatever your date
- column is called without you having to
- modify the function
- um but here the name is maturity date
- in the data frame and so this just
- directly worked
- and so that got us the years to maturity
- for each of these assets
- so then we can just assign that back
- into the data frame
- and we'll have a number of years of
- maturity for each of the bonds
- then we can just do apply again with our
- annuity approach apply function and that
- will get you
- get us the value of these bonds as well
- and we simply just sum those at
- each of these values in order to get
- the total market value of debt for the
- company
- so that's a full overview of how to
- calculate
- the market value of debt in python
- so thanks for listening and
- see you next time
Calculating the Weighted Average Cost of Capital (WACC)¶
Notes¶
The WACC is simply the weighted average of the costs of each source of capital
The weights are the percentage of the capital structure which is allocated to the type of asset, i.e. the market value of the source of capital divided by the total market value of the company
Be sure to use the after-tax cost of debt in the calculation
Companies with the same costs of capital can have very different WACCs due to a different percentage of debt and equity in the capital structure
Transcript¶
- hey everyone
- nick dierbert is here teaching you
- financial modeling today we're going to
- be talking about
- calculating the weighted average cost of
- capital or
- whack and this is part of our lecture
- segment on the discounted cash flow
- valuation model and focusing on the cost
- of capital portion of the model
- so this is our last video in this
- lecture segment
- we already covered an intro to the dcf
- enterprise and equity value uh cost and
- market value of equity
- cost and market value of debt now we are
- just
- coming to put it all together as the end
- of the cost of capital portion
- of the model to calculate the whack
- which will become the discount rate
- we use in the dcf model
- so if you have calculated a weighted
- average before
- then this should feel very familiar
- to you because all it is is just a
- weighted average
- and it's just a weighted average of the
- different
- costs of capital and
- weighted by the percentage of
- that source of capital in the overall
- capital structure
- so this is just focusing on
- debt and equity you could have a third
- term in here for preferred stock
- as well or additional terms if you had
- additional um
- you know different uh you know maybe you
- have different seniorities of debt and
- you want to include those as separate
- components
- with different costs of debt there are
- different ways to
- specify this equation but this is kind
- of the general
- format you just take each
- cost of capital and multiply it by
- the weight of that capital in the
- capital structure
- [Music]
- and for any debt components you're going
- to want to make sure that you use
- the after tax cost of debt so that's
- taking the pre-tax
- and multiplying by one minus the tax
- rate
- um so this puts together everything that
- we have
- calculated so far we've already
- calculated the cost of equity we've
- calculated the cost of debt
- calculated the tax rate so there is one
- small calculation left to do before we
- get to the whack itself
- which is then calculating the weights of
- debt and equity
- so the weights of debt and equity very
- simple it's just
- uh the market value of that type of
- capital
- divided by the total capital
- so uh here in this uh
- form of the equation where we just have
- equity and debt and one type of each
- then it would be the market value of
- debt divided by
- the market value or sorry market value
- of equity
- divided by the market value of equity
- plus the market value of debt
- and then over here it would be the
- market value of debt divided by
- market value of equity plus the market
- value of debt
- if you had additional components of the
- capital structure
- then those would get added into the
- denominator of each of those weights
- as well the market values you know all
- your different market values for the
- different components are the denominator
- when you sum them up and the market
- value of each component
- is the numerator in calculating the
- weight
- so you should have something between
- zero and one for the weights
- on each of these and then you just
- uh then we have all the components into
- this formula so you just put them
- together
- and that ultimately gets you the whack
- so and then to kind of visualize
- the effect of those weights
- i just made a quick graphic here which
- shows
- two companies which have the exact same
- cost
- of equity in debt um
- pre-tax and post-tax uh cost of debt
- the same equity cost is the same but the
- first company
- is uh evenly split between equity and
- debt
- and the second company is weighted more
- towards equity
- so you can see the resulting whack is
- substantially lower quite a bit lower
- for the 50 50 company than it is
- for the mostly equity company and this
- is generally the case
- generally the cost of debt are lower
- than the cost of equity since
- debt is paid off first in the event of
- bankruptcy
- um and so the more that a company is
- shifted towards
- debt then the lower the overall cost of
- capital
- will be um
- so it's definitely important to consider
- not only the
- rates on the uh sources of capital but
- also
- the weights that they have within the
- overall capital structure
- so that wraps up the calculation
- of whack we're going to come back
- in the next lecture segment to focus on
- the free cash flow side of the dcf
- model so we have handled this part and
- we've handled this part
- and we're just going to focus on the
- free cash flow side of the model
- in the entire next lecture series and at
- the end of that we'll also
- put the whole thing together into one
- cohesive model
- so thanks for listening and see you next
- time