formulas practical Flashcards
money supply
M = C + D
Currency deposit ratio
c = C / D
excess reserve ration
e = ER / D
Money multiplier
m = (1 + c ) / (rr + e + c)
rr
required reserve
simple deposit multiplier
D = ( 1 / rr ) x R
money base
MB = C + R
effect of money multiplier
M = m x MB
future value of a cash flow
FVn = Co ( 1+ r )^n
present value of a cash flow
PVo = Cn / (1 + r )^n
PV perptuity
= C / r
C= size of periodic payment r = intrest rate
PV annuity
= C/r x (1 - ( 1 / ( 1 + r)^n )))
FV annuity
= C / r x ( (1 + r)^n -1 )
coupon payment
CPN = (coupon rate x Face Value) / number of coupons per year
stock bonus
= number of shares x price per share
price of a security = PV all future payments
-> price o bond when it was used
PV = (C / r) x (1 - (1 / (1 + r)^n) ) + F / (1 + r)^n
price of a security = PV all future payments
-> price bond immidiately before it makes its first coupon payment
PV = PMT + (C / r) x (1 - (1 / (1 + r)^n) ) + F / (1 + r)^n
nominal intrest rate
= real intrest rate + inflation rate
expected return
E (R) = Pr x R
yield to maturity of an n-year zero-coupon bond
YTMn = (FVn / P )^(1/n) - 1
forward intrest rate for year n (*)
fn= ( (1 + YTMn)^n / (1 + YTMn-1 )^(n-1) ) -1
series of one-years interst rate over the next years
on the yield curve
int = ( it + it+1^e + it+2^e + … +(it+(n-1)) ^e ) / n
dividend discount model (DDM)
Po = (DIV + P1 ) / ( 1 + rE)
equity cost of capital
rE = DIV1 /Po + (P1 - Po) / Po
= divident yield + capital gain rate
effertice periodic rate
= ( 1 + annual rate)^(1/n periods) - 1
constant dividend growth model
Po = DIV1 / (rE - g)
-> rE = Div1/Po + g = divident yield + g
duration analysis
procentage change in market value of security =
- (procentage point change in intrest rate) x duration in years
net worth
= total asset - total liability
gap analysis
change in bank profit =
(rate sensitive asset - rate sensitive liability) x change in intrest rate
leverage ratio
= bank capital / total assets
-> should exceed 5%
Risk weighted capital ratio
= bank capital / risk weighted assed
to calculate the “interest on interest”
FV= ( PV ( 1 + i )^n ) - ( PV ( 1 + n i ) )
cash flow immidiately before payment
PV = PV perpetuity + Co
