Corporate Valuation
Lecture 3 & 4
Discounted Cash Flows Valuation
Academic Year 2023 - 2024
Laura Zanetti
Table of Content
i.
Problem 1: Recalling Capital Structure Theory
ii. Problem 2: Incorporating the Tax Benefits: an Alternative
iii. Problem 3: Asset-Side and Equity Side Models
iv. Discounted Cash Flows Valuation
v. Growth and Value
2
Recalling Capital Structure Theory
■
Problem 1
■
Problem 2
■
Problem 3
3
Does leverage create value?
■
Modigliani & Miller and the conservation of value
■
Tax benefits from leverage
■
The relationship between leverage and discount rates
Where to take tax benefits into account?
■
Adjusting the unlevered value
■
Adjusting the discount rate
Choosing the valuation standpoint
■
Asset-side
■
Equity-side
Recalling Capital Structure Theory
Accounting returns in a no-tax scenario
■
Consider a fully equity-financed company (assume no income taxes):
Capital
1.000
Equity
1.000
Debt
0
Interest rate 5,0%
EBIT
Interests
Net income
Worst case
Base case
Best case
40
100
160
-
-
-
40
100
160
Average
■
ROI
4%
10%
16%
10%
ROE
4%
10%
16%
10%
If the company financed a portion of its invested capital with debt:
Capital
1.000
Equity
600
EBIT
Debt
400
Interests
Interest rate 5,0%
Net income
Worst case
Base case
Best case
40
100
160
(20)
(20)
(20)
20
80
140
Average
4
ROI
4%
10%
16%
10%
ROE
3%
13%
23%
13%
Recalling Capital Structure Theory
Accounting returns in a no-tax scenario
■
Leverage magnifies the volatility of accounting profitability and – on
average – it increases it
■
In a scenario with no income taxes it can be derived that:
𝑅𝑂𝐸 = 𝑅𝑂𝐼 +
■
5
𝐷
𝑅𝑂𝐼 − 𝑖𝑛𝑡. 𝑟𝑎𝑡𝑒
𝐸
Does the higher profitability transfer to higher enterprise (i.e. firm) value?
Recalling Capital Structure Theory
Recalling Modigliani & Miller propositions without income taxes
■
In a world with no income taxes, a change in financial leverage (D and E mix to
finance the same invested capital) does not affect enterprise (asset) value
Balance sheet (at net
book values)
Market
[ expressed at
market values,
a.k.a. enterprise
value, EV ]
[ expressed at
market values, a.k.a.
equity value, EqV ]
6
Recall Corporate Finance Theory
Modigliani & Miller on corporate valuation with income taxes
■
The Modigliani & Miller propositions (with taxes) set up the basis of all main
three DCF valuation frameworks
■
Recall their most basic (no-growth) model:
o
Growth = 0
o
Maintenance
investments (no ∆WC
and CAPEX = D&A)
o
7
Income and CFs are
constant and perpetual
Income statement
= CF statement
Total CF = Net
income
EBIT
= +𝐸𝐵𝐼𝑇
-
Operating taxes
= −𝐸𝐵𝐼𝑇 ∗ 𝑡
=
FCFO
= +𝐹𝐶𝐹𝑂
-
Interests
= −𝐷 ∗ 𝑘𝐷
+
Tax shield of the y.
= +𝐷 ∗ 𝑘𝐷 ∗ 𝑡
=
FCFE (net income)
= 𝐹𝐶𝐹𝐸
o
Interests are taxdeductible
■
If CFs are constant and infinite: value is a constant perpetuity
𝐶𝐹
𝑉=
𝑘
Recall Corporate Finance Theory
Modigliani & Miller on corporate valuation
■
Suppose a company has no debt:
CF
FCFO
■
8
Valuation for the business and the equity is:
o
Enterprise value (market value of assets)
o
Equity value (market value of equity)
CF
B/S book values
A
E
FCFE
(=FCFO)
Gov.
Oper. tax
B/S market values
EV
EqV
Recall Corporate Finance Theory
Modigliani & Miller on corporate valuation
■
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 + 𝛽𝑈 ∗ 𝑀𝑅𝑃
■
Valuation in perpetuity
𝐸𝑉 =
9
𝐹𝐶𝐹𝑂
𝑘𝐸𝑈
𝐸𝑞𝑉 = 𝐸𝑉
Recall Corporate Finance Theory
Modigliani & Miller on corporate valuation
■
M&M 1: as debt increases, enterprise value (i.e. market value of assets)
increases thanks to higher future tax shields (TS)
CF
B/S book values
FCFO
D
Interests
E
FCFE
A
Gov.
