CFA Level 1 2007  Formula Sheet
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1
THE TIME VALUE OF MONEY
Interest rate
= Risk free rate + Inflation risk
premium + Default risk premium
FV
t
= Future Value (period
t
) = $X
x
(1+
r
)
t
PV
0
= Present Value (time 0) = FV
t
/ (1+r)
t
Stated Annual Rate =
p
p
SAR
r
n
=
*
;
,
r
Periodic rate and
p
n
Number of periods in a year
p
=
=
Effective Annual Rate
=
(1
)
1
n
p
EAR
r
p
=
+

[(1
)
1]
Future Value of an Annuity
T
PMT x
r
r
=
=
+

=
FVA
T
0
1
[1
]
(1
)
Present Value of an Annuity
PMT x
T
r
r
=

+
=
PVA
[(1
)
1]
(1
)
Future Value of Annuity Due
T
T
r
PMT x
r
r
=
+

=
=
+
FVAD
1
[1
]
(1
)
(1
)
Present Value of Annuity Due
T
T
r
PMT x
r
r
=

+
=
=
+
PVAD
Present Value of Perpetuity
=
PMT
r
Future Value of Uneven Cash Flows
=
(1
)
0
T
T
t
C
r
t
T
t

=
+
=
FV
Present Value of Uneven Cash Flows
=
0
1
(1
)
T
C
t
t
t
r
=
=
+
PV
DISCOUNTED CASH FLOW
APPLICATIONS
Net Present Value
=
0
(1
)
T
CF
t
NPV
t
t
r
=
=
+
For IRR
, solve:
0
0
(1
)
T
CF
t
NPV
t
t
IRR
=
=
=
+
If
IRR
k,
Accept
; If
IRR
< k,
Reject
.
where
k
= Cost of Capital
Dollar Weighted Return
is an IRR calculation.
Holding Period Return
=
HPR =
V
V
CF
END
END
BEG
V
BEG

+
TWR
=[(1+HPR
1
)(1+HPR
2
)..(1+HPR
n
)]
1/n
1
Then annualize the timeweighted return.
Bank Discount Yield
=
BDY
=
FaceValueMarket Price
360
100
FaceValue
x
x
T
±
² ³
´
µ
¶
·
¸
¹
º
»
¼
Money Market Yield = CD Equivalent Yield
= (360 x BDY) / (360 – t x BDY)
Bond Equivalent Yield
=
BEY
= HPY
x
360
T
STATISTICAL CONCEPTS AND
MARKET RETURNS
Gross Return
=
1
1
0
P
CF
R
P
+
=
Average gross return
=(R
1
x R
2
x .
.. x R
T
)
1/T
Arithmetic Mean
=
N
1
Y =
Y
i
i=1
n
Weighted Mean
=
1
N
W
i
i
i
Y
W Y
=
=
, where W
i
are
weights that sum to 1.
Geometric Mean
=
1
1
2
3
(
)
N
G
N
Y
Y xY xY x
xY
=
ggg
Harmonic Mean =
Inverse of arithmetic average
of inverse of observations.
z
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 Spring '08
 ORBAY
 Time Value Of Money, Corporate Finance, Future Value, Interest, Interest Rate, Net Present Value, Internal rate of return

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