Chapter 5
Equity Valuation
AIS 5203
Advanced Corporate Finance
Ayesha Siddika Arshi
Lecturer
Department of Finance & Banking
Chapter Topics
▪ Equity Valuation: The Concept
▪ Equity Valuation: Valuation Methods
▪ Equity Valuation Methods: Net Asset Value (NAV)
▪ Equity Valuation Methods: Market Comparable/Relative Valuation
▪ Equity Valuation Methods: The Concept of DCF
▪ DCF Valuation: Dividend Discount Model (DDM)
▪ DCF Valuation: Free Cash Flow (FCF) Models
▪ DCF Valuation: Growth & Required Return on Equity
Equity Valuation:
The Concept
Equity Valuation: The Concept
What is the purpose of valuation?
▪
We conduct stock valuations to identify its Intrinsic Value
▪ Intrinsic Value → What it is truly worth → The maximum you would be willing to pay to purchase that stock
▪ Sometimes also called fair value
What about the market price of the stock?
▪
▪
Well, the primary motivation and hubris behind valuation is that the analysts believe that the market makes pricing mistakes
And that he/she is smart enough identify what a stock is truly worth, and the exploit the pricing mistakes in the market
▪ Step 1: Identify Intrinsic Value of a Stock
▪ Step 2: Compare the Intrinsic Value of the Stock with its Market Price
▪ Step 3: Determine if the stock is overvalued, undervalued or fairly valued
▪ Intrinsic Value > Market Price → Undervalued (Also referred to as Underpriced)
▪ Intrinsic Value < Market Price → Overvalued (Also referred to as Overpriced)
▪ Step 4: Take your investment decision accordingly
▪ To buy the stock if it is undervalued and vice versa
Equity Valuation: The Concept
Consider an example:
Based on your analysis and valuation, you have determined the intrinsic/fair value of GP shares should be BDT 400, however you see that the shares are trading in
the market for BDT 350 at the moment. So you consider the shares to be undervalued in the market and thus take the investment decision to buy the shares at
BDT 350 from the market and hold the shares with hopes of selling them at a profit in the future.
▪ Once the other investors in the market realizes that the share is undervalued, they will also want to buy the shares of GP and this increase in demand for the
share will result in market price correction and the price of GP shares will increase
▪ You can sell the shares you had previously bought at that time to make a profit
▪ What if the market price correction does not occur?
▪ The price may not reach your expected intrinsic value
▪ The price may stay at the level it is
▪ The price may even move downwards
That is the inherent risk any and all investors take on, regardless of whether you base your decisions on sound analysis or otherwise
Food for thought: Say, you determined that the intrinsic value of GP is BDT 300 and it is trading at BDT 350 in the market. You currently do no own any GP shares.
How do you exploit this overvalued situation?
Equity Valuation:
Valuation Methods
Valuation Methods
Most Prevalent Three Methods
▪ Asset Based Approach
▪
▪
Net Asset Value (NAV)
The Value of a Firm is derived through the value of the assets it hold, net off its liabilities it needs to pay off
▪ Market Comparable or Relative Valuation Approach
▪
▪
▪
P/E, P/S, P/B, P/CF are most common → Price Based Multipliers
EV/EBIT, EV/EBITDA are also used for Special/Specific Scenarios
The economic rationale is the “Law of One Price” → Two similar assets should sell at comparable multiples of their output
▪ Discounted Cash Flow Models
▪ Dividend Discount Model (DDM), also referred to as Gordon Growth Model (GGM)
▪ Free Cash Flow Discount Models (FCFF & FCFE)
▪ The value of any asset is the present value of the benefits it would yield over its life (which can be indefinite)
Not just for valuation of shares, rather these methods or some variations and adjusted versions of these methods
are used in Finance for valuation of most types of assets
Equity Valuation Methods:
Net Asset Value (NAV)
Net Asset Value (NAV)
The Concept of Net Asset Value (NAV):
▪ In simple words, it is what the name suggests. The value is determined based on the value of the company’s assets net off its liabilities
▪ One common mistake is to take the book value (carrying value) of the assets and liabilities directly from the balance sheet of the company
▪ Book Value is the base, however it has to be adjusted as needed to reflect fair value or market value of the assets and the liabilities of the company
Cautions & Limitations:
▪ Companies with assets that do not have easily determinable market (fair) values, such as those with significant property, plant, and equipment are very difficult to analyze
using asset valuation methods
▪ Asset and liability fair values can be very different from the values at which they are carried on the balance sheet of a company
▪ Companies with major portions of intangible assets are not well suited
▪ More difficult to estimate asset values in a hyper-inflationary environment
▪ Does not capture the potential of the company to grow by utilizing its assets
When would NAV be a Suitable Method of Valuation?