B/S market values
B/S market values
EqV
↑
EV
D
EV
VU
EqV
VTS
10
CF
Oper. tax - TS
Recall Corporate Finance Theory
Modigliani & Miller on corporate valuation
■
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)
WACC
FCFO
EV
D
kEU
FCFO
VU
EqV
kD TS=D*t*kD
11
VTS
Int=ND*k
D
kD
FCFE
kEL
Recall Corporate Finance Theory
Modigliani & Miller on corporate valuation
■
The value of the perpetuity is therefore:
𝑀𝑀1 𝑡 : 𝐸𝑉 = 𝑉𝑈 + 𝑉𝑇𝑆
■
𝐹𝐶𝐹𝑂 𝑘𝐷 ∗ 𝐷 ∗ 𝑡 𝐹𝐶𝐹𝑂
=
+
=
+ 𝐷𝑡
𝑘𝐸𝑈
𝑘𝐷
𝑘𝐸𝑈
Adjusted
present value
(APV) method
Debt has book value = market value in a no growth perpetuity:
𝑘𝐷 ∗ 𝐷
𝑀𝑉 𝐷 =
=𝐷
𝑘𝐷
■
Last, the market value of equity1 is:
𝐸𝑞𝑉 = 𝐸𝑉 − 𝐷
1. Note: the definition EqV = EV – D is a temporary simplified expression that assumes that debt is the only balance sheet item between the value of assets and the value of equity. The
concept will be further developed in the next classes (refer to the "bridge to equity").
12
Recall Corporate Finance Theory
An example
Example
■
■
Consider a company with the following characteristics:
o
Constant EBIT in perpetuity = 40
o
Unlevered cost of equity = 10%
o
Cost of debt = Interest rate = 6%
o
Net debt = 200
o
Book value of assets = 300
o
Tax rate = 30%
B/S book values
Assets =
300
Debt = 200
Equity = 100
The free cash flow from operations is:
𝐹𝐶𝐹𝑂 = 𝐸𝐵𝐼𝑇 ∗ 1 − 𝑡 = 40 ∗ 1 − 30% = 28
■
Thus, the unlevered value is:
𝑉𝑈 =
13
𝐹𝐶𝐹𝑂
28
=
= 280
𝑘𝐸𝑈
10%
See Excel –
Example 1
Recall Corporate Finance Theory
An example (continued)
■
The present value of future tax shields is:
𝑉𝑇𝑆 = 𝐷 ∗ 𝑡 = 200 ∗ 30% = 60
■
The enterprise value is:
Example
𝐸𝑉 = 𝑉𝑈 +𝑉𝑇𝑆 = 280 + 60 = 340
■
And the value of the equity is:
𝐸𝑞𝑉 = 𝐸𝑉 − 𝐷 = 340 − 200 = 140
B/S market values
VU = 280
VTS = 60
14
Debt = 200
EV = 340
See Excel –
Example 1
EqV = 140
Recall Corporate Finance Theory
Modigliani & Miller on corporate valuation
■
MM 2: as debt increases, the cost of equity moves UP from the unlevered
case:
𝑀𝑀2 𝑡 :
■
15
■
E: EqV
We can compute equity value alternatively considering CF to shareholders
only:
𝐸𝑞𝑉 =
■
𝑘𝐸𝐿
𝐷
= 𝑘𝐸𝑈 +
∗ 𝑘𝐸𝑈 − 𝑘𝐷 ∗ (1 − 𝑡)
𝐸𝑞𝑉
𝐹𝐶𝐹𝐸
𝑘𝐸𝐿
Discounted cash flows (DCF)
equity-side
It can be shown that under these assumptions, it is mathematically equivalent
to APV
Recall Corporate Finance Theory
An example (continued)
■
The levered cost of equity is:
𝐷
∗ 𝑘𝐸𝑈 − 𝑘𝐷 ∗ 1 − 𝑡 =
𝐸𝑞𝑉
200
= 10% +
