CORPORATE VALUATION
 Valuation Methods





Comparable Firms
WACC (or FCF or DCF)
Adjusted Present Value (APV)
Equityholder Cash Flow (ECF or FCFE)
Other Methods? (EVA, RI)
 Beyond The Numbers
• Role of Investors’ Expectations
• Corporate Governance Issues
• Incentives Compensation
1
METHOD OF COMPARABLES VALUATION
•
The idea: identify how the valuation of comparable firms relates to some firm
characteristic (e.g., P/E ratio, etc.) and use that relationship to value the firm.
𝑉𝑓 = 𝑟𝑖 ∗ 𝑋𝑓 + 𝜀
𝑉𝑓 – firm or equity value,
𝑋𝑓 – some firm characteristic, for example earnings.
𝜀 – error term, the true relationship is likely more complex
Steps:
• Identify one or several comparable firms and collect data on their valuation
(Vf) and one characteristic important for valuation (Xf).
• Divide Vf over Xf to obtain ri.
• Use ri * Xf as a proxy for the value of your firm
2
METHOD OF COMPARABLES VALUATION
 Used when detailed data needed for other methods is hard to
obtain
 Used in stock valuation
 Can serve as a check on whole firm valuation
 Can be one way to obtain Terminal Value (TV)
 TV is discussed in more detail later in the slides
3
METHOD OF COMPARABLES VALUATION
Advantages:
 quick and easy to implement
 useful for opaque firms
 Provides a different perspective on firm value
Problems:
 the assumption it makes about the relationship between a firm
characteristic and its value is very coarse approximation of reality
 sensitive to the choice of characteristic to focus on
 sensitive to the choice of comparable firms
 Is it forward or backward looking?
4
WACC METHOD
OR DISCOUNTED CCASH FLOW METHOD
OR FREE CASH FLOW METHOD
The idea: calculate Free Cash Flows, discount them with WACC.
Start by separating Operating Assets from Non-operating Assets
1) Non-operating assets
 Financial assets
 Real estate
2) Operating assets
 Plant and Equipment
 Inventory
 Patents
Enterprise value = Value of Operating Assets + Value of Non-Operating
Assets
5
VALUE OF OPERATING ASSETS
Free Cash Flows (FCF) are generated by operating assets, so
Value of Operating Assets = PV (expected future FCFs), discounted at the WACC.
∞
𝑉𝑂𝑝 =
𝑐
=
𝑡=1
𝑡=1
𝐹𝐶𝐹𝑡
(1 + 𝑟)𝑡
𝐹𝐶𝐹𝑡
𝑇𝑉𝑐
+
1+𝑟 𝑡
1+𝑟
𝑐
𝑟 – the firm’s cost of capital (WACC)
𝑇𝑉𝑐 – Terminal Value at time c
6
VALUE OF OPERATING ASSETS:
MEASUREMENT ISSUES
 TV could be assessed using comparable firm valuation method
 Alternatively, you can assume FCF is a perpetuity starting in year c+1
with some growth rate g
𝑇𝑉𝑐 =
𝐹𝐶𝐹𝑐+1
𝑊𝐴𝐶𝐶−𝑔

FCF = NOPAT (net operating profit after taxes)
- ΔNOWC (change in net operating working capital)
- CAPEX (capital expenditures)

NOPAT = EBIT (earning before interest and taxes)
- TAX (taxes as if no interest deduction)
+ NCEXP (non-cash expenses) - NCREV (non-cash revenues)
7
NET OPERATING PROFIT AFTER TAXES (NOPAT)
Two equivalent ways to calculate:
Approach #1:
NOPAT = Earnings Before Interest and Taxes - Taxes + change in deferred taxes
– non-cash revenues + non-cash expenses
Approach #2:
NOPAT = Net Income + Interest expense (after tax) + change in deferred taxes
– non-cash revenues + non-cash expenses
8
CHANGE IN NET OPERATING WORKING CAPITAL
How we measure net investment in short-term capital depends on what short term
assets are required for operations
 Measure 1 (DNOWC ) = Dcash + Daccounts receivable
+ Dinventory – Daccounts payable
 Measure 2 (DNOWC ) = Daccounts receivable +
Dinventory – Daccounts payable
 May be in between
9
CAPITAL EXPENDITURES
Two equivalent measures:
 Measure 1: Capital expenditures = Gross PPEt – Gross PPEt-1
 Measure 2: Capital expenditures = (Net PPEt – Net PPEt-1) +
Depreciation expense
• Note: if Balance Sheet has other items on the asset side,
they all should be accounted for one way or the other.
