FIN 320 Standard Formula Sheet
TVM Formulas
𝐹𝑉# = 𝐶 × (1 + 𝑟)#
𝐶
𝑃𝑉- =
(1 + 𝑟)#
𝐶.
𝐶/
𝐶1
𝑃𝑉 = 𝐶- +
+
+ ⋯+
/
(1 + 𝑟) (1 + 𝑟)
(1 + 𝑟)1
𝐶
𝑃𝑉(𝐶 𝑖𝑛 𝑃𝑒𝑟𝑝𝑒𝑡𝑢𝑖𝑡𝑦) =
𝑟
1
1
𝑃𝑉(𝐴𝑛𝑛𝑢𝑖𝑡𝑦) = 𝐶 × × ;1 −
=
(1 + 𝑟)1
𝑟
1
𝐹𝑉(𝐴𝑛𝑛𝑢𝑖𝑡𝑦) = 𝐶 × × ((1 + 𝑟)1 − 1)
𝑟
𝐶
𝑃𝑉(𝐺𝑟𝑜𝑤𝑖𝑛𝑔 𝑃𝑒𝑟𝑝𝑒𝑡𝑢𝑖𝑡𝑦) =
𝑟−𝑔
1
1+𝑔 1
𝑃𝑉(𝐺𝑟𝑜𝑤𝑖𝑛𝑔 𝐴𝑛𝑛𝑢𝑖𝑡𝑦) = 𝐶 ×
B1 − ;
= C
𝑟−𝑔
1+𝑟
𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑛 − 𝑝𝑒𝑟𝑖𝑜𝑑 𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑅𝑎𝑡𝑒 = (1 + 𝑟)# − 1
.
𝑟
𝐸𝐴𝑅 𝑡𝑜 𝑝𝑒𝑟𝑖𝑜𝑑𝑖𝑐 𝑟𝑎𝑡𝑒:
= (1 + 𝐸𝐴𝑅)P − 1
𝑚
𝐴𝑃𝑅 P
𝐸𝐴𝑅 = ;1 +
= −1
𝑚
𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑟𝑎𝑡𝑒 − 𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑒
𝑅𝑒𝑎𝑙 𝑟𝑎𝑡𝑒 =
1 + 𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑒
Stocks, Bonds, & Capital Budgeting Formulas
𝐶𝑜𝑢𝑝𝑜𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡
𝐶𝑜𝑢𝑝𝑜𝑛 𝑅𝑎𝑡𝑒 × 𝐹𝑎𝑐𝑒 𝑉𝑎𝑙𝑢𝑒
=
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐶𝑜𝑢𝑝𝑜𝑛 𝑃𝑎𝑦𝑚𝑛𝑒𝑡𝑠 𝑝𝑒𝑟 𝑌𝑒𝑎𝑟
𝐶𝑃𝑁.
𝐶𝑃𝑁/
𝐶𝑃𝑁1 + 𝐹𝑉
𝐵𝑜𝑛𝑑 𝑃- =
+
+ ⋯+
/
(1 + 𝑦 )1
(1 + 𝑦) (1 + 𝑦)
.
.
\]
𝐵𝑜𝑛𝑑 𝑃- = 𝐶𝑃𝑁 × W X1 − (.YW)Z [ + (.YW)Z
`ab
`ab
`ab
g
𝑆𝑡𝑜𝑐𝑘 𝑃- = (.Ydc ) + (.Yd f)f + ⋯ + (.Yd Z)Z + (.YdZ )Z
e
e
e
e
𝐷𝑖𝑣.
𝑆𝑡𝑜𝑐𝑘 𝑃- (𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝐺𝑟𝑜𝑤𝑡ℎ) =
𝑟i − 𝑔
𝐷𝑖𝑣.
𝐶𝑜𝑠𝑡 𝑜𝑓 𝐸𝑞𝑖𝑡𝑦 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 = 𝑟i =
+𝑔
𝑃𝐷𝑖𝑣jY. + 𝑃jY. − 𝑃j
𝑅jY. =
𝑃j
𝑔 = 𝑅𝑒𝑡𝑒𝑛𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑒
× 𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑁𝑒𝑤 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
𝐶𝐹.