∗ 10% − 6% ∗ 1 − 30% = 14%
140
Example
𝑘𝐸𝐿 = 𝑘𝐸𝑈 +
■
The cash flow to equityholders is:
𝐹𝐶𝐹𝐸 = 𝐹𝐶𝐹𝑂 − 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡𝑠 + 𝑇𝑎𝑥 𝑠ℎ𝑖𝑒𝑙𝑑 𝑜𝑛 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡𝑠 =
= 𝐹𝐶𝐹𝑂 − 𝐷 ∗ 𝑘𝐷 + 𝐷 ∗ 𝑡 ∗ 𝑘𝐷 = 28 − 6% ∗ 200 + 6% ∗ 200 ∗ 30% =
= 28 − 12 + 3,6 = 19,6
■
Therefore, from the equity-side the value of the equity is:
𝐹𝐶𝐹𝐸 19,6
𝐸𝑞𝑉 =
=
= 140
𝑘𝐸𝐿
14%
16
(= 𝑡𝑜 𝐸𝑞𝑉 𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 𝐴𝑃𝑉)
See Excel –
Example 1
Recall Corporate Finance Theory
Modigliani & Miller on corporate valuation
■
Discounting FCFO can also be seen "blending" the two asset-side
components V(U) + V(TS) = EV as the asset generating FCFO
■
The "one-shot" discount rate, the weighted average cost of capital, will be
lower than the kEU as it incorporates the tax benefits that was otherwise a
separate item in APV
𝐸𝑞𝑉
𝐷
𝑊𝐴𝐶𝐶 = 𝑘𝐸𝐿 ∗
+ 𝑘𝐷 ∗ 1 − 𝑡 ∗
𝐷+𝐸
𝐷+𝐸
■
WACC
FCFO
EV
D
kEU
FCFO
17
Int=D*kD
kD
FCFE
kEL
VU
EqV
kD TS=D*t*kD
E = EqV in order to have
models equality
VTS
Recall Corporate Finance Theory
Modigliani & Miller on corporate valuation
■
Which leads to the perpetuity valuation:
𝐹𝐶𝐹𝑂
𝐸𝑉 =
𝑊𝐴𝐶𝐶
18
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)
Recall Corporate Finance Theory
An example (continued)
■
The WACC is equal to:
𝑊𝐴𝐶𝐶 = 𝑘𝐸𝐿 ∗
𝐸𝑞𝑉
𝐷
+ 𝑘𝐷 ∗ 1 − 𝑡 ∗
=
𝐷+𝐸
𝐷+𝐸
Example
140
200
= 14% ∗
+ 6% ∗ 1 − 30% ∗
= 8,2%
340
340
■
Therefore, the enteprise value can be derived discounting FCFO at a
rate that already embeds – as a reduction – the tax benefits:
28
𝐸𝑉 =
= 340
8,2%
(= 𝑡𝑜 𝐸𝑉 𝑖𝑛 𝐴𝑃𝑉 𝑎𝑛𝑑 𝑒𝑞𝑢𝑖𝑡𝑦 − 𝑠𝑖𝑑𝑒 𝐷𝐶𝐹)
See Excel –
Example 1
19
Asset-Side and Equity Side Models
Equivalence in the three approaches to valuation in a no-growth state
Adjusted present value
(APV)
𝐸𝑉 = 𝑉𝑈 + 𝑉𝑇𝑆 =
Discounted cash flows
(DCF) equity side
𝐸𝑞𝑉 =
Discounted cash flows
(DCF) asset side
20
𝐹𝐶𝐹𝑂 𝑡 ∗ 𝐷 ∗ 𝑘𝐷 𝐹𝐶𝐹𝑂
+
=
+ 𝑡𝐷
𝑘𝐸𝑈
𝑘𝐷
𝑘𝐸𝑈
𝐸𝑞𝑉 = 𝐸𝑉 − 𝐷
𝐹𝐶𝐹𝐸
𝑘𝐸𝐿
𝐹𝐶𝐹𝑂
𝑊𝐴𝐶𝐶
𝐸𝑞𝑉 = 𝐸𝑉 − 𝐷
𝐸𝑉 = 𝐸𝑉 =
■
This mathematical equivalence holds in the no-growth scenario
■
The equivalence in a constant growth scenario can be derived as well (with a different
assumption on the discount rate for tax shields). The equivalence could be found in a
independent/random CF scenario, yet with extensive additional assumptions on the value
of debt and on yearly discount rates (Fernandez, 1995)
Table of Content
i.
