Finance is central to all business decisions, encapsulated in the saying: "It’s always about the money." This course includes essential distinctions and foundations for understanding the financial aspects of business.
Corporate Finance: Focuses on internal financial decision-making and value creation within a business.
Valuation: Looks at businesses from an external perspective, emphasizing the determination of business value based on future expectations.
The following six building blocks establish the framework for the subject:
Finance is fundamentally about future expectations rather than past performance. The perspective is always forward-looking.
Finance revolves around cash flows, not accounting earnings. Understanding cash flow is vital.
Types of Cash Flows:
Contractual Cash Flows: Predefined cash inflows or outflows, e.g., bonds.
Residual Cash Flows: Cash available to equity holders after expenses.
Contingent Cash Flows: Cash flows that depend on uncertain future events.
Risk is a central tenet in finance.
Understanding risk means recognizing its good and bad sides.
Importance of measuring risk and its implications on decision-making.
Risk perception may vary among stakeholders like shareholders and managers.
The principle of TVM asserts that a dollar today is worth more than a dollar in the future.
$$PV = \frac{FV}{(1 + r)^n}$$
where PV is present value, FV is future value, r is the interest rate, and n is the number of periods.
Understanding valuation is crucial:
Valuation involves assessing different types of cash flows.
Valuation Methods based on cash flows:
Contractually set cash flows: Discounted at risk-adjusted rates.
Residual cash flows: Discounted based on expected investor returns.
Contingent cash flows: Valued using option pricing methods.
Financial markets facilitate business operations. Understanding trading principles is essential.
Arbitrage: Theoretically, the opportunity to earn a risk-free profit.
Challenges in finding arbitrage opportunities due to:
Trading Costs: Implicit and explicit costs that hinder arbitrage.
Taxes: Tax considerations that affect investment decisions and cash flows.
These six building blocks lay the groundwork for more advanced topics in corporate finance and valuation. Mastery of these concepts is essential for understanding the complexities of finance in business.
This session focuses on the intersection of business and finance, laying the foundation for the concept of the corporate life cycle. This concept is crucial for understanding corporate finance and valuation.
In finance, the balance sheet differs from accounting. Acc accountants classify assets and liabilities more granularly; however, from a financial standpoint, we focus on two primary items on each side:
Assets in Place : Investments that have already been made by the company, such as factories or proprietary software.
Growth Assets : Potential future investments and projects that are expected to create additional value.
Debt : Money borrowed that requires payment.
Equity : Funds raised through ownership stakes in the business.
The value of assets in place is not dictated by the historical cost but by their potential to generate future cash flows.
Value of Assets in Place = Expected Future Cash Flows
The value attached to assets in place can deviate from their accounting values:
If the assets are no longer productive, their value may be significantly lower.
Conversely, if the assets have increased productivity, their value may be significantly higher.
Growth assets are based on future investments rather than their cost. Key considerations include:
The cost of capital associated with new investments, denoted as r.
The expected return on those investments.
Excess Return = Expected Return − Cost of Capital
If excess returns are positive, investments add value; if zero or negative, they do not contribute value.
Debt must be carefully classified by certain criteria:
A contractual commitment to make future payments.
Consequences for failing to meet these obligations (e.g., bankruptcy).
Tax implications; in many jurisdictions, interest payments are tax-deductible.
Equity represents a residual claim on the cash flows of the company. The formula can be expressed as:
Residual Cash Flow = Total Cash Flows − Debt Obligations
It is important to note that residual claims may not reach the equity holders directly due to managerial discretion over dividends.
The corporate life cycle progresses through distinct phases:
Startup : Valuation relies heavily on growth assets.
Young Company : Growth assets are still valued primarily.
Mature Company : Assets in place begin to dominate the balance sheet.
Decline : Value is increasingly driven by assets in place, with negative implications for growth assets.
Early stages: Fund through equity.
Growth stages: Maintain a balance with equity but may introduce debt as opportunities arise.
Mature phases: Increased leverage from debt due to stable cash flows and tax benefits.
During each phase of the life cycle, the ability to return cash flows changes:
Startups often exhibit negative cash flows.
Maturity allows more substantial cash returns to investors.
Understanding a business’s position within the corporate life cycle provides critical insight into its financial structure. The financial balance sheet is forward-looking, focusing on expected future performance rather than past expenditures.
