Eksamenssett.no
Ressurser
Skolenytt
Hoderegning
FIE2
Formelark
Investering og finansiering
eksamenssett.no
Nåverdi og investeringsanalyse
•
N
P
V
=
−
C
0
+
∑
t
=
1
n
C
t
(
1
+
r
)
t
\displaystyle NPV = -C_0 + \sum_{t=1}^{n} \frac{C_t}{(1+r)^t}
NP
V
=
−
C
0
+
t
=
1
∑
n
(
1
+
r
)
t
C
t
•
Annuitet:
P
V
=
C
⋅
1
−
(
1
+
r
)
−
n
r
\displaystyle PV = C \cdot \frac{1-(1+r)^{-n}}{r}
P
V
=
C
⋅
r
1
−
(
1
+
r
)
−
n
•
Evig annuitet:
P
V
=
C
/
r
PV = C/r
P
V
=
C
/
r
•
Med vekst:
P
V
=
C
1
r
−
g
\displaystyle PV = \frac{C_1}{r-g}
P
V
=
r
−
g
C
1
(
r
>
g
r > g
r
>
g
)
•
EAA:
N
P
V
⋅
r
1
−
(
1
+
r
)
−
n
\displaystyle \frac{NPV \cdot r}{1-(1+r)^{-n}}
1
−
(
1
+
r
)
−
n
NP
V
⋅
r
•
PI:
1
+
N
P
V
/
I
1 + NPV/I
1
+
NP
V
/
I
•
Fisher:
(
1
+
r
n
o
m
)
=
(
1
+
r
r
e
a
l
)
(
1
+
π
)
(1+r_{nom}) = (1+r_{real})(1+\pi)
(
1
+
r
n
o
m
)
=
(
1
+
r
re
a
l
)
(
1
+
π
)
Porteføljeteori
•
E
[
r
p
]
=
∑
w
i
E
[
r
i
]
\displaystyle E[r_p] = \sum w_i E[r_i]
E
[
r
p
]
=
∑
w
i
E
[
r
i
]
•
σ
p
2
=
w
A
2
σ
A
2
+
w
B
2
σ
B
2
+
2
w
A
w
B
ρ
A
B
σ
A
σ
B
\sigma_p^2 = w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2w_Aw_B\rho_{AB}\sigma_A\sigma_B
σ
p
2
=
w
A
2
σ
A
2
+
w
B
2
σ
B
2
+
2
w
A
w
B
ρ
A
B
σ
A
σ
B
•
ρ
A
B
=
Cov
(
r
A
,
r
B
)
/
(
σ
A
σ
B
)
\rho_{AB} = \text{Cov}(r_A,r_B)/(\sigma_A\sigma_B)
ρ
A
B
=
Cov
(
r
A
,
r
B
)
/
(
σ
A
σ
B
)
•
Sharpe:
S
=
(
E
[
r
p
]
−
r
f
)
/
σ
p
S = (E[r_p]-r_f)/\sigma_p
S
=
(
E
[
r
p
]
−
r
f
)
/
σ
p
•
Treynor:
T
=
(
E
[
r
p
]
−
r
f
)
/
β
p
T = (E[r_p]-r_f)/\beta_p
T
=
(
E
[
r
p
]
−
r
f
)
/
β
p
•
w
A
M
V
P
=
σ
B
2
−
Cov
σ
A
2
+
σ
B
2
−
2
Cov
\displaystyle w_A^{MVP} = \frac{\sigma_B^2 - \text{Cov}}{\sigma_A^2+\sigma_B^2 - 2\text{Cov}}
w
A
M
V
P
=
σ
A
2
+
σ
B
2
−
2
Cov
σ
B
2
−
Cov
CAPM
•
E
[
r
i
]
=
r
f
+
β
i
(
E
[
r
m
]
−
r
f
)
E[r_i] = r_f + \beta_i(E[r_m]-r_f)
E
[
r
i
]
=
r
f
+
β
i
(
E
[
r
m
]
−
r
f
)
•
β
i
=
Cov
(
r
i
,
r
m
)
/
Var
(
r
m
)
\beta_i = \text{Cov}(r_i,r_m)/\text{Var}(r_m)
β
i
=
Cov
(
r
i
,
r
m
)
/
Var
(
r
m
)
•
α
=
r
p
−
[
r
f
+
β
p
(
r
m
−
r
f
)
]
\alpha = r_p - [r_f+\beta_p(r_m-r_f)]
α
=
r
p
−
[
r
f
+
β
p
(
r
m
−
r
f
)]
•
β
p
=
∑
w
i
β
i
\displaystyle \beta_p = \sum w_i\beta_i
β
p
=
∑
w
i
β
i
•
Hamada:
β
E
=
β
A
[
1
+
D
/
E
(
1
−
T
c
)
]
\beta_E = \beta_A[1+D/E(1-T_c)]
β
E
=
β
A
[
1
+
D
/
E
(
1
−
T
c
)]
