Corporate valuation
Topics
1. DCF valuation
2. Cost of capital
3. Forecasting and enterprise value
4. Real options I
5. Real options II
6. Multiples
,Lecture 1: DCF valuation
Introduction
Valuation
- Interchangeable terms: firm FCF, PFCF, and FCF
- Objective of a firm: create wealth by initiating and managing investments that generate
future cash flows that are worth more than the amount invested (NPV > 0)
o Net present value (NPV): value that is created and that goes to the shareholders
o Value created = output – input = -input + output
o Avoid decision errors based on incomplete analysis
o Evaluation of new investment opportunities can be done by valuation
- Valuation techniques can be applied to
o Projects (Ikea decides to open a new store)
o Enterprises (mergers and acquisitions)
o Financial assets (value of stocks and bonds etc): share price is the discounted value of
all the future cash flows that the company generates
➔ In this course we focus a lot of valuation techniques but also on strategy, valuation is
more than just crunching the numbers
- Many M&As that have failed, reasons
o Decisions made under incomplete information and uncertainty
o Wrong or inadequate valuation techniques
o Agency problems
▪ Manager favors pet project (a term that is used to describe a project that an
executive or manager is particularly focused on) and in the end manager is
decision maker
o Behavioral biases
▪ Managers go with their guts (lef)
➔ Key managerial task: design system to minimize chances of making bad investments
- Valuation is often complex
o Huge investment
o Political risk can be high
o Hard to establish the value due to uncertainties (have to go over different scenarios)
- Dealing with complexity: process and discipline
o Example of three phase investment evaluation process
▪ Phase I (financial): investment (idea) origination and analysis
- Conduct a strategic assessment
- Estimate the investment’s value (crunch the numbers)
- Prepare an investment evaluation report and recommendation to
management
▪ Phase II (strategic): managerial review and recommendation
4. Evaluate the investment’s strategic assumptions
5. Evaluate the methods and assumptions used to estimate NPV
6. Adjust for estimation error induces by bias and recommendation
▪ Phase III (decision): managerial decision and approval
7. Make decision
, 8. Seek financial managerial and possibly board approval
DCF valuation
DCF principle
- Discounted cash flow (DCF): most widely tool in valuation since there are good theoretical
reasons for using this method.
- Three steps
o Forecast the amount and timing of cash inflows (investments) and cash outflows
o Estimate appropriate discount rate (cost of capital)
o Discount the cashflows
- Can be applied to
o Projects: this lecture
o Enterprise valuation: later
DCF models
- Net present value
- Gordon growth model
o Useful variant of basis NPV formula
▪ NPV < 0 → share overpriced
▪ NPV = 0 → share correct priced
▪ NPV > 0 → share underpriced
o Assumptions made
▪ Constant discount rate for all periods
▪ Constant dividend growth (and never higher than GDP growth (2%-3%))
o Good method when the cash flows for projects or companies are stable
o Great tool to make back-of-the-envelope calculations (rough calculations)
o Caution: results are very sensitive to values of r and g
- Gordon growth model in combination with more solid approaches
o Incremental cash flows (not given in cash flow statement): difference between cash
flows that would arise if the project is taken up (cash in and outflows generated
when you start project) and the free cash flows that would arise if the project is
rejected (opportunity cost).
o Incremental cash flow = cash flows + side effect
▪ Cash flows generated by the project
▪ Side effect effects created by the project
• Cannibalization: the reduction of the sales of a company’s own
products as a consequence of its introduction of another similar
product. Example with location: sales in IKEA Breda will reduce when
IKEA opens a store in Tilburg.
• Opportunity cost: the loss of other alternatives when one alternative
is chosen.
▪ Ignore sunk cost and overhead cost
• Sunk cost: money that has already been spent and which cannot be
recovered anymore. Finance people (in contrast to accounting
people) will not use these cost because past costs are irrelevant for a
decision at this moment.
, • Allocated overhead cost: cost calculated over many products.
Finance people will not use these cost because other products are
irrelevant.