This session will delve into the concept of risk, which fundamentally influences decision-making in finance. Historically, the nature of risk has evolved from physical risks to financial risks.
Early human existence revolved around physical risks.
Approximately 600 years ago, distinctions began to form between physical risks and financial risks.
Example: A wealthy individual investing in a ship for spice trade exemplifies this distinction.
If the ship returns safely, wealth is gained.
If lost (sunk or attacked by pirates), the sailors face mortality.
The definition of risk is crucial to understanding its implications in finance.
Frank Knight’s Distinction (1920s): Uncertainty vs. Risk:
Uncertainty: Lacks known probabilities.
Risk: Has known probabilities, allowing for calculation.
Example:
Individual 1 draws from an urn without knowing the ball distribution (uncertainty).
Individual 2 knows the distribution and calculates probabilities (risk).
Risk should be seen as both positive and negative.
If viewed solely as negative: Risk avoidance would be the main strategy, hindering business growth.
Successful businesses seek appropriate risks versus avoiding them entirely.
Humans exhibit risk-averse behavior; they prefer certainty over uncertainty in financial decisions.
Coin flipping game as an illustration:
Gain \$1 for tails, $0 for heads.
Expected value for each flip = $0.50.
Historical counterpart: Nicholas Bernoulli’s findings showed:
People were only willing to pay $2 on average for the chance to play the game, highlighting risk aversion.
1. Certainty Equivalence:
Defined as the guaranteed amount an individual would accept instead of taking a risky bet.
Example:
Expected Value = 0.5 × 1000 + 0.5 × 0 = $500
If an individual accepts $400, they are risk-averse.
2. Risk Aversion Coefficient (Utility Functions):
Risk aversion can also be quantified through utility theory, measuring satisfaction or happiness.
Four major avenues of study regarding risk aversion:
Experimental studies.
Surveys on real-world risk decisions.
Observations on asset pricing, reflecting risk attitude.
Behavior in gambling and betting contexts.
1. Gender Differences:
Men are generally less risk-averse than women for small bets, equalizing as stakes increase.
2. Age:
Younger individuals tend to exhibit less risk aversion.
3. Experience:
Increased expertise generally correlates with decreased risk aversion.
4. Cultural Comparisons:
Risk aversion appears relatively uniform across different races and cultures.
Behavioral finance highlights quirks in human risk-taking behavior:
Presentation of choices affects decisions. For example:
Preference for saving 200 people over a one-third probability of saving all.
Preference shifts in loss scenarios (loss aversion).
Myopic loss aversion refers to heightened risk aversion due to frequent feedback on investments.
External money (e.g., "house money") influences willingness to take risks.
After losing, individuals may increase risk in an attempt to break even.
Understanding risk aversion and human behavior regarding risks can significantly influence financial decision-making. Key takeaways include:
Risk is multifaceted — both positive and negative aspects.
Risk aversion is deeply embedded in human nature, though variations exist.
Behavioral finance provides insights into our risk-related behaviors, often deviating from classical economic theories.
In this session, we will build on the concept of risk by transitioning from risk aversion, discussed in the last session, to various measures of risk. The primary focus will be on understanding how risk is integrated into investment valuation.
If all investors were risk neutral, they would accept the risk-free rate as the expected return for all investments, regardless of their risk.
Given that investors are generally risk averse, they will prefer guaranteed cash flows over risky expected cash flows.
The challenge lies in measuring risk and incorporating these measures into our value assessments.
The mean variance framework is pivotal in finance:
The expected return (E[R]) on an investment is viewed as the desirable characteristic.
Risk, in this context, is quantified using the variance (σ2) of returns, which represents the degree of spread from the expected return:
σ2 = E[(R − E[R])2]
where R is the actual return.
Two fundamental assumptions must hold:
Returns are normally distributed, characterized by the mean and standard deviation.
Investors have a utility function that is risk-averse, which implies that they care about both expected returns and standard deviations.
Identifying the sources of risk is crucial:
Firm-Specific Risk (Project Risk): Individual projects may yield returns that differ from expected.
Industry Risk: Competition and industry-specific events can impact expected returns.
Systematic Risk: Macroeconomic factors (e.g., interest rate changes, exchange rate fluctuations) that affect entire sectors or the overall market.
Diversification helps in risk reduction by distributing investments across various assets.
Individual risks (firm-specific) average out when a diverse portfolio is held, leveraging the Law of Large Numbers.
