Finance I – Course Summary
Lecture 1 – Fixed Income
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Bond terminology:
o Parameters: 1) Face value, 2) Maturity, 3) Coupon (rate)
o Types: Government (e.g., T-Bills) , Corporate (callable, convertible), International
o Risk: Investment-grade (>= Baa3/BBB), High-yield/Junk (<=Ba1/BB+)
Spot rates:
1
o 𝑫𝑭𝒕 = (1−𝑟 )𝑡 where 𝑟𝑡 is the annual interest (spot) rate and 𝐷𝐹𝑡 is the discount factor
o
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𝑡
Term structure/yield curve = spot rates as function of maturity
▪ Upward sloping → periods of economic expansion
▪ Downward sloping → periods of economic slowdown/recession
Forward rates:
o Forward rate 𝒕 𝒇𝑻 from year t to year t+T: (1 + 𝑟𝑡 )𝑡 (1+𝑡 𝑓𝑇 )𝑇 = (1 + 𝑟𝑡+𝑇 )𝑡+𝑇
o Expectation Hypothesis: Forward rates = Expected spot rate
▪ Upward-sloping term structure → rates will go up
▪ Downward-sloping term structure → rates will go down
Bond pricing:
𝑐
100
o Formula: 𝑁𝑃𝑉𝐵𝑜𝑛𝑑 = ∑𝑇𝑡=1 (1+𝑟 )𝑡 + (1+𝑟 )𝑇 where 𝑐 is the coupon, 𝑇 is the time to
𝑡
o
o
𝑇
maturity, 𝑟𝑡 is the spot rate at year 𝑡, and the bond has a face value of 100
Key assumption: absence of arbitrage (holds empirically, otherwise one could
synthetically replicate any bond with a portfolio of zero-coupon bonds)
Yield to maturity: interest rate that makes the present value of a bond’s payments equal
to its price (also referred to as redemption yield, IRR of a bond)
Lecture 2 – Financial Cash Flows and Accounting Numbers
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Cash Flows vs Accounting Profits: for NPV we need to reverse accounting calculations
o Deduct tax
o Add depreciation
o Deduct CAPEX (at beginning)
Free Cash Flow calculation:
o Conceptually: 𝐹𝐶𝐹𝑡 = 𝐶𝑎𝑠ℎ 𝑖𝑛𝑓𝑙𝑜𝑤 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡 − 𝐶𝑎𝑠ℎ 𝑜𝑢𝑡𝑓𝑙𝑜𝑤 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡
o Formula: 𝐹𝐶𝐹𝑡 = 𝐸𝐵𝐼𝑇(1 − 𝑇) + 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 − 𝐶𝐴𝑃𝐸𝑋 − 𝑊𝐶 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 where T is
the tax rate and WC is working capital = inventories + acc. receivable – acc. payable
o Depreciation Tax Shield: 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 ∗ 𝑇
▪ 𝐸𝐵𝐼𝑇(1 − 𝑇) + 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑜𝑛 = (𝐸𝐵𝐼𝑇𝐷𝐴 − 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛)(1 − 𝑇) −
𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑜𝑛 = 𝐸𝐵𝐼𝑇𝐷𝐴 (1 − 𝑇) + 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 ∗ 𝑇
Lecture 3 – Risk and Return
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Returns and Variability:
o Risk (or volatility) = Standard Deviation in Returns
o Risk premium = Difference between mean of assets and zero-risk (T-Bill) returns
Portfolio theory:
o Expected return of a portfolio: 𝐸(𝑅𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 ) = ∑𝑁
𝑛=1 𝑥𝑛 (𝐸𝑛 ) where 𝑛 is the number
of assets in the portfolio and 𝑥𝑛 is the % weight of any given asset 𝑖 in the portfolio
o Variance of the portfolio return:
1
With a two-asset portfolio: 𝜎𝑅2𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 = 𝑥12 𝜎𝑅21 + 𝑥22 𝜎𝑅22 + 2𝑥1 𝑥2 𝜎𝑅1 ,𝑅2 where
𝜎𝑅1 𝑅2 = 𝜌𝑅1 ,𝑅2 𝜎𝑅1 𝜎𝑅2 and 𝑥1 + 𝑥2 = 1
2
▪ With a multi-asset portfolio: 𝜎𝑅2𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 = ∑𝑁