10
AN ALTERNATIVE APPROACH TO
MEASURING FCF
The prior approaches worked off the firm’s income statement and
balance sheet.
An alternative is to work off the statement of cash flows.
 Use cash flow from operations from the statement of changes in cash
flow add back interest expense and subtract capital expenditures
11
CASH FLOW
STATEMENT
Note:
interest paid in cash
- interest tax shield
≈ (interest expense)× (1 − 𝑡)
CF(operations) = NI (net income)
+ NCEXP (non-cash expenses)
- NCREV (non-cash revenues)
- D NOWC (change in net operating working capital)
CF(investing) = - INVEST (capital expenditures)
+ DIVEST (cash flow from divestitures/sale of assets)
CF (financing) = - Common dividends
- Preferred dividends
+ Change in debt financing
+ Change in preferred stock financing
+ Change in common stock financing
Cash Balance = CF(operations) + CF(investing) + CF (financing)
FCF = unlevered CF(operations) - Capital expenditures
= CF(operations) + (interest - interest tax shield)
- Capital expenditures
12
SIMPLE EXAMPLE
FCFlast year = $20 million
WACC = 10%
g = 5%
Marketable securities = $100 million
Debt = $200 million
Preferred stock = $50 million
Book value of equity = $210 million
13
VALUE OF OPERATIONS: CONSTANT GROWTH
Suppose FCF grows at constant rate g
VOp



t 1



t 1
FCFt
1  WACC 
t
FCF0 (1  g ) t
1  WACC 
t
FCF0 (1  g )
WACC - g
20(1  0.05)

 420
(0.10 - 0.05)

14
TOTAL CORPORATE VALUE
Sources of Corporate Value
 Value of operations = $420
 Value of non-operating assets = $100
 Total corporate value = 420+100 = 520
Claims on Corporate Value
 Value of Debt = $200
 Value of Preferred Stock = $50
 Value of Equity = 520 – 200 – 50 = 270
15
VALUE OF OPERATIONS:
NON-CONSTANT GROWTH
∞
𝑉𝑂𝑃 =
𝑡=1
𝐹𝐶𝐹𝑡
1 + 𝑊𝐴𝐶𝐶
𝐹𝐶𝐹1
=
1 + 𝑊𝐴𝐶𝐶
=
𝐹𝐶𝐹1
1 + 𝑊𝐴𝐶𝐶
𝑡
𝐹𝐶𝐹2
1 + 1 + 𝑊𝐴𝐶𝐶
1+
𝐹𝐶𝐹2
1 + 𝑊𝐴𝐶𝐶
𝐹𝐶𝐹𝑛
2 + ⋯ + 1 + 𝑊𝐴𝐶𝐶
2 + ⋯+
𝐹𝐶𝐹𝑛
1 + 𝑊𝐴𝐶𝐶
𝑇𝑉𝑛
𝑛 + 1 + 𝑊𝐴𝐶𝐶
𝑛+
𝑛
𝐹𝐶𝐹𝑛+1
(𝑊𝐴𝐶𝐶 − 𝑔) 1 + 𝑊𝐴𝐶𝐶
𝑛
16
FCF METHOD: SUMMARY OF STEPS
1.
2.
3.
4.
5.