Kapitalstruktur
•
MM I (uten skatt):
V
L
=
V
U
V_L = V_U
V
L
=
V
U
•
MM I (med skatt):
V
L
=
V
U
+
T
c
D
V_L = V_U + T_c D
V
L
=
V
U
+
T
c
D
•
MM II (uten skatt):
r
E
K
=
r
A
+
D
/
E
(
r
A
−
r
D
)
r_{EK} = r_A + D/E(r_A-r_D)
r
E
K
=
r
A
+
D
/
E
(
r
A
−
r
D
)
•
MM II (med skatt):
r
E
K
=
r
A
+
D
/
E
(
r
A
−
r
D
)
(
1
−
T
c
)
r_{EK} = r_A + D/E(r_A-r_D)(1-T_c)
r
E
K
=
r
A
+
D
/
E
(
r
A
−
r
D
)
(
1
−
T
c
)
•
W
A
C
C
=
E
V
r
E
K
+
D
V
r
D
(
1
−
T
c
)
\displaystyle WACC = \frac{E}{V}r_{EK} + \frac{D}{V}r_D(1-T_c)
W
A
CC
=
V
E
r
E
K
+
V
D
r
D
(
1
−
T
c
)
Opsjoner
•
Call:
C
T
=
max
(
S
T
−
K
,
0
)
C_T = \max(S_T-K, 0)
C
T
=
max
(
S
T
−
K
,
0
)
•
Put:
P
T
=
max
(
K
−
S
T
,
0
)
P_T = \max(K-S_T, 0)
P
T
=
max
(
K
−
S
T
,
0
)
•
Put-call-paritet:
C
+
K
/
(
1
+
r
)
T
=
P
+
S
0
C + K/(1+r)^T = P + S_0
C
+
K
/
(
1
+
r
)
T
=
P
+
S
0
•
Binomisk
p
p
p
:
(
1
+
r
−
d
)
/
(
u
−
d
)
(1+r-d)/(u-d)
(
1
+
r
−
d
)
/
(
u
−
d
)
•
Black-Scholes:
C
=
S
0
N
(
d
1
)
−
K
e
−
r
T
N
(
d
2
)
C = S_0 N(d_1) - Ke^{-rT}N(d_2)
C
=
S
0
N
(
d
1
)
−
K
e
−
r
T
N
(
d
2
)
Verdsettelse
•
F
C
F
F
=
E
B
I
T
(
1
−
T
c
)
+
A
v
s
k
r
.
−
C
A
P
E
X
−
Δ
N
W
C
FCFF = EBIT(1-T_c) + Avskr. - CAPEX - \Delta NWC
FCFF
=
EB
I
T
(
1
−
T
c
)
+
A
v
s
k
r
.
−
C
A
PEX
−
Δ
N
W
C
•
E
V
=
∑
F
C
F
F
t
(
1
+
W
A
C
C
)
t
+
T
V
(
1
+
W
A
C
C
)
n
\displaystyle EV = \sum \frac{FCFF_t}{(1+WACC)^t} + \frac{TV}{(1+WACC)^n}
E
V
=
∑
(
1
+
W
A
CC
)
t
FCF
F
t
+
(
1
+
W
A
CC
)
n
T
V
•
T
V
=
F
C
F
F
n
+
1
/
(
W
A
C
C
−
g
)
TV = FCFF_{n+1}/(WACC-g)
T
V
=
FCF
F
n
+
1
/
(
W
A
CC
−
g
)
•
Gordon:
P
0
=
D
1
/
(
r
−
g
)
P_0 = D_1/(r-g)
P
0
=
D
1
/
(
r
−
g
)
•
E
K
=
E
V
−
Netto gjeld
EK = EV - \text{Netto gjeld}
E
K
=
E
V
−
Netto gjeld
•
A
P
V
=
V
U
+
P
V
(
skatteskjold
)
APV = V_U + PV(\text{skatteskjold})
A
P
V
=
V
U
+
P
V
(
skatteskjold
)
Risikostyring
•
V
a
R
α
=
z
α
⋅
σ
⋅
V
VaR_{\alpha} = z_\alpha \cdot \sigma \cdot V
Va
R
α
=
z
α
⋅
σ
⋅
V
•
V
a
R
T
=
V
a
R
1
⋅
T
VaR_T = VaR_1 \cdot \sqrt{T}
Va
R
T
=
Va
R
1
⋅
T
•
Forward:
F
0
=
S
0
(
1
+
r
)
T
F_0 = S_0(1+r)^T
F
0
=
S
0
(
1
+
r
)
T
•
Durasjon:
Δ
P
/
P
≈
−
D
∗
⋅
Δ
y
\Delta P/P \approx -D^* \cdot \Delta y
Δ
P
/
P
≈
−
D
∗
⋅
Δ
y
•
Renteparitet:
F
0
=
S
0
⋅
(
1
+
r
d
)
/
(
1
+
r
f
)
F_0 = S_0 \cdot (1+r_d)/(1+r_f)
F
0
=
S
0
⋅
(
1
+
r
d
)
/
(
1
+
r
f
)