Financially Distressed Firms
Mining Firms:
Firms facing financial distress and risk of bankruptcy where the company is
struggling to maintain itself as a going concern entity
▪ The shareholders would be better off by selling the company’s assets and
salvage the value than continuing the business operations to make losses
The value of the company is heavily depended on its mining assets and the fair
market value of those assets are easily determinable
▪ A company owning a coal mine has a general idea of how much coal is within
the mine and the market price of coal is readily available
Firms that Mostly Hold Highly Liquid Assets and Liabilities:
Mutual Funds:
The asset and liability base of Banks and FIs are highly liquid
▪ However, there is room for upward or downward adjustments as the
management and operational quality can make or break Banks & Fis
Mutual Funds, the value of which are entirely dependent on the stocks and bonds
they are made up of, is perfect for NAV based valuation
▪ The price of a Mutual Fund should closely follow its NAV
Even in other cases NAV is often utilized to form a basis for the lowest valuation of a firm
Net Asset Value (NAV): Math Example
Romi Inc. is a firm going through financial distress and is at risk of going bankrupt. Their current balance sheet details has been provided below
▪ Determine the value of the firm based on the most suitable method given their financial scenario
Assets
Value (BDT)
Liabilities & SH Equity
Value (BDT)
Land
10 MN
Long Term Debt
20 MN
Factory & Office Building
23 MN
Short Term Debt
15 MN
Machineries
15 MN
Accounts Payable
8 MN
Other Fixed Assets
3 MN
Other Liabilities
5 MN
Inventory
8 MN
Total Liabilities
48 MN
Accounts Receivables
5 MN
Shareholder’s Equity
32 MN
Cash & Cash Equivalents
16 MN
2 MN Shares Outstanding
Total Assets
80 MN
Total Liabilities & SH Equity
NAV = (Fair value of Asset – Fair Value of Liabilities)
NAV = BDT (80 MN – 48 MN) = BDT 32 MN
NAV Per Share = (32 MN / 2 MN) = BDT 16 Per Share
As there are no fair value adjustments required here, thus
the NAV is equal to Book Value of Equity
80 MN
Consider now, you have taken appraisal of the Land and Buildings owned by the company and the expert has certified that the fair market value of the land to be BDT 35 MN,
however the building values should be impaired to be considered BDT 20 MN
▪ Determine the value of the firm based on the most suitable method given their financial scenario and this updated information
Fair Value of Assets
= BDT (80 + 35 + 20 – 10 – 23) MN = BDT 102 MN
NAV = (Fair value of Asset – Fair Value of Liabilities)
NAV = BDT (102MN – 48 MN) = BDT 54 MN
NAV Per Share = (54 MN / 2 MN) = BDT 27 Per Share
If it is possible to determine fair value of liabilities, then we should
make those adjustments. However, In many cases it becomes difficult
to determine fair value of liability, and in those cases
Book Value of Debt is a good alternative.
Equity Valuation Methods:
Market Comparable/Relative Valuation
Market Comparable/Relative Valuation
The Concept of Relative Valuation
▪
▪
▪
We identify the value of a share relative to the value of its peers → Hence the name relative valuation
We use comparable peer firms from the market for the valuation → Hence the name market comparable valuation
Also called multiples valuation, because we use multipliers from peer firms to conduct the valuation
▪
Commonly Used Multiples:
▪ Price to Earnings Multiples → P/E Ratio
▪ Price to Book Value Multiples → P/B Ratio
▪ Price to Sales Multiples → P/S Ratio
▪ Price to Cash Flow Multiples → P/CF Ratio
You want to identify the value of your firm. Your rival firm who is similar to
you in all aspects has a EPS of BDT 5 and their Shares are trading at BDT 30
in the market (6 times their EPS).
