Financial Valuation Principles and Market Regulations

Time Value of Money and Interest Formulas

Time Value of Money (TVM): Money received sooner is more valuable than money received later because of the returns you can earn by investing it.

Compound Interest Formulas

• Standard Compounding: FV = PV(1+k)ⁿ (Use if asked to compound for any period > 1 day).
• Continuous Compounding: FV = PV x e^{APR x t} (Use if compounding is continuous, < 1 day, where t = years).

In these formulas, k = APR/m and n = t x m. The Future Value Interest Factor is (1+k)ⁿ, while the Present Value factor is its inverse.

The Annual Percentage Rate (APR) is also known as the Quoted Rate or Nominal Interest Rate. It should not be used directly for TVM; it must be converted to an Effective Rate based on the compounding frequency (m) and the payment frequency (f).

If f = 1 and m ≤ 365:

If f = 1 and m ≥ 365:

If f ≠ 1:

For converting rates, if m = f, then k = APR/m.

Annuities and Perpetuities

• Annuities: Equal payments with equal time intervals, a constant discount/interest rate, and a finite number of payments.
• Annuity Due: Payments occur at the beginning of each period.
• Ordinary Annuity: Payments occur at the end of each period.
• Perpetuities: Similar to annuities but continue forever.

Use a financial calculator for the following:

• Ordinary Annuity:
• Annuity Due:
• Ordinary Perpetuity:
• Perpetuity Due:

Cash Flow Timing and Growth

Ordinary Cash Flow: The Present Value (PV) is at the beginning of the first period (one period before the first payment). The Future Value (FV) is at the end of the last period (at the same time as the last payment).

Due Cash Flow: The PV is at the beginning of the first period (same time as the first payment). The FV is at the end of the last period (one period after the last payment).

Growing Perpetuities: Each payment increases at a constant growth rate (g). (Note: k must be > g).

Moving Cash Flows and Loans

To move cash flows: Step 1: Find the PV at the start year of the cash flow. Step 2: Find the final PV by making the first PV the new FV.

Installment Loans: The interest portion decreases with each payment as the balance owed decreases. The principal portion increases with each payment as the interest portion decreases. In Canada, mortgages are typically compounded semi-annually.

Investment Appraisal and Equity Valuation

Monetary policy involves Tightening (increasing rates to slow the economy) or Loosening (decreasing rates to encourage borrowing and spending).

• Depletable Projects: These deplete as they generate cash flow (e.g., oil, land).
• Renewable Projects: Examples include solar power.

Net Present Value (NPV): A positive NPV indicates a good investment, while a negative NPV indicates a bad one.

Types of Shares

• Common Shares: Represent ownership in a corporation; holders are residual claimants and have voting rights.
• Preferred Shares: No true ownership; they have priority over common shares but usually no voting rights.

Dividend Discount Model (DDM): Estimates the fair price of a stock as the PV of all future dividends discounted at the required rate of return. The Constant Growth DDM is: (where D₁ is the future dividend and D₀ is the present dividend).

Fixed Income Securities and Bond Valuation

Bonds are debt instruments issued by corporations and governments. They pay the bondholder a fixed periodic interest payment (coupon payment) and a lump sum at maturity (face value, usually $1,000).

• Par Value: The amount paid at maturity (also called face, maturity, or stated value).
• Bond Value: Found by discounting all remaining coupon payments and the face value at the market discount rate.
• Yield to Maturity (YTM): The return an investor earns if they buy the bond at the current price.

Bond Price Formula: (Use calculator). Coupon Payment:

• If Coupon Rate = YTM: The bond trades at par (Price = Face Value).
• Interest Rate Risk: Interest rates and bond prices are inversely related.
• Zero-Coupon Bonds: Regular bonds without periodic coupon payments; interest is assumed to compound semi-annually.

Risk and Bond Quality

• Treasuries and GICs: Low risk and low yield. Governments issue them with taxation power, making them safe for capital preservation.
• US Treasury Bills (T-bills): Risk-free, widely traded short-term government securities.
• 100-Age Rule: A personal finance rule suggesting you hold (100 minus your age) in stocks, with the rest in bonds.
• Junk Bonds: High-risk bonds that trade at deep discounts due to high default risk; they can be riskier than stocks.