Forecast the financial statements
Forecast free cash flows
Estimate the firm’s WACC
Discount free cash flows at WACC
Add value of operating assets to value of non-operating assets to
derive the enterprise value of the firm
17
FCF METHOD: USE
The FCF valuation requires financial statements and estimates of the
cost of capital.
Can be applied to evaluate corporate decisions
Can be applied to:
 a company that does not pay dividends
 a privately held company
 a division of a company
18
EXPANDED EXAMPLE
Acme Corporation
•
faces a 40% tax rate.
•
cost of capital (WACC) is 10%.
•
has $1,281.86 of debt outstanding.
•
has 100 million shares outstanding.
•
expected to grow at a constant rate of 6% after 2021.
•
the projected financials reported on the next page.
What is the value of Acme’s equity and its implied stock price?
19
EXPANDED EXAMPLE
(millions)
2017(A)
2018(P)
2019(P)
2020(P)
2021(P)
Operating Profit
586.62
633.55
671.56
711.85
754.56
Tax
234.65
253.42
268.62
284.74
301.82
NOPAT
351.97
NOWC
1,128.11
1,218.36
1,291.47
1,368.95
1,451.09
NPE
2,256.23
2,436.72
2,582.92
2,737.90
2,902.16
Invest in Op. Capital
279.45
FCF
72.53
20
EXPANDED EXAMPLE
(millions)
2017(A)
2018(P)
2019(P)
2020(P)
2021(P)
Operating Profit
586.62
633.55
671.56
711.85
754.56
Tax
234.65
253.42
268.62
284.74
301.82
NOPAT
351.97
380.13
402.94
427.11
452.74
NOWC
1,128.11
1,218.36
1,291.47
1,368.95
1,451.09
NPE
2,256.23
2,436.72
2,582.92
2,737.90
2,902.16
Invest in Op. Capital
279.45
270.74
219.31
232.46
246.41
FCF
72.53
109.39
183.63
194.65
206.33
21
TERMINAL VALUE
Free cash flows are forecasted for four years in this example.
Growth is constant after the horizon (4 years), so we can use
the constant growth formula to find the value of all free cash
flows beyond the horizon.
𝐹𝐶𝐹𝑐 (1 + 𝑔)
𝑇𝑉𝑐 (𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑠) =
𝑊𝐴𝐶𝐶 − 𝑔
22
EXAMPLE
𝑇𝑉2021
206.33 × 1.06
=
= 5,467.75
0.10 − 0.06
V(operations) = PV((109, 184, 195,206+5,467.75) at 10%)
= 4,272.92
V(equity) = 4,272.92 – 1,281.86 = 2,991
P = $2,991M/100M shares = $29.91 per share
23
TERMINAL VALUE
We computed the terminal value of the firm using the present value of
a growing perpetuity.
Alternative: use the method of comparables.
 Like price-to-earnings multiple, you would compute a firm value-toearnings multiple for “appropriate” firms and apply to terminal value
computation.
24
EXAMPLE: EXPANSION PLAN
The firm is expanding into new territories and
plans to finance it by borrowing $40 million.
Projected FCFs associated with this expansion are:
 Year 1 FCF = -$5 million.
 Year 2 FCF = $10 million.
 Year 3 FCF = $20 million
 FCF grows at constant rate of 6% after year 3.
Assume that the firm’s WACC is 10%.
25
Find the value of operations by discounting
the free cash flows at the cost of capital.
0
1
r =10%
2
3
4
g = 6%
FCF=
-5.00
10.00
20.00
21.2
-4.545
8.264
15.026
𝑇𝑉3 =
398.197
416.942
=
Vop
$21.2
0.10 − 0.06
=$530
26
VALUATION OF THE EXPANSION
Value of equity = Value of operations - Value of debt
= $416.94
- $40
= $376.94 million.
Need to compare this to the equity investment
necessary to fund this expansion. If less, then the
NPV is positive.
27
DIVESTITURE EXAMPLE
Phillips Corp.