▪ As your firm is similar, should value of you share also be BDT 30?
▪ No, rather your stock’s value should be 6 times your EPS
▪ Comparable similar firms shouldn’t have the same value, rather the same
value multiple of the output they generate (in this case EPS)
If we simplify the idea, if a firm similar to mine
is enjoying a market price 10 times its earnings
(EPS). In that case my firm should also enjoy a
price 10 times our earnings (EPS)
Say You and your friend have the same academic qualification, same level of experience and work in the same industry for similar sized firms. Your Friend
completes 10 tasks a month & earns 80K in salary (8k Per Task)
You complete 12 tasks a month, should you earn the same 80K? Or should you demand 96K for the value of you work?
Market Comparable Valuation Process
Step 1: Identify comparable peer firms listed in the stock exchange
▪ The firms should be from the same industry, and ideally be similar in operations, size and serving the same customer groups and in similar growth phase
▪ GP would not be a good comparable firm for BSRM Steels → Different Industry
▪ Brac Bank would not be a good comparable firm for NRB Bank → Same Industry but Large Difference in Size
▪ Ferrari would Not be a good comparable firm to Toyata → Both Giants of the Same Industry, but serves different customer groups
▪ Coca Cola & Pepsi are Perfect Comparable Firms → Both Giants of the Same Industry, serving the same customer groups and mature growth stage
Step 2: Calculate the Multipliers
▪ Say you’re valuing Pepsi, and have chosen Coca Cola as your comparable peer firm
▪ Coca Cola is trading for USD 30 per share and they have recently reported an EPS of USD 5 & a BVPS of USD 20
▪ Thus a P/E Multiple of (30/5) = 6 P/E Multiple
▪ P/B Multiple of (30/20) = 1.50 P/B Multiple
▪ If you have managed to identify more than one comparable companies than calculate the multipliers of each company and take the average of each multipliers
Step 3: Use the Multipliers to Determine Value of Your Target Stock
▪ Say you’re valuing Pepsi that has an EPS of 4 and Book Value Per Share of 18
▪ Pepsi Share Value based on P/E Multiple
▪ = (Pepsi EPS * Comparable P/E Multiple) = (4 * 6) = USD 24
▪ Pepsi Share Value based on P/B Multiple
▪ = (Pepsi BVPS * Comparable P/B Multiple) = (18 * 1.50) = USD 27
▪ Take the average of the two valuations:
▪ (24 + 27)/2 = USD 25.50 Per Share Value for Pepsi
Rationale & Shortcomings Behind the Multiples
P/E Multiple
Rationale
Shortcomings
▪ Earning power is a primary driver of investment value
▪ Widely recognized and used by investors
▪ Empirical research shows that P/E differences are significantly related to
long run average stock returns
▪ EPS can be negative which makes the P/E ratio meaningless (explained in
more details in later slides)
▪ EPS can highly volatile which can make the P/E ratio volatile
▪ Within the allowable accounting practices management may apply specific
practices to distort EPS thus effecting P/E
P/B Multiple
Rationale
Shortcomings
▪
▪
▪
▪
▪
▪ Do no reflect value of intangible assets that are not recognized in the
balance sheet such as human capital
▪ Can be misleading if the asset sizes among the peers vary significantly
▪ Share repurchases or issuances may distort historical comparisons
Book Value is a cumulative Balance Sheet item and it is rarely ever negative
More stable and less volatile compared to the other multiples
More suitable for firms in industries with very liquid assets (banks & Fis)
More suitable if the target firm is going out of business (distressed firm)
Empirical research shows that P/B differences are significantly related to
long run average stock returns
Rationale & Shortcomings Behind the Multiples
P/S Multiple
Rationale
Shortcomings
▪
▪
▪
▪
▪
▪ High growth in sales may not translate to high growth in profit. Sales at a
discount may even lead to losses
▪ Sales do not capture difference in efficiency levels of cost structure of
different companies
Sales is always positive
Less affected by accounting treatments
Usually less volatile than EPS and CF
Very effective for valuing startups and companies in cyclical industries
Empirical research shows that P/S differences are significantly related to
long run average stock returns
P/CF Multiple
Rationale
Shortcomings
▪ Harder to manipulate
▪ Cash flow is a objectively a better evaluation metric than earnings
▪ Empirical research shows that P/CF differences are significantly related to
long run average stock returns
▪ Can go in to negative. Specially for growing firms negative OCF is very
common
▪ FCFE would be the best measure of CF. However, FCFE is a lot more volatile
than OCF
