Compact Corporate Valuation summary (covering key concepts and formulas with explanation)
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Course
Corporate Valuation
Institution
Vrije Universiteit Amsterdam (VU)
Book
Valuation
A compact, yet complete corporate valuation summary. All formulas and key concepts are explained in this summary. Grab a copy if you want revise key concepts from the book and course!
Includes:
* Formulas + explanation
* Key concepts
* Lecture notes (large overlap with the two above)
Relationship between levered and unlevered cost of equity
Vu V txa D E
1. Step 1: ku + k txa = kd + k Unlevered CoE formula
V u+ V txa V u +V txa D+ E D+ E e
2. Step 2: multiply both sides by enterprise value
V u k u +V txa ( k txa ) =D ( k d ) + E (k e )
3. Step 3: divide both sides , the entire equation by E
Vu V D E V V D
( k u ) + txa ( k txa )= ( k d ) + ( k e ) k e= u ( k u ) + txa ( k txa ) − ( k d )
E E E E E E E
4. Step 4: To eliminate V u (the unknown) from the RHS use V u=D−V txa + E
this is a rearrangement of V u +V txa=Enterprise value=D+ E
D−V txa+ E V D
5. Step 5: k e= ( k u ) + txa ( k txa )− ( k d )
E E E
6. Step 6: distribute the formula into its component parts
D V V D
k e= ( k u )− txa ( k u ) +k u + txa ( k txa )− ( k d )
E E E E
D V txa
7. Step 7: k e=k u + ( k u −k d )− ( k −k )
E E u txa
8. Step 8: recall that if debt is a constant proportion of enterprise value
D
k u =k txa → so the final term drops →k e =k u + ( k −k )
E u d
Levered and unlevered bottom up beta
( 1−t m )∗D
Levered bottom-up beta = β u (1+ ) when debt is risk free + Tax
E
shield has same risk as debt
β e ( average beta across public tradedfirms )
Unlevered beta for business =
¿¿
D
Levered bottom-up beta= β e =β u+ (β u−β d ) (1) when the risk of
E
β β
interest tax shield txa = u (2) when the firm’s debt is risk free.
When debt is risk free (for most investment grade firms and not highly
D
levered firms ): → β e= 1+ ( β
E u )
Dollar level debt Dollar level of debt is Debt is risk free
fluctuates constant and debt is risky
β txa=β u D D D
β e =β u+(β −β ) β e =β u+ (β −β ) β e =(1+ )β
E u d E u d E u
β txa=β d D−V txa ( 1−t m )∗D β e =β u ¿
β e =β u+ ( β u − β d) β e =β u (βu −β d )
E E
Unlevered beta of equity
If the Ktxa = Ku, how can we solve for Ku?
, Vu V txa D E
Step 1: Set Ktxa = Ku ku+ k txa = kd + k
V u+ V txa V u +V txa D+ E D+ E e
V u+ V txa D E
k u= kd+ k
V u+ V txa D+ E D+ E e
D E
Step 2: Only leave the Ku term on the RHS 1∗k u= k + k
D+ E d D+ E e
D E
ku= k d+ k
D+ E D+ E e
When is Ktxa = Kd?
Vu V txa D E
Step 1: Set ktx= Kd ku+ k = k + k
V u+ V txa V u +V txa txa D+ E d D+ E e
Vu V txa D E
ku+ kd= kd + k
V u+ V txa V u +V txa D+ E D+ E e
Step 2: Multiply both sides by Enterprise value
Vu V txa
o ku+ k ∗¿ , where ¿ ¿
V u+ V txa V u +V txa d
Vu V txa D E
ku + k d∗EV = kd+ k ∗EV
V u+ V txa V u +V txa D+ E D+ E e
o V u ( K u ) +V txa ( K d ) =D ( K d ) + E (K e )
Step 3: Move V txa ( K d )=¿ RHS →V u ( K u ) =( D−V txa ) K d + E ( K e )
o Remove V u by equatingV u=D−V txa + E this is a rearrangement of
V u +V txa=Enterprise value=D+ E
( D−V txa ) K d E ( K e) ( D−V txa ) E ( Ke )
o Next k u = + = ∗k d + ∗k
D−V txa + E D−V txa + E D−V txa + E D−V txa + E e
Cost of Equity with build up
When we have a size, country of firm specific premium
k e=rf + ( β × MRP ) + R P¿+CR P country + R Pfirmspecific ¿
APV + M&M
V L=V U + PV ( ITS ) −PV (CFD)
Where CFD = cost of financial distress and Vu value of all equity firm.