𝑛=1 𝑥𝑛 𝑉𝑎𝑟 (𝑅𝑛 ) +
2 ∑𝑛<𝑚 𝑥𝑛 𝑥𝑚 𝐶𝑜𝑣 (𝑅𝑛 , 𝑅𝑚 ) where ∑𝑁
𝑛=1 𝑥𝑛 = 1
Portfolio frontier (or efficient frontier): set of portfolios that maximise expected return
for a given level of standard deviation
▪ Expected return of the portfolio varies linearly with weights but the variance
of the portfolio does not vary linearly with weights (see mean-variance-analysis)
▪ Correlation coefficient 𝝆 is key parameter for diversification – if 𝜌 = +1 no
benefit from diversification, if 𝜌 = −1 maximum benefit from diversification
2
▪ Mean-variance optimization: solve for min 𝜎𝑃𝑜𝑟𝑓𝑜𝑙𝑖𝑜
while 𝐸(𝑅𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 ) = 𝐸
▪ Special cases:
• Adding a risk-free asset → frontier is straight line connecting the riskfree rate and the tangent portfolio
• Multi-asset portfolio → can compute the frontier via Excel Solver
▪
o
Lecture 4 – CAPM and the Cost of Capital
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Limits of diversification:
o Specific risk can be diversified (diversifiable), but not market risk (not diversifiable)
o As 𝑛 → ∞ where 𝑛 is the number of assets in the portfolio, 𝜎𝑅2𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 → 𝜎𝑅2𝑀𝑎𝑟𝑘𝑒𝑡
o Yet, not all companies are affected alike by market risk (e.g., food, luxury, water)
Capital Asset Pricing Model (CAPM):
o Market portfolio: Risk of an asset 𝑛 depends on the correlation (covariance) of the
asset’s returns with returns on the market portfolio (𝑅𝑀 , all assets traded in the market)
o
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Asset beta: 𝛽𝑛 =
𝐶𝑜𝑣 (𝑅𝑛 ,𝑅𝑀 )
𝑉𝑎𝑟 (𝑅𝑀 )
▪ Measures part of the total variation of the individual asset that is not diversifiable
▪ Measures risk / exposure to market risk
o CAPM core theorem: 𝐸 (𝑅𝑛 ) = 𝑅𝑓 + 𝛽𝑛 ∗ 𝐸(𝑅𝑀 − 𝑅𝑓 )
▪ Expected return on an asset should be proportional to undiversifiable market risk
▪ In a market where investors can diversify by holding many assets, risk premium
is proportional to beta
▪ Specific risk can be eliminated by holding diversified portfolios and therefore
investors do not require compensation for it
o CAPM key insights:
▪ One should use the beta as a measure of asset risk and not the standard deviation
▪ Beta measures the part of an asset’s variation that moves together with the market
▪ A very volatile stock can have a low beta if its correlation with the market is low
o Estimating beta:
▪ Obtain data on security returns, returns on the market and the risk-free rate
▪ Regress security returns less risk-free rate on market returns less risk-free rate
▪ Beta is the slope of the above regression
Cost of capital:
o Terminology:
▪ Enterprise Value: 𝐸𝑉 = 𝐷𝑒𝑏𝑡 + 𝐸𝑞𝑢𝑖𝑡𝑦
𝐷𝑒𝑏𝑡
𝐷
𝐸
▪ Leverage (Ratio): 𝐿𝑅 =
=
=1−
𝐸𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑐𝑒 𝑉𝑎𝑙𝑢𝑒
o
o
𝐷+𝐸
𝐸
𝐷+𝐸
𝐷
Weighted Average Cost of Capital: 𝑊𝐴𝐶𝐶 = 𝑟𝐸 ∗
+ 𝑟𝐷 ∗
𝐷+𝐸
𝐷+𝐸
▪ 𝑟𝐸 = 𝐸 (𝑅𝐸 ) = 𝑅𝑓 + 𝛽𝐸 ∗ 𝐸(𝑅𝑀 − 𝑅𝑓 )
▪ 𝑟𝐷 = 𝐸 (𝑅𝐷 ) = 𝑅𝑓 + 𝛽𝐷 ∗ 𝐸(𝑅𝑀 − 𝑅𝑓 )
Using betas:
2
▪
▪
▪
▪
𝜷𝑫 = 𝑏𝑒𝑡𝑎 𝑜𝑓 𝒅𝒆𝒃𝒕
𝜷𝑬 = 𝑏𝑒𝑡𝑎 𝑜𝑓 𝒆𝒒𝒖𝒊𝒕𝒚 (𝑜𝑟 𝒍𝒆𝒗𝒆𝒓𝒆𝒅 𝑏𝑒𝑡𝑎)
𝐷
𝐸
𝜷𝑨 = 𝛽𝐷 ∗
+ 𝛽𝐸 ∗
= 𝑏𝑒𝑡𝑎 𝑜𝑓 𝒂𝒔𝒔𝒆𝒕𝒔 (𝑜𝑟 𝒖𝒏𝒍𝒆𝒗𝒆𝒓𝒆𝒅 𝑏𝑒𝑡𝑎)
𝐷+𝐸
𝐷+𝐸
→ used for cost of capital in DCF (cash available to equity- and debt-holders)
Some special cases:
• If equity beta is not available (e.g., for a privately held firm), use the