Market Comparable Valuation: Cautions & Suitability
EPS of a firm can be negative
▪ If our comparable firm has a negative EPS, it would result in a negative P/E multiple. However, negative multiples are meaningless and irrational, as a stock
can not have a negative value/price. The lowest price a stock can go is Zero. Thus, if a comparable firm has negative EPS, we exclude that firm from P/E based
valuation
▪ If our target firm (the one we are valuing) has a negative EPS, then we have to forego P/E based valuation altogether and depend on other multiples only
▪ The same rules apply for Operating Cash Flow and Book Value which can also be negative
Outliers or Extreme Values in Multiple
▪ Sometimes one or more of our comparable firms may have a multiple that is an outlier or extremely abnormal value
▪ Including such a value would in our calculations would distort our valuation significantly
▪ Consider you have 5 comparable firms with P/E ratios of 12, 14, 8, 10 and 100. Here we can easily understand that the 100 P/E is an extreme and abnormal value
thus we should only consider the other 4 and use a P/E multiple of 11 (average of 12, 14, 8, 10) for out P/E based valuation
▪ Some statistical methods to identify outliers include Trimming and Winsorization
▪ However the effectiveness of these technics are low if you have a small number of comparable firms
▪ Although it varies from country to country and industry to industry, however the rule of thumb for P/E ratio is that a P/E ratio higher than 40 is abnormal.
Unfortunately no such rule of thumb exists for the other multiple
Market Comparable Valuation: Cautions & Suitability
Best not to Mix Value and Growth Firms
▪ Value firms are expected to have low multiples while growth firms are expected to have high multiples
▪ If you have sufficient options, its best not to use value firms as comparable for valuing a growth firm and vice versa
Trailing Multiples & Forward Looking Multiples
▪ Trailing Multiples basically means using historical (last period) EPS, BV, CF, Sales for calculating your multiples → Lags Behind
▪ Foreword Looking Multiples uses forecasted EPS, BV, CF, Sales for calculating your multiples → Forecasts may not come true
▪ Whichever approach you take, make sure to do the same for all the firms in consideration (both target and all comparable firms)
Relative Valuation is most suitable if there are a large number of closely comparable peer firms.
Which sometimes become a major challenge for many industries in BD as the number of listed firms in DSE/CSE is quite low
Market Comparable Valuation: Math Example
Company Name
You are valuing Bank Asia that has recently reported their year end EPS to
be BDT 6, BVPS to be 20 and OCF to be 4. Your assistant have collected the
following information about potential comparable peer firms:
▪
Calculate the Value of Shares for Bank Asia Limited
Share Price
EPS
BVPS
OCF
Brac Bank
40
8
40
5
EBL
25
5
12.5
-2
NRB Bank
30
2.5
20
3
UCB Bank
40
0.40
20
8
IDLC Finance
20
3
25
2
Solution
Step 1: Identify Comparable Peer Firms
▪ NRB Bank is not a peer of Bank Asia due to its much smaller size
▪ IDLC Finance is a NBFI and is not fully comparable to the Banking Industry
▪ Thus we will be considering Brac Bank, EBL and UCB as comparable peer
firms for our valuation
Step 3: Use the Multipliers to Determine Value of Bank Asia
Step 2: Calculate the Multipliers
▪ Bank Asia Share Value based on P/B Multiple
▪ = (BA BVPS * Comparable P/B Multiple) = (20 * 1.67) = BDT 33.40
Company Name
P/E
P/BV
P/OCF
Brac Bank
40/8 = 5
40/40 = 1
40/5 = 8
EBL
25/5 = 5
25/12.5 = 2
25/-2 = -12.5
UCB Bank
40/0.40 = 100
40/20 = 2
40/8 = 5
Average
(5+5)/2 = 5.00
(1+2+2)/3 = 1.67
(8+5)/2 = 6.50
▪ P/CF of EBL has not been considered as negative multiplier is meaningless
▪ P/E of UCB has not been considered as it is higher than 40 (outlier)
▪ Bank Asia Share Value based on P/E Multiple
▪ = (BA EPS * Comparable P/E Multiple) = (6 * 5) = BDT 30
▪ Bank Asia Share Value based on P/OCF Multiple
▪ = (BA OCF * Comparable P/OCF Multiple) = (4 * 6.50) = BDT 26
▪ Take the average of the three valuations:
▪ (30 + 33.40 + 26)/3 = BDT 29.80 Per Share Value for Bank Asia
Equity Valuation Methods:
The Concept of DCF
Discounted Cash Flow Valuation: The Concept
The Concept of Discounted Cash Flow Valuation:
▪ The value of any asset is the present value of the benefits it would yield over its life
▪ As we are valuing entire companies or ownership thereof, the life of the asset in concern is normally considered PERPETUAL → Going Concern
▪ So, we forecast the potential cash flows expected to be reasonably generated by the company and base our valuation on these cash flows
Which Cash Flow to Use for Valuation?