• Considering divestiture of its unit producing light fixtures
• Phillips’ effective corporate tax rate is 30%
• The appropriate cost of capital for the unit is 8.23%
• The unit’s free cash flows are expected to grow at 3% per year
Divestiture analysis:
 Compare the value of the unit to the value of similar unit in
another company or a similar independent entity.
 Divest if the unit is worth more to another entity than to its current
owner.
28
DIVESTITURE EXAMPLE
Balance Sheet ($M)
Cash
10
AP
40
AR
12
Accurals
12
Inventory
45
Debt
75
Net Fixed Assets
155
Common Equity
95
Total Assets
222
TL&OE
222
Income Statement ($M)
Miscellaneous
Sales
65
Change in NOWC
COGS
40
Investment in PP&E 0.5
SG&A
4
Depreciation
11.625
Interest expense
3.375
EBT
6
Taxes
1.8
NI
4.2
1.2
DIVESTITURE EXAMPLE
NOPAT = (65-40-4-11.625)(1-0.30) + 11.625 = 6.5625 + 11.625
FCF = 6.5625 + 11.625 – 1.2 – 0.5 = 16.4875
WACC = 8.23%
Operating value = 16.4875 (1 + 0.03)/ (0.0823 – 0.03) = 324.706
Equity value = 324.706 – 75 = 249.706
Decision: Divest only if able to sell more than 249.706
EBITDA = (65 – 40 – 4) = 21
Equity value /EBITDA = 11.891
Method of Comparables: likely buyers have V(Equity)/EBITDA > 11.891
30
ADJUSTED PRESENT VALUE METHOD
APV = NPV(unlevered) + NPVF
Project Value
= value of the project to an unlevered firm (NPV)
+ the present value of the financing side effects (NPVF).
Four common side effects of financing:
 The Tax Subsidy to Debt
 The Costs of Issuing New Securities
 The Costs of Financial Distress
 Other Subsidies to Debt Financing
31
ADJUSTED PRESENT VALUE METHOD
Steps
 Calculate free cash flows (same as in WACC method)
 Find NPV by discounting FCFs at the cost of capital for an allequity firm (different from WACC)
 Adjust for the PV of financing side effects
 Tax savings from interest
 Effects of subsidized financing
 Issue costs for new debt and equity
 Financial distress costs
32
APV EXAMPLE
Consider a project of the Pearson Company. The timing and size
of the incremental after-tax cash flows for an all-equity firm are:
–$1,000
$125
$250
$375
0
1
2
3
The unlevered cost of equity is R0 = 10%:
NPV10%
NPV10%
$500
4
$125
$250
$375
$500
 -$1,000 



2
3
(1.10) (1.10) (1.10) (1.10) 4
 -$56.50
The project would be rejected by an all-equity firm: NPV < 0.
33
APV EXAMPLE
Now, imagine that the firm finances the project with
$600 of debt at RB = 8%.
Pearson’s tax rate is 40%, so they have an interest
tax shield worth TCBRB = .40×$600×.08 =
$19.20 each year.
 The net present value of the project under leverage is:
APV = NPV + NPV debt tax shield
4
$19.20
APV  -$56.50  
t
(
1
.
08
)
t 1
APV  -$56.50  63.59  $7.09
 So, Pearson should accept the project with debt.
34
FLOW TO EQUITY APPROACH (ECF METHOD)
Focus on the cash flow to the equity holders
Discount at the cost of levered equity capital, RS.
Steps:
1. Calculate the levered (equityholder) cash flows (LCFs or ECFs)
2. Calculate RS.
3. Value the levered cash flows at RS.
LEVERED CASH FLOWS (LCF OR ECF)
•
Since the firm is using $600 of debt, the equity
holders only have to provide $400 of the initial
$1,000 investment.
