Corporate Valuation notes
3 approaches:
1. Income approach: present value of all future benefits, excludes past benefits
2. Market approach: market prices of comparable assets
3. Cost approach: value of all individual items on the balance sheet at current
conditions
Income approach
 DCF – Asset Side (FCFO) – free cash flow from operations
 DCF Equity side (FCFE) – free cash flow to equity holders
 DCF – Adjusted present value (FCFO +TS)
Cost approach
 Sum of the parts (Break-up analysis)
Market approach
 Trading multiples
 Deal multiples
Other methods
 Current market value (market capitalization)
 LBO valuation
Discounter Cash Flows Valuation – General steps
3 main inputs: cash flows, a discount rate, a time horizon
1. Estimate the current earnings and cash flows on the company:
■ To equity investors: CF to equity (FCFE)
■ To all claimholders: CF from operations (FCFO)
2. Estimate the discount rates
■ To equity investors: cost of equity
■ To all claimholders: weighted average cost of capital (WACC)
■ Nominal (real) CF  Discount rates in nominal (real) terms
3. Estimate the forecast earnings and cash flows (with a full business plan or more synthetic
growth rates in earnings)
4. Estimate when the firm will reach stable growth and what characteristics (risk & cash
flow) it will have when it does
5. Choose the right DCF model (asset-side DCF, equity-side DCF, APV)
Ultimate Cash Flow measures
1. Operating Cash Flow
Operating Cash Flow (or sometimes called “cash from operations”) is a measure of cash
generated (or consumed) by a business from its normal operating activities.
Like EBITDA, depreciation and amortization are added back to cash from operations.
However, all other non-cash items like stock-based compensation, unrealized gains/losses,
or write-downs are also added back.
Unlike EBITDA, cash from operations includes changes in net working capital items like
accounts receivable, accounts payable, and inventory.
Operating cash flow does not include capital expenditures (the investment required to
maintain capital assets).
2. Free Cash Flow (FCF)
The cash a company generates after accounting for cash outflows to support operations and
maintain its capital assets.
Free Cash Flow can be easily derived from the statement of cash flows by taking operating
cash flow and deducting capital expenditures.
FCF = Operating Cash Flow - CapEx
FCF gets its name from the fact that it’s the amount of cash flow “free” (available) for
discretionary spending by management/shareholders. For example, even though a
company has operating cash flow of $50 million, it still has to invest $10million every year in
maintaining its capital assets. For this reason, unless managers/investors want the business
to shrink, there is only $40 million of FCF available.
FCF = EBITDA – CapEx – Cash Taxes - ΔWorking Capital
FCF = EBIT * (1 – tax rate) + Depreciation + Amortization- ΔWorking Capital – CapEx
3. Free Cash Flow to Equity (FCFE) (Levered Free Cash Flow)
This measure is derived from the statement of cash flows by taking operating cash flow,
deducting capital expenditures, and adding net debt issued (or subtracting net debt
repayment).
FCFE = Operating Cash Flow – CapEx + Net Debt Issued
FCFE = EBITDA – Interest – Taxes – ΔWorking Capital – CapEx + Net Borrowing
Equity Value = Enterprise Value + Debt – Cash
DCF Valuation – Evaluation
Pros: based upon an asset’s fundamentals ( less exposed to market moods and
perceptions), forces to think about the underlying characteristics of the firm and understand
its business
Cons: Requires far more inputs and information than other valuation methods, inputs are
noisy, can be manipulated by savvy analysts
Relative Valuation
Value of an asset or a company can be estimated by looking at how the market prices similar or
comparable assets
 Market multiples or Deal multiples
Pros: simple and easy to relate to, requires less information, much more likely to reflect market
perceptions and moods than DCF
Cons: tendency to pro-cyclicality (if market overvalues software firms, our firm will overvalued), easy
to misuse and manipulate, definition of comparable firms is subjective
Economic Profit Models
The value of a business is the sum of:
■ The book (adjusted) value of its invested capital as of today
■ The present value of the excess returns: earnings beyond a base level, considering the cost of
capital (it can be negative)
As DCF it can be modeled:
■ Asset-side: economic value added
■ Equity-side: residual income
Asset-Based Methods
These methods determine value from a careful estimate of the value of each assets (tangible and
intangible) and liability that represent the invested capital of the firm
■ Asset based methods and DCF may yield the same values if we have a firm that has no growth
assets and the market assessment of value reflect the expected cash flows
■ Mostly used for valuing real estate assets and holding companies
Holding companies because you look at NAV – value computed with the asset based methodology
Holding company - is a parent business entity—usually a corporation or LLC—that doesn't
manufacture anything, sell any products or services, or conduct any other business operations. Holds
the controlling stock or membership interests in other companies. E.g. Google’s Alphabet
Value and Uncertainty
DCF – Cash Flows
DCF - NO Tax world
For fully equity financed companies ROI=ROE
If not fully equity financed
For equity holders the creation of value is the same, because now you require a higher discount rate
so the value is the same. IN NO TAX SCENARIO!