Problem 1: Recalling Capital Structure Theory
ii. Problem 2: Incorporating the Tax Benefits: an Alternative
iii. Problem 3: Asset-Side and Equity Side Models
iv. Discounted Cash Flows Valuation
v. Growth and Value
21
Discounted Cash Flows Valuation
A generalized DCF model in practice: a one-stage, growing model
■
Under a real-life scenario, the no-growth assumption is relaxed
■
One first extension would be to set up the DCF models as a one-stage,
constant growth g scenario
■
In an asset-side DCF model:
■
In an equity-side DCF model:
■
In an APV model:
𝐸𝑉0 =
𝐹𝐶𝐹𝑂1
𝑊𝐴𝐶𝐶 − 𝑔𝐹𝐶𝐹𝑂
𝐸𝑞𝑉0 =
𝐸𝑉0 =
𝐹𝐶𝐹𝐸1
𝑘𝐸𝐿 − 𝑔𝐹𝐶𝐹𝐸
𝐹𝐶𝐹𝑂1
𝑇𝑆1
+
𝑘𝐸𝑈 − 𝑔𝐹𝐶𝐹𝑂 𝑘 𝑇𝑆 − 𝑔𝑇𝑆
= 𝑘𝐷
𝑘 𝑇𝑆 = ቊ
= 𝑘𝐸𝑈
22
Discounted Cash Flows Valuation
A generalized DCF model in practice: the two-stage models
■
■
However, the most commonly applied formats relax the constant growth
pattern, breaking down the forecast period in two stages:
■
A first stage, where T cash flows will be individually forecast and
discounted one-by-one (e.g. the first 3 to 5 forecast years)
■
A second subsequent stage (the terminal value), with a constant growth
assumption
The asset-side DCF in a two-staged model is therefore defined as follows:
𝑇
𝐸𝑉0 = ෍
𝑡=1
23
𝐹𝐶𝐹𝑂𝑡
1 + 𝑊𝐴𝐶𝐶
+
𝑡
𝑇𝑉
1 + 𝑊𝐴𝐶𝐶
𝑇
𝑇𝑉 =
𝐹𝐶𝐹𝑂𝑇+1
𝑊𝐴𝐶𝐶 − 𝑔𝐹𝐶𝐹𝑂
Discounted Cash Flows Valuation
■
Similarly, DCF equity side in a two-staged model will be:
𝑇
𝐸𝑞𝑉0 = ෍
𝑡=1
■
𝐹𝐶𝐹𝐸𝑡
1 + 𝑘𝐸𝐿
+
𝑡
𝑇𝑉
1 + 𝑘𝐸𝐿
𝑇𝑉 =
𝑇
𝐹𝐶𝐹𝐸𝑇+1
𝑘𝐸𝐿 − 𝑔
APV valuation will have a two-staged model for both unlevered value and tax
shields:
𝑇
𝑉𝑈 = ෍
𝑡=1
𝐸𝑉0 = 𝑉𝑈 + 𝑉𝑇𝑆
𝑇
𝑉𝑇𝑆 = ෍
𝑡=1
𝐹𝐶𝐹0𝑡
1 + 𝑘𝐸𝑈
+
𝑡
𝑇𝑉𝑈
1 + 𝑘𝐸𝑈
𝑇𝑆𝑡
1 + 𝑘 𝑇𝑆
+
𝑡
𝑇𝑉𝑇𝑆
1 + 𝑘 𝑇𝑆
𝑇
𝑇
𝑇𝑉𝑈 =
𝐹𝐶𝐹𝑂𝑇+1
𝑘𝐸𝑈 − 𝑔𝐹𝐶𝐹𝑂
𝑇𝑉𝑇𝑆 =
𝑇𝑆𝑇+1
𝑘 𝑇𝑆 − 𝑔𝑇𝑆
= 𝑘𝐷
𝑘 𝑇𝑆 = ቊ
= 𝑘𝐸𝑈
24
Discounted Cash Flows Valuation
A practical step-by-step approach
■
Consider an asset-side DCF. As a general implementation framework:
1. Develop
/ get a
business
plan
25
2. Estimate
discount
rates
3. Estimate
the
terminal
value
4. Discount
FCFO →
EV
5. - ND +/other items
→ EqV
■
The business plan is either given to you by management, built by yourself
based on the past or on public info, or taken from broker's CF consensus (e.g.