asset beta of a comparable, consider leverage, and assume a debt beta
• When debt of a firm is publicly traded, use the returns on corporate bonds
to estimate the debt beta
• When debt of a firm is risk free, set the debt beta to zero
Lecture 5 – Company Valuation
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Valuation techniques:
o Absolute: DCF (Disc. Free Cash Flows, Disc. Equity Cash Flows, PV of Dividends)
o Relative: Multiples (P/E, EV/EBITDA, EV/FCF, Market-to-book, etc.)
o Mixed: Discount early cash flows, then apply multiple to terminal value
Discounted FCF:
o Project FCF for T years (until firm has stabilised)
o Take FCF in T+1 and assume constant growth rate g
o Discount FCF using WACC or 𝑅𝐴
𝑭𝑪𝑭𝑻+𝟏
o Sum NPV of cash flows until year T plus terminal value (=
)
𝑾𝑨𝑪𝑪−𝒈
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PV of Dividends:
o Value shares as securities with dividends (i.e., Share price = PV(Future Dividends))
o Not used practice (many stocks do not pay dividends) but good back-of-the-envelop
𝐷
o 𝑃0 = ∑𝑇𝑡=1 (1+𝑅𝑡 )𝑡 where 𝑃𝑡 is the stock price at time 𝑡 and 𝐷𝑡 is the dividend at time 𝑡
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Constant Growth Formula (Gordon Model):
o Suppose dividends grow at a constant rate g forever: 𝐷𝑡 = 𝐷𝑡−1 (1 + 𝑔) = 𝐷0 (1 + 𝑔)𝑡
𝐷
o Then we can use the formula for a Growing Perpetuity: 𝑃0 = 1
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Discounted Equity FCF:
o Value equity by calculating the NPV of the Equity FCF
o Use the cost of equity as the discount rate and add debt to get to enterprise value
Comparables:
o Idea: certain financial ratios/multiples must be comparable between firms in an industry
(especially those of similar size), because they face the same opportunities and challenges
o Advantages:
▪ Commonly used
▪ Easy to compute
▪ Intuitive interpretation
▪ Lots of historical data
o Disadvantages:
▪ Sensitive to differences in accounting choices, leverage, strategy
▪ Varies over time and with market conditions
▪ Not easy to compute for loss making firms
o Assumptions:
▪ Companies have similar risk and growth opportunities
▪ Earnings (or some other measure) are a good measure of sustainable cash flows
Choice of valuation technique:
o In practice, a mixture is used
▪ If cash flows can be predicted “reasonably” well, emphasise DCF
▪ If there are many similar firms being valued, emphasise comparables
𝐸
𝑅𝐸 −𝑔
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3
o
Common mixed techniques:
▪ Discount cash flows for the first 5/10 years and for the terminal value uses a
multiple instead of the perpetuity formula, avoiding TV calculation via g
▪ Compute various valuations and find an average / median
Lecture 7 – Market Efficiency
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Definitions:
o Fama (1970): a market is efficient if prices fully reflect all available information
o Jensen (1978): a market is efficient if it is impossible to make excess profits by trading on
information → takes into account transaction costs
Forms of market efficiency:
o Weak-form: security prices reflect all information contained in past prices
→ Technical analysis does not provide excess returns.