How do we forecast Cash Flow for an Infinite Period?
▪ Dividend (D)
▪ Free Cash Flow (FCF)
▪ Free Cash Flow to Firm (FCFF)
▪ Free Cash Flow to Equity (FCFE)
▪ Residual Income (RI)
▪ We Don’t
We will be focusing on Dividend & FCF models
Single Stage Models
▪ We Identify/calculate the expected Cash Flow for the Next 1 Period
▪ And then consider that the cash flow would continue grow (or shrink) at a constant rate
▪ Stream of Cash Flows going indefinitely growing at a constant rate → Sounds Familiar?
▪ That’s right, we use the Growing Perpetuity Formula for our Valuation
Key Inputs Other than Cash Flow?
Multi-Stage Models
▪ Long Term Constant Growth Rate
▪ Discount Rate
▪ Required Return on Equity, if the cash
flow corresponds to equity/share holders
(Dividend, FCFE, RI)
▪ WACC if the cash flow corresponds to
both Equity and Debt Holders (FCFF)
▪ We forecast the expected Cash Flow for a Reasonable period in to the future
▪ Usually 3, 5, 10 Years → 5 Being the most common and standard practice
▪ If the firm is going through some major changes that would impact its cash flows, then we need to
forecast up to a point when the impact is fully realized and the new normal Cash Flow is reached
▪ The further in to the future we try to forecast, the less accurate our forecasts are likely to be
▪ We use the last cash flow from our forecast to calculate one extra period using long term growth rate
▪ Use Growing Perpetuity formula on the extra period CF → Terminal Value
▪ Discount each Cash Flow & the Terminal Value individually to determine their present value (PV)
▪ Sum of all the PV is the value of the Firm or Value of Equity depending on which CF we used
▪ If we have used FCFF to calculate the value of the firm, we can simply deduct value of the firm’s debt to
identify value of equity [Remember, VF = (VE + VD)]
We have to be very careful regarding the
assumptions behind these two inputs, as the
valuation is very sensitive to both of these inputs
Feels like it’s a lot to take in? Fortunately, it gets a little easier to understand once we get to the calculations
DCF Valuation:
Dividend Discount Model (DDM)
DCF Valuation: Dividend Discount Model (DDM)
Dividend Discount Model:
▪ Theoretically Justifiable. As a shareholder, you receive dividends from the stock
▪ Furthermore, Dividends are also less volatile and are easier to forecast compared to other types of cash flows
▪ Primary disadvantage is that it is difficult to apply DDM to firms that currently do not pay dividends
▪ We can try to forecast up to a point of time when the firm starts paying dividend, however that far in to the future raises questions about accuracy of forecast
▪ Emphasizing on dividend as the cash flow measure is the perspective of a minority shareholder who believes;
▪ The controlling shareholders are implementing a dividend policy that bears a meaningful relationship with the firm’s underlying earnings capability
▪ Specially in BD, we see a lot of firms that try to pay 10% of Paid up capital as dividend to ensure their “A” category regardless of their profitability level (high or low)
When is the DDM most appropriate?