In cases where the capital structure is expected to change a lot, assuming
a constant cost of capital can lead to mis-valuation. So, don’t embed
, capital structure in the cost of capital, instead model capital structure
explicitly.
The APV model separates the value of operations into two components:
(1) the value of operations as if the firm were all-equity financed and (2)
value of tax shield that arise from debt financing.
The ITS is discounted at the cost of debt, unless stated differently.
A firm must be profitable to capture tax shields.
Capital Cash Flow model
∞ ∞ ∞
FC Ft IT S t FC F t + IT S t
V =∑ t ∑
+ t
=∑ t
t =1 ( 1+ k u ) t=1 ( 1+ k u ) t=1 ( 1+k u )
Capital Cash Flow model: above equation when a firm actively manages
its d/e ratio, then both FCF and ITS should be discounted by k u .
Only when is CCF = DFC or FCF method? when debt is proportional to
value.
Difference APV and CCF
When firm changes capital structure use APV and when it actively
manages it CCF.
For APV the discount rate can be either Ku or Kd depending on your risk
perspective.
Relationship APV method and M&M: follows directly from their teachings,
they proposed that in a market with no taxes , a firm’s choice of cs will not
affect the value of its economic assets. Only market imperfections e.g.
taxes and distress costs will affect EV.
o Why do we often think that capital structure affects value, in a
perfect world? So that when we increase debt, knowing that cost of
debt is lower than cost of equity, we should NOT forget to increase
the cost of equity it is increases risk from equity holders!
APV separately values APV explicitly measures and values the cash flow
effects of financing separately.
Key value driver formula
At the point where predicting the individual key value drivers on a year-
by-year basis becomes impractical, do not vary the individual drivers over
time. Instead use a perpetuity based continuing value.
, g
NOPLA T t +1 (1− )
RONIC
Continuing valu et =
WACC−g
NOPLAT: Why use NOPLA T t+1 in particular? This is the Net Operating
Profit Less Adjusted Taxes in the year following the explicit forecast
period. Note that growth is also in year 1 terms, same from RONIC so we
use year 1 after explicit forecast period.
o NOPLAT= the profits from the firm’s core operations after
subtracting the income taxes related to the core operations.
o If NOPLAT changes: The KVD formula goes up if NOPLAT increases
o Where NOPLAT reflects a normalized level of earnings at the
midpoint of the business cycle.
o Proportion of NOPLAT: likely to be less if the growth in the CV is
less than in explicit and NOPLAT should be based on ROIC,
sustainable margin and normalized level of revenues.
NOPLAT = EBITA (1-t)
g
= Investment rate where g is the expected growth rate in
ROIC
NOPLAT in perpetuity and ROIC the expected return on invested capital.
G = IR x ROIC and ROIC = G/IR
o growth Expected T rate of consumption growth for industry
products = inflation.
E D
Where WACC = ( K e)+ ( K ) (1−t m) so changes in E, D, Ke , Kd
D+ E D+ E d
and tax will affect the WACC.
o The higher the tax rate, the lower the WACC becomes. But the
lower the tax rate, the higher the WACC. Note that changes in tax
rate are only relevant if the firm actually has debt!!
o The lower the WACC, the higher the firm value !!!
o The lower the cost of debt,
o The lower the cost of equity
o When a firm changes its debt or equity depends
Note: All WACC components are measured in market values.
Note: The cost of debt is reduced by the marginal tax rate.
ROIC = consistent with (1) competitive conditions (2) WACC and (3)
RONIC: must be consistent with market competitive conditions (2) RONIC
must be set equal to WACC econ theory suggests that competition
eliminates abnormal returns so RONIC =WACC.
ROIC with and without goodwill: ROIC with goodwill and acquired
intangibles measures a company’s ability to create value after paying
acquisition premiums. ROIC without goodwill and acquired intangibles
measures the competitiveness of the underlying business.
o What does it usually mean when the ROIC without goodwill is
(much) higher than the ROIC with goodwill? The firm has not
been able to extract value from its acquisition. However, this
doesn’t mean that no improvement has taken place or synergies,
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