IBES estimates on Bloomberg)
■
WACC is (usually) constant across all periods
■
Explicit period (years 1 to T): 3/5 years, according to the available business
plan
■
The terminal value assumptions usually should represent a steady state: no
real growth investments, only inertial growth. Its FCFO is adjusted to
represent this condition (see later)
Discounted Cash Flows Valuation
A practical step-by-step approach
■
The definition of FCFO and FCFE also needs to be revised in a growing
scenario, as the assumptions on made earlier in the zero-growth scenarios
are no longer applicable
■
Estimating FCFO and FCFE will be
further explored in the dedicated lecture
on cash flows
Cash flows in a growing
scenario
EBIT
- Operating taxes
Cash flows in a zerogrowth scenario
+ D&A
- Change in working capital
26
EBIT
- Capital expenditures
-
Operating taxes
= FCFO
=
FCFO
- Interests
-
Interests
+ Tax shields
+
Tax shields
+ Change in debt
=
FCFE
= FCFE
Discounted Cash Flows Valuation
Recall the Netflix example: applying a simplified version
Source: https://plus.credit-suisse.com/rpc4/ravDocView?docid=_XWaA2AN-Ytkb
27
Discounted Cash Flows Valuation
Recall the Netflix example: applying a simplified version
Period
Free cash flows from operations
WACC
9,8%
Terminal growth rate
3,0%
Discount factor
PV of FCFO
Value from FCFO in 2019 - 2023
Case study
28
Enteprise value on 31/12/2018
Net debt
Equity value
2020
2021
2022
2023
1
2
3
4
5
2.550,0
4.004,0
5.535,0
7.526,0
9.382,0
0,911
0,829
0,755
0,688
0,627
2.322,4
3.321,2
4.181,3
5.177,9
5.878,7
20.881,5
Terminal value
PV of the TV: value from FCFO beyond 2023
2019
142.109,7
89.045,5
109.927,0
See Excel –
Example 2
6.924,0
103.003,0
■
This shortened application takes the first 5 years in forecast FCFO only
■
Observe that this value is significantly lower than what Credit Suisse's report
determined ($m 228.986), because Credit Suisse also discounted as part of Stage 1
the FCFO in 2024 – 2044, which grew considerably. FCFO 2023 (our last in Stage 1)
is $b 9 while in 2044 it was expected to be $b 58 !!
■
Such a long – and growing - Stage 1 is very uncommon: however it was reasonable
in Netflix's case because it was a very high-growth developing business at the time
of the equity research report (mid 2017)
Discounted Cash Flows Valuation
Generalizing the DCF models
■
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
Tax benefits as a separate
value
Equity-side
Asset-side
Tax benefits into the
discount rate
■
29
Note that it would have little significance to adopt an equity-side version of the APV,
since an unlevered version of FCFE isn't defined
Table of Content
i.
Problem 1: Recalling Capital Structure Theory
ii. Problem 2: Incorporating the Tax Benefits: an Alternative
iii. Problem 3: Asset-Side and Equity Side Models
iv. Discounted Cash Flows Valuation
v. Growth and Value
30
Discounted Cash Flows Valuation
The terminal value
Terminal growth rate
31
■
The TV growth rate should not 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: it implies that the firm will disappear in time
■
In a high-GDP growth economy, the stable growth rate should be lower (e.g.
long-term estimated inflation rate, such as 2%)
■
Such an inflationary / stable growth assumptions might require adjustment to
the FCFO on the numerator (more on this later on in the course)
Growth and Value
The relationship between return on investment, EBIT growth and reinvestment needs
■
Define the capital reinvestment rate (CRR) as all the after-tax EBIT (i.e.
NOPAT) that gets reinvested into operations:
𝐶𝑅𝑅 ≡ 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑟𝑒𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑟𝑎𝑡𝑒 ≡ 1 −
𝐹𝐶𝐹𝑂𝑡
𝑁𝑂𝑃𝐴𝑇𝑡
𝑁𝑂𝑃𝐴𝑇 ≡ 𝐸𝐵𝐼𝑇 ∗ (1 − 𝑡)
■
Consider ROI. It can be proven that, if the return on investments is constant
(see the Appendix), then:
𝑅𝑂𝐼 ≡
𝑁𝑂𝑃𝐴𝑇𝑡
𝐴𝑠𝑠𝑒𝑡𝑠𝑡−1
𝒈𝑬𝑩𝑰𝑻 = 𝑹𝑶𝑰 ∗ 𝑪𝑹𝑹 → 𝐶𝑅𝑅 =
𝑔𝑁𝑂𝑃𝐴𝑇
𝑅𝑂𝐼
This is a fundamental relationship: under constant returns (which is
reasonable in the long term) the growth rate in earnings (g) should be equal to
the product of the reinvestments into the business (CRR) and the return on
these investments (ROI)
32
Growth and Value
Incorporating implied growth and reinvestment into an asset-side DCF
■
As a consequence of the previous formula:
𝐹𝐶𝐹𝑂𝑡 = 𝑁𝑂𝑃𝐴𝑇𝑡 ∗ 1 − 𝐶𝑅𝑅 = 𝑁𝑂𝑃𝐴𝑇𝑡 ∗ 1 −
■
𝑔𝑁𝑂𝑃𝐴𝑇
𝑅𝑂𝐼
Replace it into a one-stage, growing asset-side DCF1:
𝑔
𝑁𝑂𝑃𝐴𝑇1 ∗ 1 − 𝑁𝑂𝑃𝐴𝑇
𝐹𝐶𝐹𝑂1
𝑅𝑂𝐼
𝐸𝑉 =
=
𝑊𝐴𝐶𝐶 − 𝑔𝑁𝑂𝑃𝐴𝑇
𝑊𝐴𝐶𝐶 − 𝑔𝑁𝑂𝑃𝐴𝑇
■
In the LT, ROI should converge to WACC. This has a powerful consequence:
value no longer depends on long term growth!