Two ways to value projects
- Use financial statements of pro forma statements (forecasted financial statements)
- Method 1 (related to APV method)
o Equity free cash flow (EFCF)
o Forecast FCF to equity holders
o Discount EFCF at cost of equity
o Get equity value
- Method 2 (most used)
o Project free cash flow (PFCF)
o Forecast FCF to all claimholders in the project
o Discount PFCF at WACC
o Get project value
- Value (project) = value (equity) – value (debt)
FCF calculation definitions
- Depreciation and amortization expense (DA)
o Does not present an actual cash payment, arises out of the matching principle of
accrual accounting, the actual expenditure of cash may have taken place many years
earlier when the assets were required
o Depreciation: of tangible assets (real estate)
o Amortization: of intangible assets
- Capital expenditures (CAPEX)
o Maintenance CAPEX: physically wear out of assets and need for replacement
o Growth CAPEX: investments in new PPE and acquisitions of businesses to achieve
growth in future cash flows
- Changes in net working capital (∆NWC)
o Change in net working capital (∆NWC): difference between current NWC and
previous year NWC
o Net working capital (NWC): the difference between a company's current assets, such
as cash, accounts receivable (customers' unpaid bills) and inventories of raw
materials and finished goods, and its current liabilities, such as accounts payable
Valuation methods used in practice
- Large companies: NPV and IRR
- Small companies: payback period (simpler approach)
- For us: NPV > IRR > payback
,Internal rate of return (IRR)
- Internal rate of return (IRR): the discount rate that makes NPV zero
o IRR > WACC/ discount rate/required rate of return/ hurdle rate → NPV > 0
o IRR = WACC/ discount rate/required rate of return/ hurdle rate → NPV = 0
o IRR < WACC/ discount rate/required rate of return/ hurdle rate → NPV < 0
- Caution: Descartes “rule of signs” which means that there may be multiple IRRs for one and
the same project in case there are sign changes in CF stream.
- Using IRR only possible and only gives same answer as NPV if there is only one cash outflow
and if that outflow precedes the inflows.
Payback
- Payback period: time it takes for the project to pay back its initial investment, number of
years to recover initial costs
o Actual payback period > target payback period → do not undertake
o Actual payback period = target payback period → (do not) undertake
o Actual payback period < target payback period → undertake
OR
o Value after target payback period number of cash flows > 0 → undertake
o Value after target payback period number of cash flows = 0 → (do not) undertake
o Value after target pay back period number of cash flows < 0 → do undertake
- Example: assume payback period of three years. -600 + 100 + 150 + 200 = -150 < 0
- Disadvantages
o Ignores time value of money (solution: discounted payback period)
o Ignores CFs after payback period
o Biased against long-term projects
o Requires an acceptance criteria (often three years, based on decision manager)
o Does not check whether NPV is positive (a project accepted based on the payback
criteria may not have a positive NPV)
- Use payback only if liquidity is only issue
Sensitivity analysis methods
- Scenario analysis
o Make different sets of assumptions and calculate NPV for each of them (worst case,
base case, best case)
- Breakeven sensitivity analysis
o Look at sensitivity of NPV regarding to different inputs
o Columns
- Variable: identify a set of variables which you think could critically influence NPV
- Expected value: expected value for each value driver used in base case NPV
- Critical value: critical of breakeven values for each value driver that results in a
zero NPV for the project
- Percentage change: the percentage change required in each value driver to
produce a zero NPV. The lower this percentage the less the value driver has to
change for a zero NPV, so the more sensitive to NPV. If you change the value a
little bit, the NPV will change very much. These are the key drivers
o Example
, o Limitations
▪ Probability to misleading results if two or more of the critical value drivers
are correlated with one another, since you consider only one value driver at
a time, holding all others equal to their expected values
▪ No formal way of incorporating interrelationships among the variables
▪ We do not know how the NPV will change if several will change at same time
▪ We do not have any idea about probabilities of exceeding or dropping below
the breakeven value drivers
→ simulation analysis will give more insight on most uncertain value drivers
- Simulation analysis
o Look at the stability of the NPVs
o Step 1: prepare the spreadsheet model and think about which are the most
risk/uncertain factor (bv cost, sales, etc)
o Step 2: characterize the value driers using a probability distribution
▪ Left corner graph below: uniform distribution
▪ Rule of thumb: if you talk about a rate of return or rate of growth you mostly
talk about a normal distribution. If you talk about price or sales you mostly
talk about a log normal distribution. Log normal distribution looks like
normal distribution but then only positive (only right corner above)
coefficients.