Investment Vehicles and Risk Analysis

• Mutual Funds: Investors pool money to invest collectively. They charge a Management Expense Ratio (MER), historically around 2% of Assets Under Management (AUM).
• Exchange-Traded Funds (ETFs): Similar to mutual funds but traded on stock exchanges like individual stocks.
• Hedge Funds: For accredited investors (at least $2M net worth); they include incentive fees.
• Real Estate Investment Trusts (REITs): Mutual funds for real estate.

Sharpe Ratio: Measures investment performance. (Higher is better; the numerator is the risk premium, the denominator is risk).

Registered Accounts and Risk Profiles

• RRSP: Contributions are based on earned income; unused space carries over. Can be converted to an RRIF.
• TFSA: Not tax-deductible; starts at age 18. Withdrawals are added back to contribution room the following year.
• RESP: Tax-free for a child's tuition; contributions are tax-deductible for parents.
• RDSP: Disability savings where the government matches a percentage of contributions.

Risk Attitudes: Risk Averse investors require a risk premium; Risk Neutral investors are indifferent to risk.

Modern Portfolio Theory and Statistics

Systematic Risk cannot be eliminated through diversification, whereas Unsystematic Risk can be reduced. Total risk is the sum of both.

• Certainty Equivalent (CEQ): The risk-free outcome yielding the same utility as a risky one.
• Expected Utility: Satisfaction expected from a risky event. To solve: 1. Find Expected Utility. 2. Find CEQ by setting the utility function equal to Expected Utility. 3. Subtract CEQ from current wealth.

Statistical Measures: Population Variance , Sample Variance , and Standard Deviation (√ of variance). Limitations of standard deviation include Symmetry (treats gains and losses equally), Stationarity (relies on historical data), and Discrete Distributions.

Value at Risk (VaR): Uses cumulative probabilities for decision-making. Beta Factors: Use regression to estimate risk. Factor Model Return: . CAPM: (The parenthesis represents the market risk premium; the formula finds the required return, k).

Market Dynamics and Economic Efficiency

Supply and Demand: Total Economic Surplus is the sum of Consumer Surplus (CS), Producer Surplus (PS), and government surplus/deficit. It is maximized at equilibrium. Deadweight Loss (DWL) = ΔCS + ΔPS + Government Cost - Government Revenue.

• Price Floor/Quota: Consumers are always worse off; producers may be better or worse off depending on elasticity.
• Price Ceiling (Cap): Producers are always worse off; consumers may be better or worse off.

Price Elasticity: Sensitivity of quantity demanded to changes in price. . The less elastic side pays a greater portion of a tax.

Market Efficiency Types

• Operational Efficiency: Minimizing waste.
• Informational Efficiency: Markets reflecting all public information in prices quickly.
• Allocational Efficiency: Optimal resource allocation to maximize welfare.

Financial History and Regulatory Frameworks

• Tulip Mania (1630): A bubble characterized by a rapid price increase followed by a sharp crash.
• Irrational Exuberance: Excessive optimism driven by greed and fear.
• 1929 Crash: Included an 11% drop on Black Thursday and 12.5% on Black Monday. Led by heavy margin buying (borrowing money to buy stocks).
• 1987 Crash: Driven by computerized high-frequency/algorithmic trading.
• Dot-com Bubble (2000): Surge in stock prices for internet companies.
• 2008 MBS Crisis: Involved Mortgage-Backed Securities and Credit Default Swaps (derivatives used to hedge or transfer risk).

Key Financial Regulations

• Securities Act of 1933: Improved informational efficiency and disclosure (Prospectus requirements).
• Securities Exchange Act of 1934: Regulated the secondary market and created the SEC.
• Glass-Steagall Act (1933): Separated investment and commercial banking; created the FDIC.
• Sarbanes-Oxley Act: Targeted public companies, protecting whistleblowers and limiting evidence destruction.
• Dodd-Frank (2010): Included the Volcker Rule to restrict proprietary trading by banks.
• Magnitsky Act: Allows Canada to seize assets of foreigners involved in human rights violations.
• Basel III Accords: Post-2008 standards including Non-Viability Contingent Capital (NVCC) and Contingent Convertible bonds (CoCos).
• Pareto Efficiency: A state where markets maximize benefits without wasting resources.