𝐸𝑉 =
𝑔𝑁𝑂𝑃𝐴𝑇
𝑊𝐴𝐶𝐶 = … = 𝑁𝑂𝑃𝐴𝑇1
𝑊𝐴𝐶𝐶 − 𝑔𝑁𝑂𝑃𝐴𝑇
𝑊𝐴𝐶𝐶
𝑁𝑂𝑃𝐴𝑇1 ∗ 1 −
1. The same rationale can certainly be applied to the terminal value of a two-stage DCF model; 𝑇𝑉𝑇 =
33
𝐹𝐶𝐹𝑂𝑇+1
𝑊𝐴𝐶𝐶−𝑔𝑁𝑂𝑃𝐴𝑇
=
𝑔
𝑁𝑂𝑃𝐴𝑇𝑇+1 ∗ 1− 𝑁𝑂𝑃𝐴𝑇
𝑅𝑂𝐼
𝑊𝐴𝐶𝐶−𝑔𝑁𝑂𝑃𝐴𝑇
Growth and Value
An example
Example
■
Consider the following company inputs:
■
NOPAT year 1 = 100
■
WACC = 10%
■
ROI = 10%
■
Expected growth = 4%
𝐶𝑅𝑅 =
𝐸𝑉 =
■
34
See Excel –
Example 3
𝑔
4%
=
= 40%
𝑅𝑂𝐼 10%
𝑁𝑂𝑃𝐴𝑇1 ∗ (1 − 𝐶𝑅𝑅) 100 ∗ (1 − 40%)
=
= 1.000
𝑊𝐴𝐶𝐶 − 𝑔
10% − 4%
Would EV increase if the expexted growth rate increased beyond 4%?
Growth and Value
An example
Observe a sensitivity analysis on the previous example:
1 If ROI = WACC (e.g. in the example), a change in the growth rate is
1.
irrelevant for value
Example
2 If ROI > WACC, an increase in the growth rate increases value
2.
3 If ROI < WACC, an increase in the growth rate decreases value
3.
Growth rate
ROI
1.000,0
6,0%
8,0%
10,0%
12,0%
14,0%
-
1.000,0
1.000,0
1.000,0
1.000,0
1.000,0
1,0%
925,9
972,2
1.000,0
1.018,5
1.031,7
1,5%
882,4
955,9
1.000,0
1.029,4
1.050,4
2,0%
833,3
937,5
1.000,0
1.041,7
1.071,4
2,5%
777,8
916,7
1.000,0
1.055,6
1.095,2
3
35
1
2
See Excel –
Example 3
Growth and Value
A link between valuation and strategy: which growth strategies do increase value?
A. High-value creating growth strategies (ROI >> WACC)
■
Create new markets through new products: there are no competitors
■
Convince existing customers to buy more of a product: all competitors benefit;
low risk of retaliation
■
Attract new customers to the market: all competitors benefit; low risk of
retaliation
An example: Beiersdorf and L'Oreal
■
Consumer goods companies Beiersdorf and L’Oreal accelerated growth in
skin-care products by promoting their Nivea and Bio-therm products,
respectively, to male clients.
■
Investments were low due to similarities with women's skin-care products. The
major incremental cost was for marketing and advertising
■
Their competitors didn't retaliate because they also gained from the expansion
Source: Koller et al (2015).
36
Growth and Value
A link between valuation and strategy: which growth strategies do increase value?
B. Average-value creating growth strategies (ROI > WACC)
■
Gain market share in fast-growing market: competitors can still grow despite
losing share; moderate risk of retaliation
■
Make small acquisitions to accelerate product growth: might be expensive,
absorbing much of the value creation
An example: IBM
■
IBM has been successful in acquiring smaller software companies and
subsequently marketing their applications through its existing global sales and
distribution system, which can absorb the additional sales without too much
extra investment
■
Because such acquisitions are relatively small to IBM’s size, they boost IBM’s
growth but add little cost and complexity
Source: Koller et al (2015).
37
Growth and Value
A link between valuation and strategy: which growth strategies do increase value?
