Finance Exam Enclosure: Formula Sheet
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4Finance
Exam enclosure: Formula sheet
C
Calculating returns
1
P V =
r : return, P : price , D : dividend, all at time t, E[]: ex-
r
g
pectation.
T
C
1
1
P V =
= C
t
T
(1
r)
r
r(1 + r)
(P
P
) + D
P
P
D
t=1
t
t 1
t
t
t 1
t
r
=
=
+
t
P
P
P
r
mt
t 1
t 1
t 1
F V
= P V 1 +
t
m
P
P
t
t 1
rt
Capital gain
F V
= P V (e
)
t
P
t 1
r
mt
P V = F V
1 +
D
t
t
m
Dividend yield.
P
rt
t 1
P V = F V
(e
)
t
T
E[C
]
(E[ ˜ P
) + E[ ˜ D
]
P
]
t
t+1
t
t+1
N P V =
C
E[˜ r
] =
0
t+1
t
(1 + r)
P
t
t=1
E[ ˜ P
E[ ˜ D
]
P
]
T
t+1
t
t+1
E[C
]
=
+
t
N P V = 0 =
C
P
P
0
t
t
t
(1 + IRR)
t=1
N
Compounding
E[˜ r
] =
ω
E[˜ r
]
p
i
i
r : interest rate with discrete compounding, n: compound-
ing periods per year. r: interest rate with continuous com-
i=1
pounding, t: time to maturity.
T
1
Discrete compounding
Aritmetric avg. return =
r
t
T
r
nt
n
t=1
Future value = 1 +
n
1
T
1
Geometric avg. return =
(1 + r
)
1
t
Present value =
nt
r
1 +
t=1
n
Present values
Continous compounding
C cash flow at time t, d : discount factor, r : spot interest
rate, both for cash received at time t. P V present value,
rt
Future value = e
N P V net present value. r: (constant) interest rate, g (con-
stant) growth rate. IRR: Internal rate of return.
rt
Present value = e
Translating
C
t
N P V = P V
C
=
C
0
0
r
t
(1 + r
)
n
t
r = n ln 1 +
t=1
n
r
= n e
1
C
t
n
P V =
t
(1 + r)
Bond valuation
t=1
B
: bond price (at time 0). C : coupon at time t. F : face
0
value paid at time T (maturity). r: interest rate. P V ( )
present value.
P V =
d
C
t
t
t=1
T
C
C
E[C
]
E[F
]
t
T
P V =
=
B
=
+
0
t
t
T
(1 + r)
r
(1 + r)
(1 + r)
t=1
t=1
1
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