However, macroeconomic or systematic risks remain present and cannot be diversified away.
Consider two stocks:
Stock 1: Expected Return = 1.5%, Standard Deviation = 10%
Stock 2: Expected Return = 4%, Standard Deviation = 15%
If the correlation (ρ) between these stocks is 0.2, and half of the portfolio is equally invested in both stocks:
Portfolio Variance = w12σ12 + w22σ22 + 2w1w2ρσ1σ2
where w1 and w2 are the weights in each stock.
Calculating the portfolio’s standard deviation yields:
σP = 9.81%
which is lower than either stock’s individual standard deviations.
In a market context, the marginal investor is essential for determining asset prices.
Marginal investors are typically diversified investors.
This indicates that they price assets based on the risk of the asset in relation to the overall market portfolio, not just individual stocks.
The CAPM states that:
E[Ri] = Rf + βi(E[Rm] − Rf)
where:
E[Ri] = Expected return on investment i
Rf = Risk-free rate
βi = Measure of the risk of investment i relative to the market
E[Rm] = Expected return of the market
Beta (β) reflects an asset’s covariance with the market:
$$\beta_i = \frac{\text{Cov}(R_i, R_m)}{\sigma^2_m}$$
where σm2 is the variance of the market returns.
Various models have evolved to account for limitations in the CAPM:
Multi-Factor Models: Allow multiple sources of market risk.
Proxy Models: Risk characteristics inferred from historical data, e.g., small-cap companies earning higher returns than large-cap.
Risk is critical to finance; however, not all risks warrant reward.
Investors must consider the perspective of marginal investors who dictate asset prices.
Effective risk measurement is essential for sound finance practices and helps guide investment decisions.
In this session, we will integrate the concepts of cash flows and discount rates into a single framework called the Time Value of Money (TVM). The fundamental premise of TVM is captured in the saying: "A dollar today is worth more than a dollar tomorrow."
There are three primary reasons why present cash flows are valued higher than future cash flows:
Consumption Preference: Humans prefer to consume today rather than wait for future consumption. To compensate for deferring consumption, lenders demand a real interest rate.
Inflation: Inflation decreases the purchasing power of money over time. Thus, a dollar today can buy more than a dollar in the future.
Uncertainty: A dollar received today is certain, whereas a dollar received in the future depends on factors beyond our control, leading to higher risk and less value placed on future cash flows.
As these factors increase, the time value of money will also increase.
The mechanics of TVM involve two operations:
Discounting: Bringing future cash flows back to the present.
Compounding: Taking present cash flows forward into the future.
The discount rate captures the combined effects of preference for current consumption, inflation, and uncertainty.
1. Cash flows must be evaluated at the same point in time to be aggregated. 2. Investment decisions should consider both the magnitude and timing of cash flows.
A timeline is useful for visualizing cash flow occurrences over time. An example could be a representation of receiving $100 at the end of each year for four years, also known as an annuity.
I will discuss five types of cash flows:
Simple Cash Flow: A single payment at a future date. For example, receiving $10 million in ten years.
Annuities: Equal cash flows received at regular intervals. E.g., $100 received every year for five years.
Growing Annuities: Cash flows that grow at a constant rate over time. E.g., $100 growing at 5% per year for 25 years.
Perpetuities: Constant cash flows that continue indefinitely. E.g., receiving $100 every year forever.
Growing Perpetuities: A cash flow that grows at a constant rate indefinitely. E.g., receiving $100 that grows at 2% every year forever.
The present value (PV) of different cash flows can be calculated using specific equations.
Simple Cash Flow:
$$PV = \frac{FV}{(1 + r)^n}$$
where FV is the future value, r is the discount rate, and n is the number of years.
Annuity:
$$PV = C \times \frac{1 - (1 + r)^{-n}}{r}$$
where C is the cash flow per period.
Growing Annuity:
$$PV = \frac{C \times (1 - (1 + g)^{n} / (1 + r)^{n})}{r - g}$$
where g is the growth rate.
Perpetuity:
$$PV = \frac{C}{r}$$
Growing Perpetuity:
$$PV = \frac{C \times (1 + g)}{r - g}$$
The frequency of compounding interest affects the overall returns. For instance: If an investment has an annual rate of 10% and is compounded:
Annually: it remains 10%.
Semi-annually: the effective return becomes approximately 10.125%.
Monthly: 10.471%.
Continuously: 10.517%.