CF0 = −$400
•
Each period, the equity holders must pay interest
expense. The after-tax cost of the interest is:
B×RB×(1 – TC) = $600×.08×(1 – .21) = $37.92
LEVERED CASH FLOWS
CF3 = $400 – 37.92
CF2 = $275 – 37.92
CF1 = $125 – 37.92
CF4 = $500 – 37.92 – 600
–$400
$87.08
$237.08
$362.08
–$137.92
0
1
2
3
4
DISCOUNT RATE: COST OF EQUITY RS
Can use Modigliani-Miller transformation
𝐵
𝑅𝑠 = 𝑅0 + 1 − 𝑇𝑐 𝑅0 − 𝑅𝐵
𝑆
This is needed if
• unlevered cost of capital 𝑅0 is known or
• capital structure is about to change
For a publicly traded firm
• 𝑅𝑠 can be just the expected return on the firm’s
stock estimated using, for example, CAPM.
• 𝑅0 may need to be calculated with this formula
DISCOUNT RATE: COST OF EQUITY RS
We can calculate the debt to equity ratio
PV =
$125
1.10
+
$275
(1.10)2
+
$400
(1.10)3
+
$500
(1.10)4
+
𝐵
𝑆
as follows:
$10.08
4
𝑡=1 (1.08)𝑡
PV = $1,017.06 + $33.39 = $1,050.45
B = $600 when V = $1,050.45 so S = $450.45.
$600
𝑅𝑆 = .10 +
1 − .21 .10 − .08 = 12.10%
$450.45
FCFE VALUATION
RS = 12.10%
–$400
$87.08
$237.08
$362.08
–$137.92
0
1
2
3
4
NPV = $36.04
FCFE SUMMARY
Value the equity of a firm based on the cash available for distribution to
shareholders
ECF = FCF - Interest expense (after taxes)
- preferred stock dividends
+ D Debt (& other non-equity) Financing
Note: net issuance of debt or preferred stock is added, and net repurchase is
subtracted.
𝐸𝐶𝐹𝑡+1
𝐸𝐶𝐹𝑡+𝑛
𝑇𝑉𝐸𝑡+𝑛
𝑃𝑡 =
+ ⋯+
+
1
𝑛
1 + 𝑅𝑆
1 + 𝑅𝑆
1 + 𝑅𝑆 𝑛
41
RESIDUAL INCOME VALUATION MODEL
Another valuation model for a firm’s equity that is favored by
accountants is the residual income valuation model.
Residual income = earnings – required return on invested capital
𝑅𝐼𝑡 = 𝑁𝐼𝑡 – 𝑅𝑠 ∗ 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑒𝑞𝑢𝑖𝑡𝑦 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 (𝐸𝑡−1 )
∞
𝑉0 = 𝐵0 +
𝑡=1
𝑅𝐼
1 + 𝑅𝑠
𝑡
B0 - current book value of equity