Gordon Growth Model (for Single Stage DDM)
▪ The company has a history of dividend policy
▪ Dividend policy is clear and related to the earnings of the firm
▪ Valuation is from the perspective of a minority shareholder
The single stage DDM uses Gordon Growth Model (GGM) brought forward by Myron J. Gordon. It is so
widely accepted that the DDM and GGM are sometimes referred to as interchangeably. The GGM
makes the following assumptions for it to work:
▪ The firm expects to pay dividend in the future
▪ Dividends will grow perpetually at a constant rate “g” (negative growth is also possible)
▪ The Growth Rate is less than the Required Rate of Return (g < r)
▪ This assumption is rationale, as “g” is the perpetual growth rate and no firm can grow
perpetually at a high rate
Most Common Approaches to DDM:
▪ Single Stage DDM Model
▪ Multi Stage DDM Model
DDM: Single Stage Example Math
Example Math 1: Rohee Inc. has recently paid a USD 20 dividend per share.
You expect the company’s long term earnings and dividend growth rate to be
5% and have determined the appropriate Required Rate of Return to be 8%
Example Math 2: Rohee Inc. is expected to pay a USD 20 dividend. You expect
the company’s long term earnings and dividend growth rate to be 5% and
have determined the appropriate Required Rate of Return to be 8%
▪
▪
Calculate the Value of the Shares
Example Math 1 Solution:
𝑽𝑺𝟎 =
𝑽𝑺𝟎 =
Example Math 2 Solution:
D1
D0 (1+𝑔)
or
(𝑟−𝑔)
(𝑟−𝑔)
20 (1+5%)
=
(8%−5%)
21
= 700
3%
Example Math 3: Rohee Inc. is expected to earn an EPS of USD 20 and has a
pay out policy to distribute 50% of their earnings. You expect the company’s
long term earnings growth rate to be 5% and have determined the
appropriate Required Rate of Return to be 8%
▪
Calculate the Value of the Shares
Calculate the Value of the Shares
𝑽𝑺𝟎 =
𝑽𝑺𝟎
=
D1
D0 (1+𝑔)
or
(𝑟−𝑔)
(𝑟−𝑔)
20
=
(8%−5%)
20
= 666.67
3%
Example Math 3 Solution:
Expected Dividend Per Share = (EPS*Payout Ratio)
𝑫𝟏 = (20*50%) = 10
𝑽𝑺𝟎 =
10
=
(8%−5%)
10
= 333.33
3%
DDM: Multi-Stage Example Math
Rohee Inc. is expected to earn an EPS of USD 20 and their EPS is expected
to grow by 10% each year for the next 4 years after that. Ms. Rohee has set a
pay out policy to distribute 50% of their earnings.
You expect the company’s long term earnings growth rate to be 5% and have
determined the appropriate Required Rate of Return to be 8%
▪
Step 1: Calculate the Expected Dividend for the next 5 years
▪
▪
▪
𝐷1 = (20*50%) = 10.00
𝐷2 = [10*(1+10%)] = 11.00
𝐷3 = [11*(1+10%)] = 12.10
▪
▪
𝐷4 = [12.10*(1+10%)] = 13.31
𝐷5 = [13.31*(1+10%)] = 14.64
Calculate the Value of the Shares
Step 2: Calculate the Terminal Value (TV)
𝑻𝑽𝟓
=
𝑻𝑽𝟓 =
𝐷5 (1+𝑔)
14.64(1+5%)
=
(𝑟−𝑔)
(8%−5%)
15.37
3%
= 512.33
▪ Remember in the single stage model, we used
𝑫𝟏 to calculate 𝑽𝟎
▪ Similarly, based on 𝐷6 we calculate Terminal
Value at the end of period 5 (𝑇𝑉5 )
Step 3: Discount the Dividends & TV to Present Value & Sum them
10
11
12.10
13.31
14.64
512.33
𝑽𝑺𝟎 = (𝟏+𝟖%)
+ (𝟏+𝟖%) + (𝟏+𝟖%) + (𝟏+𝟖%) + (𝟏+𝟖%) + (𝟏+𝟖%)
𝟏
𝟐
𝟑
𝟒
𝟓
𝑽𝑺𝟎 = 𝟗. 𝟐𝟔 + 𝟗. 𝟒𝟑 + 𝟗. 𝟔𝟏 + 𝟗. 𝟕𝟖 + 𝟗. 𝟗𝟔 + 𝟑𝟒𝟖. 𝟔𝟗
𝑽𝑺𝟎 = 𝟑𝟗𝟔. 𝟕𝟑
▪ A very Common mistake in step 3 is to discount the Terminal Value (TV) using the wrong exponent (power) value → BE CAREFUL
𝟓
DCF Valuation:
Free Cash Flow (FCF) Models
DCF Valuation: FCF Models
Free Cash Flow Models:
▪ As the owner/shareholder of a firm you are entitled to the entirety of the free cash flow (net of debt) your firm has generated and not just the dividend it pays out of its FCF
▪ Thus FCF models have sound justification
▪ Two types of Free Cash Flows:
▪ Free Cash Flow to Firm (FCFF): The cash flow generated by the firm in excess of its Capex & Working Capital needs.
