Grace Savadogo 72 IFM: Finance Formulas Review

Vocabulary and formula-based flashcards covering key financial concepts from Chapters 3, 4, 5, 6, 12, and 13.

Present Value (PV)

$PV = \frac{CF_N}{(1+i)^N}$.

Present Value of an Annuity

$PV_0 = C \times \frac{1 - (1 + r)^{-n}}{r}$.

Future Value

$FV_N = PV \times (1 + i)^N$.

Simple Loan YTM

$i = \left(\frac{FV}{PV}\right)^{\frac{1}{N}} - 1$.

Fixed-Payment Loan Value

$LV = \frac{FP}{i} \left(1 - \frac{1}{(1 + i)^N}\right)$ .

Fixed Payment Amount

$FP = \frac{LV \times i}{1 - \frac{1}{(1 + i)^N}}$.

Growing Annuity PV

$PV = \frac{CF}{r - g} \left[1 - \left(\frac{1 + g}{1 + r}\right)^n\right]$ .

Future Value of Annuity

$FV = \frac{C}{i} [(1 + i)^n - 1]$.

Coupon Bond Price

$P = \frac{C}{(1+i)} + \frac{C}{(1+i)^2} + \dots + \frac{C}{(1+i)^N} + \frac{F}{(1+i)^N}$.

Expected Cash flow under default risk

$E[CF] = p_{\text{good}}CF_{\text{good}} + p_{\text{default}}CF_{\text{default}}$.

Perpetuity Price & YTM

$P_c = \frac{C}{i} \implies i = \frac{C}{P_c}$.

Growing Perpetuity

$P = \frac{C}{i - g}$.

Current Yield (Ch. 3)

$CY = \frac{C}{P_c}$.

Discount Bond YTM

$i = \frac{F - P}{P}$.

Fisher Equation (approx.)

$i \approx i_r + \pi^e$.

Real Rate (approx.)

$i_r \approx i - \pi^e$.

Rate of Return (bond)

$R = \frac{C + P_{t+1} - P_t}{P_t}$.

Current Yield component

$\frac{C}{P_t}$.

Capital Gain component

$\frac{P_{t+1} - P_t}{P_t}$.

Duration (Macaulay)

$DUR = \frac{\sum_{t=1}^n \frac{t \times CF_t}{(1+i)^t}}{\sum_{t=1}^n \frac{CF_t}{(1+i)^t}}$.

% Price Change (Duration)

$\%\Delta P \approx -DUR \times \frac{\Delta i}{1+i}$.

Portfolio Duration

$DUR_p = w_1 \cdot DUR_1 + w_2 \cdot DUR_2 + \dots$.

Expected Return

$R_e = P_1(R_1) + P_2(R_2) + \dots + P_n(R_n)$.

Standard Deviation (Risk)

$\sigma = \sqrt{ P_1 (R_1 - R_e)^2 + P_2 (R_2 - R_e)^2 + \dots + P_n (R_n - R_e )^2 }$.

Portfolio Expected Return

$E[R_P] = w_A E[R_A] + w_B E[R_B]$.

Portfolio Variance

$\sigma_P^2 = w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2w_Aw_B\rho\sigma_A\sigma_B$.

Bond Interest Rate (1-yr discount)

$i = R_e = \frac{F - P}{P}$.

Expectations Theory (n-yr)

$i_{nt} = \frac{i_t + E[i_{t+1}] + \dots + E[i_{t+n-1}]}{n}$.

Forward Rate (Generalized)

$i_{t+n}^e = \frac{(1 + i_{(n+1)t})^{n+1}}{(1 + i_{nt})^n} - 1$.

Liquidity Premium Theory (Forward Rate)

$i_{t+n}^e = \frac{(1 + i_{(n+1)t})^{n+1}}{(1 + i_{nt})^n} - l_{(n+1)t} - 1$.

Forward rate fundamental relationship

$(1 + s_n)^n = (1 + s_{n-1})^{n-1} \times (1 + f_n)$.

Liquidity Premium Theory n-year bond formula

$i_{nt} = \frac{i_t + E[i_{t+1}] + \dots + E[i_{t+n-1}]}{n} + l_{nt}$.

Adjusted Forward Rate (LPT)

$f_n = \frac{(1 + s_n)^n}{(1 + s_{n-1})^{n-1}} - 1$.

Rate of Return (EMH)

$R = \frac{P_{t+1} - P_t + C}{P_t}$.

Expected Return (EMH)

$R^e = \frac{P_{t+1}^e - P_t + C}{P_t}$.

Current Yield (Bond) [Ch. 12]

$CY = \frac{\text{Annual Coupon}}{\text{Market Price}}$.

Semi-Annual Bond Price

$P = \frac{C/m}{i/m} \left[1 - \frac{1}{(1 + i/m)^{N \times m}}\right] + \frac{F}{(1 + i/m)^{N \times m}}$.

One-Period Stock Valuation

$P_0 = \frac{Div_1 + P_1}{1 + r_e}$.

Generalized Dividend Model

$P_0 = \sum_{t=1}^{\infty} \frac{Div_t}{(1 + r_e)^t}$.

Gordon Growth Model

$P_0 = \frac{Div_1}{r_e - g}$.