Summary EC226 Term2 Time Series Formula Sheet (ALL CONTENTS) - First Grade

Notebook Paper to
Paperless



tec .
2
Chapter 2 PresentVale Lee . 3
Chapter 3 Perpetuities and Annuities

years
CF
in




E Investmenta mount
0 Cl
Rate of Return ro , To-1
Simple Perpetuity PV
=




Popu/CF
= =
Co (
in year - forever
=
W
rate
Future Value of Money Ct =
COL1+ Vit
( o
&
IF grows at
growth
PV =C
CF1CItyjt-t #
Growing Perpetuity
+=
+=
14 CHtr) r-g
applicate
Ct
It
E
t-year return rate =
Co
=
To -1 > cash
CF-- only when
OR + flow of the r>
-


(1+ Vt) (1 + r) g
Next year (yr1)
=


↳
one-year return The Gordan Growth Model (GGM) cFz
↓
: =
-
rate H Dividends next year
only applicable Stock Price Po
1
Today
=



for growing
.

r-9t
re = -1 growth rate of
the dividend
perpetuity
* Price / Value of 5th in Finance

E Cert
.




Lefets Profit next year
Present Value of
to the present value
PV Firm Valuation
Money
- -
.
2 Firm Value
-




P> growth rate of
= =
r
g
-




of what
thing
& evaluated
profit
by the
thing's future cFs
-
next year D


r Ac
.
-


FU %
of capital
>
Eltr)"
-

PV . Cost
3 +
g
=



↳
converted from share price Dividend He so
1 current
Discount Factor TITV) year P

Simple Annuities PV = = [ πnt] .




Net Present Valu NPV Co = + E 11 Ht
=
Ca
+


= Eg [1- ]
T Ct
E Growing PV
-
t
=
(1+V) Annuities .
t




Sal
- # of periods between
opportunity cost of Capital (Occ) r Special : Rate conversion : 1 + (-
Er(1 70
↳
=( + Us
t


rate for shorter periods
capital cost (
rate for longer
calso referred to as
periods -> 4 quarters
↳ without uncertainty rannual =
(1 + quarter) =
7
year .

, Lee .
5 Bond and bond Pricing
periodic interest paymentNotebook
Paper to

Bond - Coupon Payment = Paperless
-
Face Value payment = one-time
- payment at maturity
Lec
. 4 Capital Budgeting Rules Cl

Price of 0 couponbond NPU =
0 = Co -
+
L +IRR
FU
Rule 1 (Best rule) :
accept projects with the .
NPV NPU = 0 = -
P +
TFYTM IRR in CF terms =




Y TM in bond terms




Rult 2 Internal Rate of Return (IRR)
P =

TTM)- - > bond's ten .




: coupon payment
rate at which NPV =0 E
+ CONTMSE
I the NPV
Price of coupon bond
=
0 = -
Po +
Ct T
NPV = 0 =
Co + IRR) +RR) + ... HERRIT
-

simple annuity for all coupon payments

Accept projects with IRR the hurdle rate . Given Po =
(NM) ·



(1 -

IMT) +T
FU
(1+YTM)



Coupon Payment (CPN) FV
Internal of of the incremental cash Coupon To 5c
rate return flows rate x
=




↳ use when NPU & IRR give different suggestions
.


CI , CB1 t Cast * Use Capital Budgeting Rules to choose bonds (e
g. highest YTM/IRR)
-
=
+ .




NPVI = =
R +
RR +RM)3 +...


steps : /CA 01 ,
< /CB , 01 Bond Price Movement :


L - P* keep YTM Cst .
Hold the bond
maturity Th (in order to
>
Yes On No
-


: IRRA > : A 1 .
to :



/ -
Yes IRRI :
> Un NO : IRRB< Un 2 . Sell early V no
:
longer care about the YTM , as it involves all CPN + FU
-

Yes project B To
: : A Yes Projet B
: No : Neither U case about the bond's market P .
at selling
Equilibrium P condition
.
:
YIM =
OCC
Up risk-free rate set by CB

Rule 3 : The
Profitability Index (PI) for the next buyer Lunder risk neutrality (

PI =
① bond P & risk-free rate : inverse relationship : Po x t
ol
.




Invest if Pl > 1 ; Otherwise reject & long-term bonds =
more sensitive to A .




↳ therefore :
higher YTM to .
offset the risk
FU
Rule 4 Payback
: Time (PT) Yield to Maturity O = -P **M
)
↑ >
-
discount factor
vinitial
the time
period until cash inflows exceed cash outflows high YTM >
-
either high Fr (of price is
high
II

Invest if PT < cutofftime discount EV more or low price (if IV is low)
I a chose time period for CFic Oo