o Semi-strong-form: security prices reflect all publicly available information
→ Fundamental analysis does not provide excess returns.
o Strong-form: security prices reflect all information, whether public or private
→ Inside information does not provide excess returns
o Strong-form implies semi-strong-form implies weak-form efficiency
Key assumptions:
o If information is not incorporated, arbitrage is possible, but by trading information
becomes incorporated (only need a few “smart” investors)
o Private information can be inferred from trades, thus becoming incorporated
o Excess profits after adjusting for risk and cost
Recent challenges to market efficiency:
o Violations of Weak-Form:
▪ Recency bias → Overextrapolation (e.g., long-run reversal: “losers” overperform)
▪ Confirmation bias → Underreaction (e.g., short-run momentum: “winners”
overperform)
o Violations of Semi-Strong-Form:
▪ Numerous profitable trading strategies (e.g., shorting suppliers on bad news for
customer, “sin” stocks, value vs “glamour” stocks, small stocks)
▪ Earnings announcements drift (adjustments take time – e.g., 60 days on average)
▪ Corporate governance (e.g., provisions, jets, CEO incentives)
▪ CSR (e.g., Best Companies to Work for, American Customer Satisfaction Index)
o Support for Semi-Strong-Form:
▪ Active Equity Funds (few outperform the market)
▪ Adjustment to new info (happens instantaneously – e.g., Challenger Crash)
o Violations of Strong-Form:
▪ Insider trading (e.g., insiders can obtain superior returns by trading)
o Other challenges to “traditional” finance:
▪ Sentiment affects trading (e.g., football game outcomes)
Lecture 8 – Capital Structure
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Capital structure matters for firm value:
o Too high leverage → firm can go bankrupt
o Too low leverage → firm can pay high cost of capital
o Suboptimal capital structure → risks takeover or management change (e.g. hostile LBOs)
Leverage:
o Systematic differences in leverage
▪ Across industries
▪ Across countries
4
o
o
▪ Over time
Yet, leverage is irrelevant in perfect markets
▪ Intuition: total cashflows stay the same, so 𝑅𝐴 stays the same
▪ Common mistake: if 𝑟𝐸 > 𝑟𝐷 , leverage decreases the WACC and increases firm
value as future cash flows are less discounted
▪ But: equity beta is determined by the asset beta (business risk) and the debt beta
(financial risk), the more leverage the more sensitive/volatile equity returns get
▪ In other words: an increase in the debt/equity ratio results in an increase in the
expected return on equity, such that the WACC stays the same
▪ Why it matters: it tells us that capital structure choice should only be driven by
market imperfections (e.g., taxes, bankruptcy cost)
The effect of corporate taxes:
▪ Tax advantage of debt: interest payments are tax-deductible
▪ Adjusted present value: value of the levered firm is equal to that of the
unlevered firm plus the PV of the tax shields on the debt
▪ Tax shield = 𝑡𝑐 𝐷𝐿 where 𝑡𝑐 is the tax rate and 𝐷𝐿 is the value of debt
▪ Debt fixed vs rebalanced: if the value of debt is fixed, the tax shield is safe and
we can discount at 𝑟𝐷 ; if the value of debt is dynamically rebalanced the tax
shield is risky and discounted at 𝑟𝐴
▪ Discount rates in different scenarios:
▪
▪
o
Limit from effective vs. statutory tax rates: tax losses can only be carried