▪ It is the cash flow available to the firm to service its debt holders & shareholders
▪ Free Cash Flow to Equity (FCFE): The cash flow generated by the firm in excess of its Capex, Working Capital & debt servicing (net-off new debt) needs
▪ It is the cash flow available to the firm to service its shareholders
▪ FCF models can be applied to many firm, regardless of their dividend payment history
When are FCF Models most appropriate?
FCFE Vs. FCFF
▪ FCF is corresponds with earnings of the firm
▪ Valuation is from the perspective of a controlling shareholder
▪ Also applicable from a Minority shareholders perspective
▪ Generally, FCFE is a more preferred model for stock valuation
▪ FCFE uses Required Return on Equity (Cost of Equity) as the discount rate while FCFF uses WACC
▪ In case we are uncertain or less confident in the accuracy of the Required Return on Equity (Re)
we are using in our valuation, in that case FCFF model would be more preferred
▪ The FCFF model uses WACC as the discount rate. WACC uses cost of capital of all types of
capital that has been used (debt, equity, preferred equity). Thus impact of Cost of Equity
(Re) in the valuation is somewhat reduced
Common Approaches to FCF Models:
▪ Single Stage FCF Model: Less Common
▪ Multi Stage FCF Model: FCF models are usually done in a very
detailed manner, thus multi-stage FCF models are more
common
▪ FCFF = EBIT * (1-Tax Rate) + Dep & Amort – Capex - ∆ Working Capital Requirement
▪ FCFE = FCFF – [ Interest * (1-Tax Rate) ] + Net Borrowing
Where, Net Borrowing = (New Debt Availed – Debt Repayment)
FCF: Single Stage Example Math
FCFE Example Math: Rohee Inc. has recently reported FCFE of USD 25 MN.
They have a total of 10 MN Shares Outstanding. The cost of equity of the firm
is 11.50% and the expected FCFE growth rate is 4.50%
FCFF Example Math: Rohee Inc. has recently reported FCFF of USD 5 MN.
They have USD 10 MN in debt & a total of 2 MN Shares Outstanding. The
WACC of the firm is 13.76% and the expected FCFF growth rate is 5%
▪
▪
Calculate the Value of the Shares
FCFE Example Math: Solution
▪ FCFE Per Share = (25 MN / 10 MN) = 2.50
𝐹𝐶𝐹𝐸
1
𝑽𝑺𝟎 = (𝑟−𝑔) or
𝑽𝑺𝟎 =
𝐹𝐶𝐹𝐸0 (1+𝑔)
(𝑟−𝑔)
2.5 (1+4.5%)
2.61
=
= 37.28
(11.5%−4.5%)
7%
Calculate the Value of the Shares
Example Math 2: Solution
𝑽𝑭𝟎 =
𝑽𝑭𝟎 =
FCFF1
FCFF0 (1+𝑔)
or
(𝑟−𝑔)
(𝑟−𝑔)
5(1+5%)
=
(13.76%−5%)
5.25
= 59.93 MN
8.76%
VE = (VF - VD) = (59.93 MN – 10 MN) = 49.93 MN
Value Per Share = (VE / Number of Shares)
Value Per Share = (49.93 MN / 2 MN) = 24.97
FCFF: Multi-Stage Example Math
Rohee Inc. is expected to earn an EBIT of USD 100MN & their EBIT is
expected to grow by 10% each year for the next 2 years after that. The firm
has a D&A of 5 MN and planned capex of 20 MN each year. ∆ WC
Requirement is expected to be 30MN, -5MN & 30MN over the next 3 years.
