Key Formulas
Present value of a cash flow stream
-
𝑃𝑉# = %
'./
𝐶'
(1 + 𝑟 )'
Future value of a cash flow P0 at date t
𝐹𝑉 = 𝑃𝑉# × (1 + 𝑟)'
Present value of a perpetuity starting in date 1
𝑃𝑉# =
𝐶/
𝑟
Present value of an annuity starting in date 1
𝑃𝑉# =
𝐶/
1
× 21 −
4
(1 + 𝑟 )𝑟
Present value of a constantly growing perpetuity starting in date 1
𝑃𝑉# =
𝐶/
𝑟−𝑔
Present value of a growing annuity starting in date 1
𝑃𝑉# =
𝐶/
1+𝑔 × 61 − 7
8 9
𝑟−𝑔
1+𝑟
9
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Measures of risk for individual assets
Variance:
C
𝑉𝑎𝑟 (𝑅< ) = 𝜎<? = 𝐸 (𝑅< − 𝑅A)? = % 𝑝< × (𝑅< − 𝑅A )?
<./
Standard deviation (volatility):
𝑆𝐷 (𝑅< ) = 𝜎< = F𝜎<?
Covariance:
𝐶𝑜𝑣I𝑅< , 𝑅K L = 𝜎<K = 𝐸[(𝑅< − 𝑅A< ) × I𝑅K − 𝑅AK L]
Correlation:
𝐶𝑜𝑟𝑟I𝑅< , 𝑅K L = 𝜌<K =
𝜎<K
𝜎< × 𝜎K
Portfolio analysis
Expected return of a portfolio p consisting of N assets where wi is the weight of i-th
asset in the portfolio:
C
𝐸I𝑅P L = % 𝑤< × 𝐸(𝑅< )
<./
Variance of the portfolio p:
C
C
C
C
𝜎P? = % % 𝑤< 𝑤K 𝜎<K = % 𝑤<? 𝜎<? + % 𝑤< 𝑤K 𝜎<K
<./ K./
𝛽< =
<./
<./
K./
<RK
𝐶𝑜𝑣(𝑅< , 𝑅T )
𝑉𝑎𝑟(𝑅T )
Capital Asset Pricing Model
𝐸 (𝑅< ) = 𝑟U + 𝛽< × (𝐸 (𝑅T ) − 𝑟U )
Weighted average cost of capital
𝑅VWXX =
𝐸
𝐷
× 𝑅Y +
× 𝑅Z × (1 − 𝑇X )
𝐸+𝐷
𝐸+𝐷
10
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