forward a limited amount of time
The effect of bankruptcy costs:
▪
▪
-
Direct cost: fees for administrators (lawyers, accountants, consultants etc.) and
difficulty in recovering collateral
▪ Indirect cost: assets fetch less in fire sale, intangible assets worth significantly
less in bankruptcy, loss of employees/customers/suppliers
o Trade-off theory of capital structure: weigh btw. tax advantage and bankruptcy cost
Key takeaways:
5
Lecture 9 – Mergers and Acquisitions
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Definitions:
o Merger (= merger of equals): when two firms join together and form a single firm
o Acquisition (or takeover): when an acquirer or bidder buys a target, which then becomes
a subsidiary of the acquirer
o Buyout: when a public firm is bought and then taken private
o Horizontal merger: between firms in the same industry and the same stage of the
production process
o Vertical merger: between firms in the same industry (or, more broadly, value chain) but
different stages of the production process
o Conglomerate merger: between firms in different industries
Types of mergers:
o Mergers that create value (i.e., grow the pie)
o Mergers that redistribute value (i.e., split the pie differently)
o Mergers that destroy value (i.e., shrink the pie)
Mergers that create value:
o Operational synergies → > contracts if high relationship specificity (hold-up problem)
▪ Revenue synergies (Economies of scope, combining complementary assets)
▪ Cost synergies (Economies of scale, consolidation of excess capacity)
o Financial synergies → Create internal capital markets
o Disciplinary → get rid of underperforming target management
Mergers that redistribute:
o Tax inversion or unused tax shields: redistribute from government
o Market power: redistribute from customers and suppliers
o Market inefficiency: redistribute from target shareholders
Mergers that destroy value:
o Size: empire building by management
o Behavioural: overconfidence/hubris, escalation of commitment
o Surplus funds: firm has more cash than investment opportunities
o Diversification: conglomerates avoid idiosyncratic risks
o EPS accretion (vs dilution): EPS increase if 𝑃/𝐸𝐴 > 𝑃/𝐸𝑇 (stock financed), 𝑃/𝐸𝐷 =
1
1
> 𝑃/𝐸𝑇 (debt financed), 𝑃/𝐸𝐷 =
> 𝑃/𝐸𝑇 (cash financed)
𝑟𝐷
-
-
-
-
𝑟𝐷
Economic gains from mergers:
o Δ𝑉𝐴𝑇 = 𝑉𝐴𝑇 − (𝑉𝐴 + 𝑉𝑇 ) where 𝑉𝐴 and 𝑉𝑇 are the equity values of the companies
o Δ𝑉𝐴𝑇 > 0 if there are economic gains regardless of how the merger is financed
o Acquisition premium = difference btw. price paid for the target and standalone value
→ acquirer should only proceed if premium < value created (and it can capture)
o Acquirer gain = 𝑉𝐴𝑇 − 𝑉𝐴 − 𝑃, Target gain = 𝑃 − 𝑉𝑇
o 𝑃 = 𝑥𝑉𝐴𝑇 in stock financed deals
Empirical evidence on merger value creation:
o Targets gains significantly
▪ Gain more in cash- vs stock-financed deals (risk of merger value creation)
▪ Get most of the value because i) auctions and ii) bad mergers
o Acquirers gains close to zero
Merger structures:
o Friendly: Deal with management
o (Often) Hostile: Deal with target shareholders (tender offer)
Takeover resistance:
o Objectives: Increase price (creates shareholder value), Avoid takeover (may not)
o Methods pre-offer: Staggered board, Supermajority, Poison pills
o Methods post-offer: Litigation, Public relations, White knight, Asset restructuring,
Implementing bidder recommendations
6