time value

Question 1

continuous PV

Answer 1

FV=PVe^(rT)

Question 2

fixed income

Answer 2

o stałym dochodzie

Question 3

fixed income/debt instruments

Answer 3

ZCB - zero cupon bonds: single CF, also T-bills

CB - Cupon bonds = notes - 2-10 y, bonds 10< y

fully amortizing bond (loans) payments are always intrest + principle

Question 4

zerocupon bond

Answer 4

1. we pay once at the begining and then we earn on the price raise at the end
2. calculate as normal pV/fv
3. when we dont have any FV we just type 100

Question 5

cupon bonds

Answer 5

every cashflow is like a zerocupon bond

1. count like a annuity
2. PMT - cupon/period; r=r/period; n=period
3. k=r FV=PV = parbond
   k>r FV>PV premium bond
   k<r FV<PV discount bond

Question 6

FRM - fixed rate mortgage

Answer 6

interest + principal

Question 7

loan

Answer 7

time value of money keys
PMT - rata;
r*Balance = interest
principal = rata-interest Balance=b0-pricipal

Question 8

growing dividend

Answer 8

D1/r-g (real estate) = Net operating income/cup rate

Question 9

variable dividend growth

Answer 9

2 stage model
1. liczymy PV od wzrostu ze znanego nam okresu n.
2. liczymy rente wieczystą od D z ostaniego okresu prognozy i robimy z niej PV
3. dodajemy 1 i 2

Question 10

implied return (fixed income)

Answer 10

(FV/PV)^(1/t) -1

cupon bond - we need to asure reinvestation so FV would be fv of every cupon + price

Question 11

implied return (equity)

Answer 11

required return or growth rate

1. przekształcenie wzoru dywidendy r = required return, g = growth rate

Question 12

P/E

Answer 12

divide the gordons model by earnings

PV/E = D1/E/r-g

valuable when we want to tell what is the price telling about the required return and growth

Question 13

D0/E

Answer 13

dividend payout ratio (zarząd wyznaczył 50% zn na dywidende)

Question 14

forward P/E

Answer 14

next 4q earnings

Question 15

trailing P/E

Answer 15

last 4q earnings

Question 16

issuance

Answer 16

emisja

Question 17

indefinely

Answer 17

na czas nieokreslony

Question 18

implied return

Answer 18

past return

Question 19

expected return

Answer 19

future return

Question 20

implied/expected

Answer 20

(1+implied)^n*(1+expected)^n - 1 = all return
expected return = ytm

Question 21

CF additivity

Answer 21

comparing 2 strategies
1. divide CF
2. make a present value of these
3. 0 = 1 and 2 the same value

Question 22

implied forward rate

Answer 22

F1,1 (the one-year forward rate starting in one year).

FV2 = PV0×(1+r2)2= PV0×(1 + r1)(1+F1,1)

F1,1 = (1 + r2)2/(1 + r1) – 1.

r1,r2 are implied rate

if not there will be a arbitrage opportunity

Question 23

Early redemption feature

Answer 23

wczesny wykup

Question 24

Par value

Answer 24

wartość nominalna