o Step 3: run the simulation and interpret the results
▪ Get average and standard deviation etc. of all the different NPVs
, o Example
▪ Outcome of the 10000 different NPVs
▪ On average we found a positive NPV of 144.25
▪ Most of the time the NPV is positive (dark bars) but also scenarios where
NPV is negative (light bars)
▪ This is how simulation works, we are not going to apply it because the
software @risk and crystal ball is too expensive.
o Summary
▪ Benefits arise from the process and from the actual output
▪ Simulation models require deep consideration about the underlying sources
of uncertainty that affect investment’s profits. Require explicit assumptions
▪ Caution: simulation as a mindless number crunching exercise can probably
do more harm than good. Complexity is no value per se. KISS principle: keep
it simple and straightforward.
Summary
- DCF is method of choice for most project valuations
- Important to identify and forecast incremental revenues and costs
- Use caution when using other methods like IRR and payback
o IRR works sometimes but not always, particularly not if you have a change in signs
- Uncertainty complicates the valuation process
- Three basis tools to assess the impact of uncertainty on a project and to understand the key
factors that drive a project’s success or failure
o Scenario analysis
o Breakeven sensitivity analysis
o Simulation analysis
Announcement 1 nov: regarding the simulation, you have to understand how simulation works, but
you should not be able to apply it as the software At Risk and Crystal Ball is expensive. I have added
an additional exercise to the recommended exercises of chapter 3. Exercise 1 of chapter 3 is the
additional exercise.
,Lecture 2: cost of capital
Planning
- Last lecture: derive cash flows (project or firm)
- This lecture: derive discount rates
o Discount rates: the rate of return required by the providers of funds. They need this
as a minimum, otherwise they will invest their money somewhere else. Opportunity
cost of capital: rate of return that investors forgo (=afzien) from not investing into
alternative investment opportunity with equivalent risk
WACC
- WACC: weighted average on the required rates of return
o For the firm’s interest-bearing debt (debtholders)
▪ Where the cost of debt is adjusted downward to reflect the interest tax
shield. Interest rates are tax deductible, so it is not a full cost for the firm.
o For the firm’s equity (equityholders)
- Steps of WACC
o Step 1: estimate the capital structure and determine the weights
▪ Equity and debt weight
- Use market weighs: market value of equity and debt
- Use only interest bearing debt: short term notes payable, current
portion of long-term debt, long-term debt
o Step 2: estimate the opportunity cost of each of the sources of financing and adjust
for the effects of taxes where appropriate
▪ Cost of equity
- Asset pricing models
o CAPM
o CAPM plus size premium
o Multifactor models (Fama-French)
- Inverting (=omkeren) the GGM
▪ Cost of debt
- Use average cost of debt of portfolio bonds with similar credit rating
and maturity
- Low default risk:
o Use YTM for investment grade bonds with low default risk
(bonds from BBB- to AAA)
- High default risk
o The higher the default risk, the greater the difference
between expected returns (probability * promised return)
and promised returns
o Assume probabilities of default and recovery rates and
calculate promised return directly
o Use large debt beta (around 0.4) in the CAPM for low-grade
bonds with higher default risk
o Step 3: compute a weighted average of the estimated after-tax costs of capital
sources used by the firm.
,Claimers
- Residual claimers are the ones that are coming last.