You have higher expected return on equity, but it does not mean that there is value credit --> you
desire higher discount rate
𝐷
𝑅𝑂𝐸 = 𝑅𝑂𝐼 + (𝑅𝑂𝐸 − 𝑖)
𝐸
Does the higher profitability transfer to higher firm value?
No, in this case you have higher expected return on equity (ROE), than ROI
This higher profitability is not really creation of value.
■ The required return to equity-holders is the cost of (unlevered) equity which is = to the required
return on the assets financed with that
■ It is either estimated with CAPM or other model/target
𝐾𝐸𝑈 = 𝑟𝑓 + 𝐵𝑈 ∗ 𝑀𝑅𝑃
Valuation in perpetuity:
𝐹𝐶𝐹𝑂
𝐸𝑉 =
𝐾𝐸𝑈
𝐸𝑉 = 𝐸𝑞𝑉
TAX WORLD
■ M&M 1: as debt increases, enterprise value (i.e. market value of assets) increases thanks to higher
future tax shields
From the sources' perspective, D and E holders now have their own separate required returns
CE at market value now also includes a new CF, the PV of all future tax shields (assume its risk is
equivalent to debt)
The value of the perpetuity is therefore:
Adjusted present value (APV) method:
𝐹𝐶𝐹𝑂 𝑘𝐷 ∗ 𝐷 ∗ 𝑡 𝐹𝐶𝐹𝑂
𝑀𝑀1 (𝑡): 𝐸𝑉 = 𝑉𝑈 + 𝑉𝑇𝑆 =
+
=
+ 𝐷𝑡
𝐾𝐸𝑈
𝐾𝐷
𝑘𝐸𝑈
Debt has book value = market value in a no growth perpetuity
𝐾𝐷 ∗ 𝐷
𝑀𝑉 (𝐷) =
=𝐷
𝐾𝐷
The market value of equity is:
𝐸𝑞𝑉 = 𝐸𝑉 − 𝐷
MM 2: as debt increases, the cost of equity moves UP from the unlevered case:
𝐷
𝑀𝑀2 (𝑡): 𝑘𝐸𝐿 = 𝑘𝐸𝑈 +
∗ (𝑘𝐸𝑈 − 𝑘𝐷 ) ∗ (1 − 𝑡)
𝐸𝑞𝑉
We can compute equity value alternatively considering CF to shareholders only:
𝐹𝐶𝐹𝐸
𝐸𝑞𝑉 =
𝑘𝐸𝐿
𝐸𝑉 = 𝐸𝑞𝑉 + 𝐷 >>> Discounted cash flow equity-side
It can be shown that under these assumptions, it is mathematically equivalent to APV
FCFE = FCFO – interests + tax shield on interests
Which leads to the perpetuity valuation:
𝐹𝐶𝐹𝑂
𝐸𝑉 = 𝑊𝐴𝐶𝐶
𝐸𝑞𝑉 = 𝐸𝑉 − 𝐷 >>> Discounted cash flows (DCF) asset-side
■ The D/E ratio in WACC and in MM 2 computation are market values and the same values resulting
from valuation itself: the circularity problem mentioned earlier
■ However, the circularity is here solved by exploiting the existence of 3 different valuation method
which mathematically give the same results for EV (D+E) and EqV (E)
A generalized DCF model in practice
In practice, there is no need to seek an equivalence among DCFs. The formulas below apply to an
independent CF scenario and will generate different results, depending on the fit between a
company and the method
■ Under a real-life scenario, the steady state hypotheses are relaxed
■ FCFO and FCFE will depend on the company's business plan for a few first explicit years, which are
independently discounted
■ Years beyond will be valued through a synthetic terminal value, under a steady growth scenario
(therefore, a two-staged model)
Terminal Value and Growth Rate
Terminal growth rate
■ TV growth rate cannot exceed the growth rate of the economy
■ The “borders” of the economy should be consistent to the markets where the firm operates
(domestic vs. multinational);
■ TV growth can be negative: assuming the firm will disappear in time
■ High growth economy: stable growth rate will be lower (e.g. LT inflation rate, 2%)
■ In the LT, Rf  GDP growth (in both real and nominal terms)
Terminal FCF
■ FCFO should be normalized to represent the steady state
o CAPEX = maintenance investments only (note: it requires re-computing EBIT) and fixed assets grow
as much as the LT growth rate (i.e. still CAPEX > D&A by a moderate amount
o WC grows as much as the LT growth rate (therefore modest change in WC)
■ Several practitioners commonly set CAPEX = D&A and the change in WC = 0
■ Yet this assumption is inconsistent with a positive long term growth rate!
o Under these assumptions, the reinvestments to support growth are = 0 and therefore growth is
null
This is because there is a fundamental relationship between growth and investments
The relationship between return on investment, EBIT growth and reinvestment needs
Cost of Capital
Cost of Equity
𝟏. 𝐼𝑚𝑝𝑙𝑖𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 ∶ 𝑘𝐿𝑆 =
𝑃1 −𝑃0
𝑃0
+
𝐷𝑃𝑆1
𝑃0
Equals to price appreciation plus dividends. Main drawback is that applies to listed securities and it
also depends on the time frame.