Understanding these principles and calculations surrounding the time value of money can be immensely beneficial in both corporate finance and valuation. Knowing how to compute present value for various types of cash flows will serve as a vital skill as you navigate the complexities of finance.
In this session, we will build on the previous discussion on the time value of money by applying those principles to the valuation of contractual claims, particularly focusing on bonds.
When entering into a contract, a promisor agrees to pay cash flows over the life of the contract. These cash flows can be:
Fixed Cash Flows: For example, a bond that pays $50 million annually for 10 years.
Variable Cash Flows: Such as a floating rate loan where the payment is defined as 1% above inflation each year.
Default risk arises when a promisor fails to fulfill their payment obligation.
Risk-Free Claims: Only promises from governments are typically considered risk-free, because they can print money. However, not all government obligations are without risk (e.g., bonds from Argentina, Venezuela, or Greece).
To value a fixed-rate risk-free bond, we discount the known future cash flows (coupons and face value) at the risk-free rate.
Consider a U.S. government bond with:
Maturity: 10 years
Coupon Rate: 3% (Annual payment of $30 for a bond with a face value of $1000)
Current Market Interest Rate: 2%
The present value PV of the bond can be computed as:
$$PV = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n}$$
Where:
C = Annual coupon payment ($30)
F = Face value ($1000)
r = Discount rate (2%)
n = Number of years (10)
Thus, the bond value is computed as:
$$PV = \sum_{t=1}^{10} \frac{30}{(1 + 0.02)^t} + \frac{1000}{(1 + 0.02)^{10}} \approx 1089.83$$
Note: Bonds typically pay interest semi-annually; for accuracy, adjust for this in calculations.
The yield to maturity is the internal rate of return (IRR) that equates the present value of future cash flows with the bond price.
If the price of the bond drops to $1043.76, we calculate YTM as follows:
$$1043.76 = \sum_{t=1}^{10} \frac{30}{(1 + r)^t} + \frac{1000}{(1 + r)^{10}}$$
After solving, if r = 2.5%, the yield to maturity represents the new market interest rate.
The price sensitivity of bonds to interest rate changes is further characterized by:
Longer Maturity = Higher Sensitivity
Lower Coupon Rate = Higher Sensitivity
For instance, if interest rates rise from 2.5% to 3.5%, the bond price drops significantly compared to the effect of lowering rates.
To account for default risk, adjust the discount rate includes a default spread.
For example, if the risk-free rate is 2.5% and the default spread is 1.75%, the adjusted discount rate becomes:
Discount Rate = Risk-Free Rate + Default Spread = 2.5% + 1.75% = 4.25%
For a bond with a face value of $1000, 10-year maturity, and a coupon rate of 3%:
$$PV = \sum_{t=1}^{10} \frac{30}{(1 + 0.0425)^t} + \frac{1000}{(1 + 0.0425)^{10}} \approx 899.87$$
This adjustment reflects the additional risk from potential default.
Understanding how to value bonds involves knowing the principles of time value of money and recognizing the implications of default risk. Sensitivity to interest rates varies based on maturity and coupon rates, impacting the pricing of both risk-free and risky bonds.
In this session, we explore the time value concepts for valuing bonds and extend them to value equity or residual claims. As an equity investor, you are essentially a part-owner in a business, and your claims to cash flows come after all other obligations (e.g., debt payments) have been settled.
Residual Cash Flow: The cash flow left over after all contractual obligations have been met.
Equity Valuation Approaches:
Direct Approach: Focus on cash flows to equity, which are the cash flows available to equity investors after debt payments. These cash flows are discounted at the cost of equity.
Indirect Approach: Value the business as a whole, considering cash flows to all claim holders and discounting them at the cost of capital (weighted average of cost of equity and cost of debt).
In equity valuation, we focus on cash flows after reinvestment needs and debt payments.
Cash Flows to Equity: Cash flows remaining after all necessary payments, including interest, principal, taxes, and reinvestment expenses.
Free Cash Flow to Equity (FCFE): Represents the cash that could potentially be paid out to equity shareholders. Formally, the FCFE can be defined as:
FCFE = Net Income + Depreciation − Change in Working Capital − Capital Expenditures − Debt Repayments + New Debt
The discount rate used to evaluate the equity cash flows should reflect the risk associated with the investment. Commonly, this is assessed using the Cost of Equity.
The cost of equity is the return required by equity investors to compensate for the risk of their investment.
