IBBC CAPITAL ACADEMY / REFERENCE
Keep the essentials close.
Core formulas, definitions and assumptions. Read the lesson before using a shortcut.
Time value of money
FV = PV × (1+r)^n; PV = FV ÷ (1+r)^n
r: effective rate per period; n: matching periods. Single cash flow, fixed rate.
Worked example and practice →Cash flows & annuities
PV = A[1−(1+r)^−n]/r; FV = A[(1+r)^n−1]/r
Ordinary annuity; A: equal payment. At r=0 use A×n. For annuity due, multiply by (1+r) at the same valuation dates.
Worked example and practice →Percentages, rates & purchasing power
Real return = (1+R)/(1+π)−1
R: nominal return; π: inflation, same period. Total multi-period return = product of (1+Rₜ), minus 1.
Worked example and practice →Read financial statements
CFO ≈ NI + depreciation − Δreceivables − Δinventory + Δpayables
Simplified indirect bridge. Positive Δ means an increase; other cash-flow adjustments are excluded.
Worked example and practice →Business ratios & interpretation
Margin = NI/revenue; turnover = revenue/average assets; ROA = NI/average assets
Average assets = (opening+closing)/2. Current ratio = current assets/current liabilities. Definitions must match.
Worked example and practice →Statistics, probability & uncertainty
E[R] = ΣpᵢRᵢ; σ² = Σpᵢ(Rᵢ−E[R])²
Complete scenario model: probabilities nonnegative and sum to 1. Standard deviation σ = square root of variance.
Worked example and practice →Bonds, yields & rate risk
P = Σ C/(1+y)^t + F/(1+y)^n
Annual coupon bond on a coupon date. C: annual coupon; F: face; y: annual yield; n: remaining whole years.
Worked example and practice →Equity & valuation fundamentals
P₀ = D₁/(r−g), with r > g
D₁: next dividend; r: required equity return; g: stable perpetual growth. Sensitivity is high when r−g is small.
Worked example and practice →Portfolios, diversification & risk
E[Rp] = wE[RA]+(1−w)E[RB]; σp² = w²σA²+(1−w)²σB²+2w(1−w)σAσBρ
Two unlevered assets with matching return periods. ρ: correlation between −1 and +1; volatility does not measure every risk.
Worked example and practice →Economics & market context
Real GDP growth = (1+gN)/(1+πD)−1
gN: nominal GDP growth; πD: GDP deflator growth, same period. Do not substitute an unrelated price index silently.
Worked example and practice →Instruments, leverage & payoff
Long forward: Sₜ−K; long call: max(Sₜ−K,0); long put: max(K−Sₜ,0)
Terminal payoff per unit. Simplified long-option profit subtracts premium; timing, fees and taxes are excluded.
Worked example and practice →Ethics, evidence & a research case
Question → Evidence → Assumptions → Calculation → Risks / gaps → Conditional conclusion
A research structure, not a numerical verification score. Disclose conflicts and obtain appropriate review.
Worked example and practice →IBBC Capital Finance Foundations · Original content drafted with AI assistance. IBBC Capital is responsible for editorial review and content. General education, not an official CFA Institute curriculum or credential.