The firm has a total of USD 80 MN debt and 10MN Shares outstanding. Long
term FCFF growth rate is expected to be 4%, WACC stands at 10% and the
Tax Rate is 30%
▪
Calculate the Value of the Shares
Step 2: Calculate the Terminal Value (TV)
𝑻𝑽𝟑
𝐹𝐶𝐹𝐹3 (1+𝑔)
39.70(1+4%)
=
=
(𝑟−𝑔)
(10%−4%)
𝑻𝑽𝟑 =
41.288
6%
= 688.13 MN
Step 1: Calculate the Expected FCFF for the next 3 years
Particulars
Year 1
Year 2
Year 3
EBIT
100
110
121
EBIT (1 – 30% Tax Rate)
70
77
84.70
Add: Dep & Amort
5
5
5
Less: Capex
20
20
20
Less: ∆ WC Requirement
30
-5
30
FCFF
25
67
39.70
Step 3: Discount the FCFFs & TV to Present Value & Sum them
25
67
39.70
688.13
𝑽𝑭𝟎 = (𝟏+𝟏𝟎%)
+ (𝟏+𝟏𝟎%) + (𝟏+𝟏𝟎%) + (𝟏+𝟏𝟎%)
𝟏
𝟐
𝟑
𝟑
𝑽𝑭𝟎 = 𝟐𝟐. 𝟕𝟑 + 𝟓𝟓. 𝟑𝟕 + 𝟐𝟗. 𝟖𝟑 + 𝟓𝟏𝟕. 𝟎𝟎
𝑽𝑭𝟎 = 𝟔𝟐𝟒. 𝟗𝟑
Step 4: Calculate Value of Equity & Value Per Share
Value Per Share = (VE / Number of Shares)
VE = (VF - VD) = (624.93 MN – 80 MN) = 544.93 MN
Value Per Share = (544.93 MN / 10 MN) = 54.49
FCFE: Multi-Stage Example Math
Step 1: Calculate the Expected FCFF for the next 3 years
Romi Inc. is expected to earn an EBIT of USD 50MN & their EBIT is expected to grow by
20% each year for the next 2 years after that. The firm has a D&A of 5 MN and planned
capex of 20 MN each year. ∆ WC Requirement is expected to be 10 MN each year for
the next 3 years.
Particulars
The firm will take new long term loans of 20 MN, 10 MN, 5 MN and repay short term
loans of 5 Mn, 10 MN, 20 MN over the next 3 years. Finance Cost over the 3 years are
expected to be around 10 MN each year
The firm has 10MN Shares outstanding. Long term FCFE growth rate is expected to be
5%, Cost of Equity stands at 10% and the Tax Rate is 30%
▪
Calculate the Value of the Shares
Step 2: Calculate the Terminal Value (TV)
𝑻𝑽𝟑
=
𝑻𝑽𝟑
=
𝐹𝐶𝐹𝐸3 (1+𝑔)
3.40(1+5%)
=
(𝑟−𝑔)
(10%−5%)
3.57
5%
= 71.40 MN
Step 4: Calculate Value Per Share
Year 1
Year 2
Year 3
EBIT
50
60
72
EBIT (1 – 30% Tax Rate)
35
42
50.40
Add: Dep & Amort
5
5
5
Less: Capex
20
20
20
Less: ∆ WC Requirement
10
10
10
FCFF
10
17
25.40
Less: Interest * (1 - 30% Tax Rate)
7
7
7
Add: Net Borrowing
15
0
-15
FCFE
18
10
3.40
Step 3: Discount the FCFFs & TV to Present Value & Sum them
18
10
3.40
71.40
𝑽𝑬𝟎 = (𝟏+𝟏𝟎%)
+ (𝟏+𝟏𝟎%) + (𝟏+𝟏𝟎%) + (𝟏+𝟏𝟎%)
𝟏
𝟐
𝟑
𝟑
𝑽𝑬𝟎 = 𝟏𝟔. 𝟑𝟔 + 𝟖. 𝟐𝟔 + 𝟐. 𝟓𝟓 + 𝟓𝟑. 𝟔𝟒 = 𝟖𝟎. 𝟖𝟏
Value Per Share = (VE / Number of Shares)
Value Per Share = (𝟖𝟎.𝟖1 MN / 10 MN) = 8.08