Residual claim: shareholders get only what is left-over after everyone has been paid. Discount rate: the rate at which present and future values are traded off. Future value of cash flow: C x (1+ r)^n. R= (FV/PV)^1/n - 1. Present value= C/(1+ r)^n. Compound interest: exponential growth in wealth, initial amount of money + the interest that has been added the previous years. Perpetuity, Growing Perpetuity, Annuity: multiple payments overtime, same amount, regular interest. NPV: the difference between and investment's value and its cost. Positive NPV=investment yes; NPV=0 project earns the required rate. . IRR measures the average return on the investment: accept project if IRR is greater than the discount rate(minimum return you want). Payback

Statistical Goals

• Describe: Explain what's happening in the data (e.g., mean, mode, average, minimum, variation).
• Explore: Understand how different variables relate to each other.
• Draw Inference: Test hypotheses or theories to make generalizations. Important: Correlation doesn't equal causation.
• Predict: Forecast future outcomes (e.g., weather networks).
• Draw Causal Inference: Determine cause-and-effect relationships, which requires experiments.

Variables in Statistics

Variable Types

1. Categorical (e.g., color, name, religion) vs. Numerical (Discrete: whole numbers OR Continuous: decimals, e.g., movie ranking).
2. • Nominal: Categories with no inherent order.
   • Ordinal: Categories with a meaningful order.
   • Interval: Ordered, equal intervals, but zero is arbitrary

Investment Analysis II: Key Cash Flow Components

Financial leverage is debt. "Unleveraged" Free Cash Flow (FCF) means we calculate FCF without regard to how the firm is financed. Ultimately, we are valuing the assets of the project. We achieve this by estimating how much cash is generated by the asset side of the balance sheet.

Capital Expenditure (CAPEX)

Capital Expenditure (CAPEX) is defined as the original cost of investment in property, plant, or equipment and other long-term assets.

Formula for CAPEX

NET PPE (current) - NET PPE (prior) + Depreciation

Depreciation and Asset Valuation

Depreciation: Depreciation charges are intended to represent the cost of wear and tear over the asset's life. The Straight-Line Depreciation method divides the asset’s... Continue reading "Capital Budgeting: Calculating Cash Flows and Valuation Metrics" »

Gross Income and Business Deductions

Gross Income: Includes revenue from sales, services, rents, dividends, interest, etc. Exclusions include life insurance proceeds and municipal bond interest. Expenses associated with the production of tax-exempt income are not deductible.

Deductions Above the Line (for AGI)

Deductions for Adjusted Gross Income (AGI) include business expenses, rental expenses, self-employed health insurance, and IRA contributions.

• Ordinary & Necessary Test: An expense must be customary and appropriate for the business.
• Meals Deduction: Can deduct 50% of meals if the expense is ordinary, necessary, and reasonable, the employee is present, the person eating is a current or potential client, and the meal is purchased separately

SAP S/4HANA Financial and Treasury Functions

The following table details various aspects, components, and features related to SAP S/4HANA, particularly focusing on Cash Management and Treasury functions.

Bond Valuation and Interest Rate Premiums

Calculating Bond Rates and Premiums

1. Long-Term Treasury Bond Rate Calculation

You read in The Wall Street Journal that 30-day T-bills are currently yielding 2%. Your brother-in-law, a broker at Kyoto Securities, has provided the following estimates of current interest rate premiums on a 1-year bond:

• Liquidity Premium: 3%
• Maturity Risk Premium (MRP): 1.5%
• Default Risk Premium (DRP): 1.2%

Based on these data, what is the long-term Treasury bond rate?

For a Treasury bond, the Liquidity Premium and Default Risk Premium are typically not applicable. The 30-day T-bill yield (2%) can be considered the short-term risk-free rate plus inflation premium (r* + IP). To find the long-term Treasury bond rate, we add the... Continue reading "Financial Calculations: Bond Valuation & Stock Risk Analysis" »

Matrices and Determinants

• Inverse Matrix: |A|⁻¹ = 1/|A|; A⁻¹ = (Adj A)ᵀ / |A|; A⁻¹ · A = I.
• Multiplication: Row by column (fila por columna).
• Determinants: |A₃,₃| = 4, det(2A) = 2³ · 4.
• Resolution (Cramer's Rule): x = |B c₂ c₃| / |A|, y = |c₁ B c₃| / |A|...

Geometry and Spatial Relationships

Areas and Volumes

• Area of a Parallelogram: |a × b|
• Area of a Triangle: |a × b| / 2
• Volume of a Parallelepiped: [u, v, w]
• Volume of a Tetrahedron: [u, v, w] / 6

Relative Positions

• Position of 3 Planes:
  • rg(A) = rg(A*) = 3: System Consistent Determined (1 point).
  • rg(A) = rg(A*) = 2: Line (recta).
  • rg(A) = rg(A*) = 1: Coincident.
  • rg(A) = 1, rg(A*) = 2: Parallel.
  • rg(A) = 2, rg(A*) = 3: Two cases: if two rows are proportional, two planes are parallel

Consider an European call option with strike equal to 10, T = 1, r = 0.05 and σ = 0.2. Using the following time-series:

1. For every time moment t = 0, 1/360, 2/360:

• Calculate the Black-Scholes price.
• Calculate the corresponding delta.
• Calculate the price of the corresponding replicating portfolio and its composition, if we consider a dynamic hedging.

2. Calculate a static hedging. What is the final value of the portfolio? Compare with the dynamic hedging results.

Solution

• At time 0, time to maturity is 1, and then
  • The Black-Scholes price is given by S0N(d1)−Ke−rT N(d2) = 10N(0.35)−10e−0.05N(0.15) = 1.0450
  • The Delta is given by N(d1) = N(0.35) = 0.6368
  • At time t = 0, the value of the replicating portfolio coincides with the Black-Scholes price