The cost of equity is dependent on the perceived risk. Higher risk equates to a higher cost of equity. The Capital Asset Pricing Model (CAPM) is one method used to estimate the cost of equity:
re = rf + β(rm − rf)
where:
re = cost of equity
rf = risk-free rate
β = measure of systemic risk (volatility relative to the market)
rm = expected market return
Consider a fictitious public company, "Cornette" with the following assumptions:
Last dividend (D0) = $4 per share.
Dividend growth rate (g) = 2% in perpetuity.
Cost of equity (re) = 8%.
To find the value of Cornette’s stock using the DDM:
$$V_0 = \frac{D_1}{r_e - g}$$
where D1 = D0 × (1 + g):
D1 = 4 × (1 + 0.02) = 4.08
Thus,
$$V_0 = \frac{4.08}{0.08 - 0.02} = \frac{4.08}{0.06} = 68$$
With Cornette’s stock trading at $70, this suggests the stock is slightly overvalued.
If we consider the Free Cash Flow Equity model, and assume potential dividends (PD) are $4.25:
$$V_0 = \frac{P_D \times (1 + g)}{r_e - g}$$
Substituting gives:
$$V_0 = \frac{4.25 \times (1 + 0.02)}{0.08 - 0.02} = \frac{4.335}{0.06} = 72.25$$
To value an entire business (firm), consider cash flows to both equity and debt holders. The cash flow to the firm (CFF) is discounted at the Weighted Average Cost of Capital (WACC):
$$WACC = \frac{E}{V} r_e + \frac{D}{V} r_d (1 - T)$$
Where:
E = market value of equity
D = market value of debt
V = E + D
rd = cost of debt
T = corporate tax rate
The business’s value can then be found, and subtracting the debt provides the equity value:
Vequity = Vfirm − D
Cash Flows: The actual monetary flows generated by the firm that can be distributed to stakeholders.
Growth Prospects: The expected future growth of those cash flows.
Risk Assessment: How risk is measured and incorporated into the discount rates used for valuation.
In summary, successful equity valuation hinges on consistent assumptions about cash flows, growth rates, and risk. Future classes will delve deeper into these valuation processes, enhancing your ability to evaluate residual claims in a business effectively.
An option is a financial derivative that provides its holder with the right, but not the obligation, to buy or sell a specified asset, known as the underlying asset, at a fixed price, known as the strike price, anytime before the expiration of the option.
Underlying Asset: The asset on which the option contract is based.
Strike Price (K): The predetermined price at which the holder can buy (call option) or sell (put option) the underlying asset.
A call option gives the holder the right to buy the underlying asset at the strike price (K).
It can be exercised at any time before expiration if it’s an American option.
It can only be exercised at expiration if it’s a European option.
The payoff for a call option can be represented as:
Payoff = max (ST − K, 0)
Where ST is the stock price at expiration.
A put option gives the holder the right to sell the underlying asset at the strike price (K).
The payoff for a put option can be represented as:
Payoff = max (K − ST, 0)
Payoff diagrams visually depict the potential profit or loss from options:
For a call option, if the stock price ST is less than the strike price K, the option is not exercised, resulting in a loss equal to the premium paid for the option.
For a put option, if the stock price ST is lower than the strike price K, the option is exercised, leading to a profit equal to the difference K − ST.
The value of an option is influenced by several factors:
Value of the Underlying Asset (S): As the asset price increases, call options become more valuable and put options become less valuable.
Variance of the Underlying Asset: Increased volatility increases the value of both call and put options due to the potential for greater cash flows.
Dividends: Dividends decrease the stock price when paid out, impacting the values of both call and put options.
Strike Price (K): A lower strike price increases the value of a call option and decreases the value of a put option.
Time to Expiration (T): More time until expiration increases the value of both call and put options.
Risk-Free Rate (r): Higher interest rates increase the value of call options while decreasing the value of put options.
Option pricing revolves around creating a replicating portfolio. This portfolio replicates the cash flows of the option using the underlying asset and riskless borrowing or lending.
In a binomial model, the stock price can move to one of two prices in successive time steps.
Consider a stock priced at S that can either rise to U or fall to D in successive time periods.
The value of a call option can be valued by working backwards from the potential payoffs at expiration through a binomial tree diagram.