There are other ways to estimate 𝑅𝐼 in the literature
42
EQUIVALENCE OF RI AND CASH FLOWS TO
EQUITY MODELS
𝑅𝐼𝑡 = 𝑁𝐼𝑡 − 𝑅𝑆 𝐸𝑡−1
𝐸𝐶𝐹𝑡 = 𝐸𝐵𝐼𝑇 1 − 𝑇𝑐 − Δ𝑁𝑂𝑊𝐶𝑡 − 𝑁𝐶𝑆𝑡 − 𝐼𝑡 1 − 𝑇𝑐 + 𝐷𝑡 − 𝐷𝑡−1
∞
𝑅𝐼𝑡
𝑉𝐸 = 𝐸0 +
(1 + 𝑅𝑆 )𝑡
∞
= 𝐸0 +
𝑡=1
∞
= 𝐸0 +
∞
=
𝑡=1
𝑡=1
𝑡=1
𝑁𝐼𝑡 − 𝑅𝑆 𝐸𝑡−1
(1 + 𝑅𝑆 )𝑡
𝐸𝐵𝐼𝑇 1 − 𝑇𝑐 − 𝐼𝑡 1 − 𝑇𝑐 − Δ𝑁𝑂𝑊𝐶𝑡 − 𝑁𝐶𝑆𝑡 + 𝐷𝑡 − 𝐷𝑡−1 + 𝐸𝑡 − 𝐸𝑡−1 − 𝑅𝑆 𝐸𝑡−1
(1 + 𝑅𝑆 )𝑡
𝐸𝐶𝐹𝑡
1 + 𝑅𝑆
𝑡
43
EQUIVALENCE OF EVA AND DCF
𝐸𝑉𝐴𝑡 = 𝐸𝐵𝐼𝑇 1 − 𝑇𝑐 − 𝑊𝐴𝐶𝐶 ∗ 𝐸𝑡−1 + 𝐷𝑡−1
𝐹𝐶𝐹𝑡 = 𝐸𝐵𝐼𝑇 1 − 𝑇𝑐 − Δ𝑁𝑂𝑊𝐶𝑡 − 𝑁𝐶𝑆𝑡
Δ𝑁𝑂𝑊𝐶𝑡 + 𝑁𝐶𝑆𝑡 = 𝐷𝑡 + 𝐸𝑡 − 𝐷𝑡−1 − 𝐸𝑡−1
∞
𝐸𝑉𝐴𝑡
𝑉 = 𝐷0 + 𝐸0 +
1 + 𝑊𝐴𝐶𝐶 𝑡
𝑡=1
∞
= 𝐷0 + 𝐸0 +
𝑡=1
∞
= 𝐷0 + 𝐸0 +
𝑡=1
∞
= 𝐷0 + 𝐸0 +
∞
=
𝑡=1
𝑡=1
𝐸𝐵𝐼𝑇 1 − 𝑇𝑐 − 𝑊𝐴𝐶𝐶 ∗ 𝐸𝑡−1 + 𝐷𝑡−1
1 + 𝑊𝐴𝐶𝐶 𝑡
𝐸𝐵𝐼𝑇 1 − 𝑇𝑐 − Δ𝑁𝑂𝑊𝐶𝑡 − 𝑁𝐶𝑆𝑡 + 𝐸𝑡 + 𝐷𝑡 − (1 + 𝑊𝐴𝐶𝐶) 𝐸𝑡−1 + 𝐷𝑡−1
1 + 𝑊𝐴𝐶𝐶 𝑡
𝐸𝐵𝐼𝑇 1 − 𝑇𝑐 − Δ𝑁𝑂𝑊𝐶𝑡 − 𝑁𝐶𝑆𝑡
+
1 + 𝑊𝐴𝐶𝐶 𝑡
𝐹𝐶𝐹𝑡
1 + 𝑊𝐴𝐶𝐶
∞
𝑡=1
𝐸𝑡 + 𝐷𝑡
1 + 𝑊𝐴𝐶𝐶
∞
𝑡
−
𝑡=1
𝐸𝑡−1 + 𝐷𝑡−1
1 + 𝑊𝐴𝐶𝐶 𝑡−1
𝑡
44
EXPECTATIONS AND FINANCIAL FORECASTS
Need to manage expectations with:
 Analysts, and shareholders (external communications)
 Internal management team (internal communications)
Need to exceed expectations to have total shareholder
returns (TRS) meet or exceed cost of equity
TRS = Cost of equity
+ Unexpected market movements
+ Unexpected company performance
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CORPORATE GOVERNANCE AND FIRM VALUE
Controversy over roles of
 CEO shareholdings and compensation
 Board size and composition
 Corporate charter/bylaws
Examples of recent research:
 “Product Market Competition in a World of Cross-Ownership: Evidence
from Institutional Blockholdings” by Jie (Jack) He & Jiekun Huang, The
Review of Financial Studies, 2017, Volume 30, Issue 8, Pages 2674–
2718, https://doi.org/10.1093/rfs/hhx028.
 “Good and Bad CEOs” by Dirk Jenter, Egor Matveyev, and Lukas Roth.
Working paper. March 2016
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