𝐷𝑃𝑆1
𝐷𝑃𝑆1
→ 𝑟 = 𝐾𝐸𝐿 =
+𝑔
𝑟−𝑔
𝑃0
𝑔 = 𝑅𝑂𝐸 ∗ (1 − 𝑝𝑎𝑦𝑜𝑢𝑡)
𝟐. 𝐷𝐷𝑀 𝑟𝑒𝑡𝑢𝑟𝑛: 𝑃0 =
𝟑. 𝐴𝑐𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑟𝑒𝑡𝑢𝑟𝑛: 𝐾𝐸𝐿 = 𝑅𝑂𝐸
Pros: applies both to listed or unlisted securities, but is too poor, model or last result
𝟒. 𝐶𝐴𝑃𝑀: 𝐾𝐸𝐿 = 𝑟𝐹 + 𝐵𝐿 (𝑟𝑀 − 𝑟𝐹 )
Normal return + market risk premium (extra premium investors demand for risk of equity markets)
CAPM
1. Risk- free rate: no default risk and no reinvestment risk, yield to maturity on riskless
Government bonds, or else the IRS rate
2. Rm as historical return on a market index, dominating index of a country based on sales,
implied risk premium approach: rm as implied in estimates of CF returned to all shareholders
in the index
Beta for stock x is the regression slope on a sample of returns on x and on M
𝛿𝑖,𝑀 𝜌𝑖,𝑀 ∗ 𝛿𝑖
𝛽𝑖 = 2 =
𝛿𝑀
𝛿𝑀
The more the company takes on debt, the higher the beta. Dividends are discretionary, debt
payments are compulsory -> you have to pay interest and that's why debt is riskier than equity
■ Beta can be cleaned from its increasing effect coming from financial leverage: more "fixed
financing costs" (interests) than "variable financing costs" (dividends): can be done with existing data
on listed companies
■ Beta could be cleaned from its increasing effect coming from operating leverage: more "fixed
operating costs" than "variable operating costs": not measurable with accounting data, therefore
never applied in practice
Hamada’s Formula
A company's beta converges to market beta over time thanks to getting more mature and
diversified: Blume formula for adjusted levered beta:
Computational Approach to finding beta
Advantages of approach 3:
- Private firms
- Not dependent on own stock prices
- Much lower standard error
- Business units/single projects
- Allow to have an unlevered beta that facilitates moving financial leverages across future
years
Cost of Debt
1. Contractual cost of debt: weighted average of the contractual interest rate on each loan or
security
2. Accounting cost of debt
3. Market cost of debt
- YTM on the target’s listed bonds (weighted average)
- YTM on peers’ listed bonds with a similar rating (not industry!)
Ratings-based cost of debt:
𝑘𝐷 = 𝑌𝑇𝑀 = 𝑟𝐹 + 𝑠𝑝𝑟𝑒𝑎𝑑
Reorganizing Financials and Cash Flows for Valuation
Restated Balance Sheet
■ Capital employed represents the cumulative amount the business has invested in its
operations
■ Sources of financing represents all the financing sources of the company
■ Items can be dragged within sides (= sign) and across sides (change sign)
Fixed assets: tangible assets, intangibles, capitalized leasing assets
Non-Cash WC
Equity: Share capital, reserves, Minority interest
Net debt
Surplus assets & other non-operating liabilites
Restated BS example
Income Statement
Statutory income statements show either:
o Costs by their nature / type
• Personnel, raw materials, D&A, leasing cost, advertising...
• Used in national EU GAAPs
o Costs by function of sourcing
• Cost of goods sold, selling general & administrative expenses (SG&A), ...
• Used in IFRS / US GAAP
• Issue: it doesn’t show D&A → EBITDA?
Cash Flows Statement
𝐼𝑛𝑐𝑜𝑚𝑒 𝑡𝑎𝑥𝑒𝑠
𝐸𝐵𝑇
𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑡𝑎𝑥𝑒𝑠 = 𝐸𝐵𝐼𝑇 ∗ 𝑡
𝑇𝑎𝑥 𝑠ℎ𝑖𝑒𝑙𝑑 = 𝐼𝑛𝑐𝑜𝑚𝑒 𝑡𝑎𝑥𝑒𝑠 − 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑡𝑎𝑥𝑒𝑠
𝑁𝑂𝑃𝐿𝐴𝑇 = 𝐸𝐵𝐼𝑇 − 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑡𝑎𝑥𝑒𝑠
𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒 = 𝑡 =


Operational taxes are taxes that would have been paid on EBIT only
NOPLAT represents operational performance generated by capital employed
FCFO and closing cash balances
■ Free cash flows from operations (FCFO) represents the CF generated by CE:
■ FCFO = NOPLAT - increase in capital employed during the year
■ FCFE = cash that would be available to shareholders (after repaying debtholders) = a
"potential" dividend
Reorganizing the Balance Sheet