C. Low-value creating growth strategies (ROI ≈ WACC)
■
Catch rivals' market share through new offerings: competitors can replicate
and take back their customers
■
Catch rivals' market share through strong product promotion and pricing: also
easy to retaliate
■
Make large acquisitions: might be very expensive, absorbing much of the value
creation
An example: Amazon and Wal-Mart (2009)
■
As Amazon continued expanding into the U.S. consumer electronics retails
market, Wal-Mart retaliated with price cuts on key products, such as top-selling
video games and game consoles, even though Amazon’s $20 billion in sales in
2008 were a fraction of Wal-Mart’s $406 billion in sales in the same year
■
In concentrated markets, share battles often lead to a cycle of market share
give-and-take, but rarely a permanent share gain for any one competitor
Source: Koller et al (2015).
38
Growth and Value
An application to the equity-side DCF model
■
An equivalent reasoning can be derived for an equity-side DCF
■
The equity reinvestment rate represent the portion of net income (NI) that is
not available to be paid out, potentially, to shareholders (in terms of FCFE)
𝐸𝑞𝑢𝑖𝑡𝑦 𝑟𝑒𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑟𝑎𝑡𝑒 (𝐸𝑅𝑅) ≡ 1 −
■
Considering return on equity (ROE), if ROE is constant, it can be proven that:
𝑅𝑂𝐸 ≡
39
𝐹𝐶𝐹𝐸𝑡
𝑁𝐼𝑡
𝑁𝐼𝑡
𝐸𝑞𝑢𝑖𝑡𝑦 𝑡−1
𝑔𝑁𝐼 = 𝑅𝑂𝐸 ∗ 𝐸𝑅𝑅 → 𝐸𝑅𝑅 =
𝑔𝑁𝐼
𝑅𝑂𝐸
Growth and Value
An application to the equity-side DCF model
■
As a consequence:
𝐹𝐶𝐹𝐸𝑡 = 𝑁𝐼𝑡 ∗ 1 − 𝐸𝑅𝑅 = 𝑁𝐼𝑡 ∗ 1 −
■
Consider a one-stage, growing, equity-side DCF model:
𝐸𝑞𝑉0 =
■
𝑔𝑁𝐼
𝑅𝑂𝐸
𝐹𝐶𝐹𝐸1
𝑘𝐸𝑙 − 𝑔𝑁𝐼
Therefore:
𝑔
𝑁𝐼1 ∗ 1 − 𝑁𝐼
𝐹𝐶𝐹𝐸1
𝑅𝑂𝐸
𝐸𝑞𝑉0 =
=
𝑘𝐸𝑙 − 𝑔𝑁𝐼
𝑘𝐸𝑙 − 𝑔𝑁𝐼
40
Growth and Value
An application to the dividend discount model
■
The same rationale applies to stock valuation with a dividend discount model,