The Black-Scholes formula calculates the price of European call and put options. The value of a call option is given by:
C = S0 ⋅ N(d1) − Ke − rt ⋅ N(d2)
where
$$d_1 = \frac{\ln(S_0/K) + (r + \sigma^2/2) t}{\sigma \sqrt{t}}$$
$$d_2 = d_1 - \sigma \sqrt{t}$$
Here, N(d) is the cumulative distribution function of the standard normal distribution, and the variables are:
S0: Current stock price
K: Strike price
r: Risk-free rate
t: Time to expiration
σ: Volatility of the underlying asset
To adjust the Black-Scholes model for dividends, the adjusted stock price becomes:
S0′ = S0e − yT
Where y is the dividend yield. This leads to adjustments in d1 and d2.
In financial modeling, understanding options and their pricing mechanisms is crucial. The Black-Scholes model provides a robust framework for valuing European options, and the binomial model offers a more flexible alternative.
Inflation is commonly described by two primary definitions:
Rising Price Levels: An increase in the general price levels of goods and services over time.
Decreasing Purchasing Power: The same amount of money buys fewer goods and services than before.
However, there are subtleties in understanding inflation that are critical, especially regarding its impact on investments and businesses.
General Inflation: Measures the overall decrease in purchasing power.
Relative Inflation: Measures changes in prices relative to one another.
For example, if gasoline prices increase by 25% while food prices decrease by 15%, the overall cost may not increase, indicating that a perceived inflationary effect may not exist.
Inflation can be considered a hidden tax, as it effectively reduces the real returns on investments and business profits without being labeled as a tax.
Inflation must be measured systematically. The following approaches are commonly used in the U.S.:
Consumer Price Index (CPI): Measures inflation based on goods and services purchased by consumers.
Producer Price Index (PPI): Measures the average changes in selling prices received by domestic producers for their output.
GDP Deflator: Reflects the broader measure of inflation for all goods and services produced in the country.
The selection of the ’basket of goods’ is crucial. If the basket does not accurately reflect consumer behavior or is misweighted, inflation measurement can be skewed. Factors include:
Changes in consumer spending patterns and weights assigned to different goods.
Potential biases from government agencies which may want to reflect favorable inflation rates.
These challenges result in different inflation rates among measures.
Three primary forces drive inflation:
Government Spending: Increased government deficits tend to lead to higher inflation, especially when economic growth is low.
Economic Growth: Generally, higher economic growth leads to increased inflationary pressure.
Monetary Policy: Excessive money printing can lead to significant inflation, particularly in extreme cases (hyperinflation).
In finance, it is essential to distinguish between nominal and real returns:
Nominal Returns (R): The percentage increase in the value of an investment without considering inflation.
Real Returns (r): Adjusted for inflation, reflecting the actual increase in purchasing power. The relationship is given by:
(1 + R) = (1 + r) ⋅ (1 + i)
where i is the inflation rate.
To convert nominal returns to real returns:
Start with the nominal return R:
$$r = \frac{1 + R}{1 + i} - 1$$
Using historical data from 1929 to 2019:
An investment of $100 in stocks would grow to $500,000 in nominal terms, but only $33,000 in real terms when inflation is taken into account.
Nominal Value = 100 ⟹ Final Nominal Value ≈ 500, 000
Real Value = 100 ⟹ Final Real Value ≈ 33, 000
Understanding inflation is crucial not only for investors but also for businesses. Key takeaways include:
Recognize the difference between nominal and real values.
Always account for inflation when considering cash flows or investment returns.
Inflation affects perceptions of financial returns significantly.
In the next session, we will discuss interest rates and their relationship with inflation.
Interest rates are pervasive in our financial interactions, as they dictate the cost of borrowing and the return on lending money. These rates can vary widely based on context, and understanding their origins and behaviors is crucial.
Interest rates can be categorized broadly into four types:
Market Set Rates: Determined by supply and demand in the financial markets. Examples include the rates on commercial paper and U.S. Treasury bonds (T-bonds).
Market Influencer Rates: Set by institutions but influenced by market conditions. For instance, mortgage rates and fixed deposit rates are affected by treasury rates.
Bank and Central Bank Rates: Rates established by financial institutions and central banks, often with a more rigid structure. These may still indirectly be affected by market determined rates.
Negotiated Rates: Rates established through negotiation, impacted by market rates but dependent on individual circumstances.
Nominal Interest Rate: The stated interest rate before adjustments for inflation.