𝐶𝐹/
𝐶𝐹1
𝑁𝑃𝑉 = −𝐼- +
+
+⋯+
/
(1 + 𝑟 )1
(1 + 𝑟) (1 + 𝑟)
Annual Realized Return:
𝑅k##lmn = (1 + 𝑅. )(1 + 𝑅/ )(1 + 𝑅o )(1 + 𝑅p ) − 1
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐴𝑛𝑛𝑢𝑎𝑙 𝑅𝑒𝑡𝑢𝑟𝑛:
1
𝑅q = (𝑅. + 𝑅/ + ⋯ + 𝑅s )
𝑇
CAPM or SML:
𝐸 [𝑅a ] = 𝑟v + 𝛽a x𝐸[𝑅yzj ] − 𝑟v {
𝑊𝐴𝐶𝐶 = 𝑟i 𝐸% + 𝑟~v• 𝑃% + 𝑟` (1 − 𝑇€ )𝐷%
𝐹𝐶𝐹 = 𝐶𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑓𝑟𝑜𝑚 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑠 − 𝐶𝑎𝑝𝐸𝑥
− 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑁𝑊𝐶
Financial Ratios
𝑀𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑒𝑞𝑢𝑖𝑡𝑦 (𝑜𝑟 𝑀𝑎𝑟𝑘𝑒𝑡 𝐶𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛)
= 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔
× 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒
𝑀𝑎𝑟𝑘𝑒𝑡 − 𝑡𝑜 − 𝐵𝑜𝑜𝑘 𝑅𝑎𝑡𝑖𝑜
𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦
=
𝐵𝑜𝑜𝑘 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦
𝐵𝑜𝑜𝑘 𝐷𝑒𝑏𝑡 − 𝑡𝑜 − 𝐸𝑞𝑢𝑖𝑡𝑦 𝑅𝑎𝑡𝑖𝑜
𝐿𝑇 & 𝑆𝑇 𝐷𝑒𝑏𝑡
=
𝐵𝑜𝑜𝑘 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦
𝑀𝑎𝑟𝑘𝑒𝑡 𝐷𝑒𝑏𝑡 − 𝑡𝑜 − 𝐸𝑞𝑢𝑖𝑡𝑦 𝑅𝑎𝑡𝑖𝑜
𝐿𝑇 & 𝑆𝑇 𝐷𝑒𝑏𝑡
=
𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦
𝐸𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒 𝑉𝑎𝑙𝑢𝑒
= 𝑀𝑘𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦
+ 𝐿𝑇 & 𝑆𝑇 𝐷𝑒𝑏𝑡 − 𝐶𝑎𝑠ℎ
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐴𝑠𝑠𝑒𝑡𝑠
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑅𝑎𝑡𝑖𝑜 =
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐴𝑠𝑠𝑒𝑡𝑠 − 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦
𝑄𝑢𝑖𝑐𝑘 𝑅𝑎𝑡𝑖𝑜 =
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠
𝐺𝑟𝑜𝑠𝑠 𝑃𝑟𝑜𝑓𝑖𝑡
𝐺𝑟𝑜𝑠𝑠 𝑀𝑎𝑟𝑔𝑖𝑛 =
𝑆𝑎𝑙𝑒𝑠
𝑂𝑝𝑒𝑎𝑟𝑡𝑖𝑛𝑔 𝐼𝑛𝑐𝑜𝑚𝑒
𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑀𝑎𝑟𝑔𝑖𝑛 =
𝑆𝑎𝑙𝑒𝑠
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒
𝑁𝑒𝑡 𝑃𝑟𝑜𝑓𝑖𝑡 𝑀𝑎𝑟𝑔𝑖𝑛 =
𝑆𝑎𝑙𝑒𝑠
𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝐼𝑛𝑐𝑜𝑚𝑒
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝐶𝑜𝑣𝑒𝑟𝑎𝑔𝑒 𝑅𝑎𝑡𝑖𝑜 =
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝐸𝑥𝑝𝑒𝑛𝑠𝑒
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒
