Equations and Derivations Flashcards
Yield to maturity on a simple loan?
PV = CF / (1+i)^n
where
PV = Present Value
CF = Future Cash Flow
i = annual interest rate (yield to maturity)
n = number of years
Yield to maturity on a Fixed-Payment loan?
LV = FP / (1 + i) + FP / (1 + i)^2 …. + FP / (1+ i)^n
LV = loan value
i = annual interest rate
n = number of years
FP = Future Payment
Yield to maturity and Bond price for a coupon Bond?
P = C / (1 + i) + C / (1 + i)^2 …. + C / (1+ i)^n + F / (1+i)^n
where
P = Price of coupon bond
C = yearly coupon payment
F = Face value of the bond
n = years to maturity date
Yield to Maturity on a Perpetuity?
Pc = C / ic
Pc = Price of the perpetuity (consol)
C = yearly payment
ic = yield to maturity of the perpetuity
Yield to maturity on a discount bond?
PV formula
then more generally
i = F - P / P
F = face value of discount bond
P = current price of the discount bond
Return on bond held from time t to time t+1?
R = C + Pt+1 - Pt / Pt
R = return from holding bond
C = coupon payment
Pt = price of the bond at time t
Pt+1 = price of the bond at time t + 1
rate of capital gain?
g = Pt+1 - Pt / Pt
Fisher equation?
i = r + pi^e
i = nominal interest rate
r = real interest rate
pi^e = expected rate of inflation
The One-Period Valuation Model?
P0 = D1 / (1+ke) + P1 / (1 + ke)
P0 = the current price of the stock
D1 = the dividend paid at the end of year 1
ke = the required return on investments in equity
P1 = the price at the end of year 1
generalised dividend model?
P0 = Σ Dt / (1 + ke)^t
t=1
where
Dt = dividend paid at end of time t
The Gordon Growth Model
P0 = D0 * (1 + g)^1 / (1 + ke)^1 …… same equation again to infinity
D0 = the most recent dividend paid
g = the expected constant growth rate in dividends
ke = the required return on an investment in equity
Simplified Gordon Growth Model
P0 = D1 / (ke - g)