Real Interest Rate: The rate of interest an investor receives after adjusting for inflation. It can be calculated using the Fisher Equation:
$$1 + r = \frac{1 + i}{1 + \pi}$$
where:
r = real interest rate
i = nominal interest rate
π = expected inflation rate
TIPS provide a safeguard against inflation. Instead of a fixed nominal rate, TIPS offer a real interest rate. The return adjusts based on inflation. For example, if you receive a guaranteed real interest rate of r = 1%:
If inflation = 2%, nominal return = 3%.
If inflation = 10%, nominal return = 11%.
Central banks do not set all interest rates. They primarily influence rates through the federal funds rate, the rate at which banks lend to each other. Changes in this rate send signals to the market. The influence of central banks is significant but limited to perception.
Since the 2008 financial crisis, central banks have employed quantitative easing, buying bonds to lower rates further. While this has had some effect, the fundamental drivers of interest rates remain inflation and real economic growth.
The yield curve represents the relationship between interest rates and the maturities of debt. It generally takes one of three forms:
Upward Sloping: Long-term rates are higher than short-term rates. This is the most common form.
Flat: Long-term and short-term rates are similar.
Downward Sloping (Inverted): Long-term rates are lower than short-term rates, often seen as a predictor of economic recessions.
An inverted yield curve historically has been associated with recessions.
When analyzing the slope of the yield curve against GDP growth, correlations can provide insight:
A strongly upward sloping yield curve is traditionally believed to correlate with significant economic growth.
However, empirical evidence suggests that the correlation between the steepness of the yield curve and GDP growth has weakened in recent years.
In summary, interest rates are influenced by various factors, including inflation and real growth. Central banks play a role in influencing but not setting these rates. Understanding these concepts is vital as we move forward in discussing interest rates in the context of financial valuation.
In this session, we examine the importance of currencies in financial and economic analyses. With globalization, analysts must navigate multiple currencies, valuing companies not just in domestic currencies but also in foreign ones.
Historically, financial analysis focused solely on domestic currencies. However, the emergence of globalization necessitates an understanding of multiple currencies.
Country Risk: Not the primary reason for currency differences.
Inflation Rates: The key driver of currency value differentials.
Higher Inflation ⇒ Higher Interest Rates
Conversely, lower inflation rates correlate with lower interest rates.
Government bond rates reflect both inflation expectations and country risk. The risk-free rate, adjusting for default risk, may be represented as:
rrf = rb − rd
where rrf is the risk-free rate, rb is the bond rate, and rd is the default risk premium.
When direct government bonds are not available:
RForeign = RDomestic + (IForeign − IDomestic)
where RForeign is the risk-free rate in the foreign currency, RDomestic is the risk-free rate in the domestic currency, IForeign is the foreign expected inflation rate, and IDomestic is the domestic expected inflation rate.
Given:
The approximation is:
REGP ≈ 2.27% + (9.7% − 1.5%) = 10.47%
For precision, use:
$$R_{\text{EGP, precise}} = \frac{(1 + R_{\text{USD}})}{(1 + I_{\text{USD}})} \times (1 + I_{\text{EGP}})$$
When conducting project analyses, all elements must be currency consistent:
Discount rates must match the currency of cash flows.
To maintain currency consistency:
Expert Forecasting: Often unreliable; macroeconomic predictions tend to perform worse than random guesses.
Market Forecasts: Using forward and futures markets when available.
Parity Conditions:
Interest Rate Parity (IRP): For two currencies, the forward exchange rate can be determined by the interest rates.
Purchasing Power Parity (PPP): Forecasting exchange rates using inflation differentials:
$$E(t) = E(0) \times \left( \frac{1 + I_{\text{domestic}}}{1 + I_{\text{foreign}}} \right)$$
Let:
Then,
$$E(1) = E(0) \times \left( \frac{1 + r_{USD}}{1 + r_{EUR}} \right)$$
Indicating a depreciation of the Euro as the USD interest rate is higher.
Given two currencies and their respective inflation rates,
$$\text{Expected Change} = \frac{I_{\text{Foreign}} - I_{\text{Domestic}}}{1 + I_{\text{Domestic}}}$$
This relationship implies that higher inflation in a currency leads to greater depreciation against a lower inflation currency.
The interplay between inflation, interest rates, and currency exchange rates is crucial in financial analysis. Keeping analyses consistent across currencies ensures that results remain valid irrespective of the currency used.