- Sequence of payment in case of a liquidation: state (taxes etc), bond holders, equity holders
- Equity holders get their value from dividend and the value increase in a stock
CAPM
- Idea: investors are risk avers so they want to be compensated for the risk that cannot be
diversified away (systematic risk), but not for diversifiable risk (idiosyncratic risk)
o Systematic risk: macroeconomic shocks (interest rates, energy prices, etc) → beta
o Idiosyncratic risk: firm-specific risk (lawsuits, product defect, CEO death)
- CAPM formula
o Risk-free rate
▪ use the rate of government bonds, treasury bonds (in principal, government
bonds are considered as risk free, but since the financial crisis you can realize
that government bonds are not completely risk free. So for some shaky
countries there might be a sort of default risk)
o Equity risk premium (ERP) or market risk premium (MRP)
▪ Spread of the market portfolio over the risk-free rate
▪ Compensation per unit of risk you assume
▪ Ranges
- Historically: 7.5%
- Recent studies: 3%-5% (lower due to risk sharing since globalization)
→ seems appropriate to use 5%
o Beta
▪ Measure of systematic risk
▪ Measure of the sensitivity of the stock return to the return in the market
▪ Expression of the covariance of a stocks return with the return on the
market, standard covariance of the return-volatility with the market. A beta
of 2 means that the stock return-volatility is twice higher than the market. If
the market has 10% return, then the stock is expected to be 20%.
▪ Obtained by running the regression of stock returns on market returns
▪ Caution: these estimates can be quite noisy (large standard errors)
▪ Ranges
- 0.4: low betas for companies with stable cash flows (electricity firm)
- 2.5: high betas for companies with more market exposure (tech firm)
▪ Problems
- Beta very different from 1, three options
o Very low beta thus very low risk
o Very high beta thus very high risk
o Bias in the beta
▪ Bias correction (Vasicek or Blum)
▪ Longer time period of data
▪ Impact of unusual market events like bubbles
▪ Use average of industry comparables as benchmark
- Betas work well for portfolios, but less good for individual stocks
- A lot of dispersion in the betas
▪ Problem when using beta of comparables: beta based on capital structure of
comparable which may be different → solution: take out the leverage effect
, Levering and unlevering betas
- Hamada assumptions
o Current debt will never be paid down → D = constant
o Debt is risk free → 𝛽𝐷 = 0
o Tax savings are certain → 𝛽𝑇𝑋𝑆 = 0
- Miles & Ezzell assumption
o Firm will retire debt if firm value goes down → D/V = constant (levering=constant)
and issue debt if firm value rises, so that the
optimal debt-to-firm value ratio
(leverage ratio) remains constant
o Debt is risk free → 𝛽𝐷 = 0
o Tax savings same risk as operating assets → 𝛽𝑇𝑋𝑆 = 𝛽𝑂𝐴
- Other
o Firm will retire debt if firm value goes down → D/V = constant (levering=constant)
and issue debt if firm value rises, so that the
optimal debt-to-firm value ratio
(leverage ratio) remains constant
o Debt beta is given → 𝛽𝐷 ≠ 0
o Tax saving same risk as operating assets → 𝛽𝑇𝑋𝑆 = 𝛽𝑂𝐴
➔ “Other not needed, because in the exam they probably will assume debt beta is zero
Definitions
- OA: operating assets
- E: equity
- D: debt
- TXS: tax shield
- D/V: debt-to-firm value ratio or leverage ratio
- 𝛽𝑂𝐴 /𝛽𝑈
o Beta of operating assets
o Asset beta
o Unlevered beta
o Operation risk
o Business risk
- 𝛽𝐸 /𝛽𝐿
o Beta of equity
o Equity beta
o Levered beta
o Operation risk (depend on 𝛽𝑂𝐴 in formula) + financial risk (depend on D/E in formula)
o Business risk (depend on 𝛽𝑂𝐴 in formula) + financial risk (depend on D/E in formula)
- 𝛽𝐷
o Beta of debt
o Debt beta
- 𝛽𝑇𝑋𝑆
o Beta of tax shield
o Tax shield beta