in other words an alternative equity-side valuation model:
𝐷𝐷𝑀: 𝑃0 =
■
Similarly to the case of an equity-side DCF, in a DDM the equity reinvestment
rate is replaced by the "retention ratio", i.e. one minus the dividend payout
ratio. The implied growth rate can be similarly derived:
𝑅𝑒𝑡𝑒𝑛𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 ≡ 1 − 𝑝𝑎𝑦𝑜𝑢𝑡 ≡ 1 −
■
𝑁𝑜𝑡𝑒: 𝑃0 = 𝑣𝑎𝑙𝑢𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒
𝐸𝑞𝑉0
=
# 𝑠ℎ𝑎𝑟𝑒𝑠
𝐷𝑃𝑆1
𝐸𝑃𝑆1 ∗ 𝑝𝑎𝑦𝑜𝑢𝑡
=
𝑘𝐸𝐿 − 𝑔𝐸𝑃𝑆
𝑘𝐸𝐿 − 𝑔𝐸𝑃𝑆
𝐷𝑃𝑆𝑡
𝐸𝑃𝑆𝑡
𝑔𝐸𝑃𝑆 = 𝑅𝑂𝐸 ∗ 𝑟𝑒𝑡𝑒𝑛𝑡𝑖𝑜𝑛
The DDM's dividend per share and value per share would be expressed as:
𝐷𝑃𝑆𝑡 = 𝐸𝑃𝑆𝑡 ∗ 1 − 𝑟𝑒𝑡𝑒𝑛𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 = 𝐸𝑃𝑆𝑡 ∗ 1 −
𝑔
𝐸𝑃𝑆1 ∗ 1 − 𝐸𝑃𝑆
𝐷𝑃𝑆1
𝑅𝑂𝐸
𝑃0 =
=
𝑘𝐸𝐿 − 𝑔𝐸𝑃𝑆
𝑘𝐸𝐿 − 𝑔𝐸𝑃𝑆
41
𝑔𝐸𝑃𝑆
𝑅𝑂𝐸
Appendix
Deriving the relationship between growth in NOPAT, ROI and capital reinvestments
𝑔𝑡𝑁𝑂𝑃𝐴𝑇 ≡
𝑁𝑂𝑃𝐴𝑇𝑡 − 𝑁𝑂𝑃𝐴𝑇𝑡−1
1
𝑁𝑂𝑃𝐴𝑇𝑡−1
𝑅𝑂𝐼𝑡−1 ≡
𝑁𝑂𝑃𝐴𝑇𝑡−1
𝑏𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑 𝑟𝑒𝑡𝑢𝑟𝑛𝑠
𝐶𝐸𝑡−2
2
→ 𝑁𝑂𝑃𝐴𝑇𝑡−1 =𝑅𝑂𝐼𝑡−1 ∗ 𝐶𝐸𝑡−2
→ 𝑁𝑂𝑃𝐴𝑇𝑡 =𝑅𝑂𝐼𝑡 ∗ 𝐶𝐸𝑡−1 (3)
𝐶𝐸𝑡−1 ≡ 𝐶𝐸𝑡−2 + ±∆± 𝑁𝑊𝐶𝑡−1 + 𝐶𝐴𝑃𝐸𝑋𝑡−1 − 𝐷&𝐴𝑡−1 ≡ 𝐶𝐸𝑡−2 + 𝑅𝑒𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑠𝑡−1 (4)
𝑅𝑒𝑝𝑙𝑎𝑐𝑒 4 𝑖𝑛𝑡𝑜 3 :
𝑁𝑂𝑃𝐴𝑇𝑡 =𝑅𝑂𝐼𝑡 ∗ 𝐶𝐸𝑡−2 ± ∆± 𝑁𝑊𝐶𝑡−1 + 𝐶𝐴𝑃𝐸𝑋𝑡−1 − 𝐷&𝐴𝑡−1
𝐼𝑓 𝑅𝑂𝐼 𝑖𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑜𝑣𝑒𝑟 𝑡𝑖𝑚𝑒: 𝑅𝑂𝐼𝑡−1 = 𝑅𝑂𝐼𝑡 ≡ 𝑅𝑂𝐼. 𝑁𝑜𝑤 𝑟𝑒𝑝𝑙𝑎𝑐𝑒 2 𝑎𝑛𝑑 4 𝑖𝑛𝑡𝑜 1 :
𝑔𝑡𝑁𝑂𝑃𝐴𝑇 =
𝑅𝑂𝐼𝑡 ∗ 𝐶𝐸𝑡−2 ± ∆± 𝑁𝑊𝐶𝑡−1 + 𝐶𝐴𝑃𝐸𝑋𝑡−1 − 𝐷&𝐴𝑡−1 − 𝑅𝑂𝐼𝑡−1 ∗ 𝐶𝐸𝑡−2
𝑁𝑂𝑃𝐴𝑇𝑡−1
𝑔𝑡𝑁𝑂𝑃𝐴𝑇 =
𝑅𝑂𝐼𝑡 ∗ 𝐶𝐸𝑡−2 + 𝑅𝑂𝐼𝑡 ∗ ±∆± 𝑁𝑊𝐶𝑡−1 + 𝐶𝐴𝑃𝐸𝑋𝑡−1 − 𝐷&𝐴𝑡−1 − 𝑅𝑂𝐼𝑡−1 ∗ 𝐶𝐸𝑡−2
𝑁𝑂𝑃𝐴𝑇𝑡−1
𝐹𝐶𝐹𝑂𝑡
𝑁𝑂𝑃𝐴𝑇𝑡 − 𝐹𝐶𝐹𝑂𝑡 𝐶𝐴𝑃𝐸𝑋 − 𝐷&𝐴 ± ∆± 𝑁𝑊𝐶
𝑅𝑒𝑐𝑎𝑙𝑙 𝑡ℎ𝑎𝑡 𝐶𝑅𝑅 ≡ 1 −
. 𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒 𝐶𝑅𝑅 =
=
𝑁𝑂𝑃𝐴𝑇𝑡
𝑁𝑂𝑃𝐴𝑇𝑡
𝑁𝑂𝑃𝐴𝑇𝑡
𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒: 𝑔𝑡𝑁𝑂𝑃𝐴𝑇 = 𝑅𝑂𝐼𝑡 ∗ 𝐶𝑅𝑅𝑡−1 (𝑄𝐸𝐷)
42
Not part of exam
materials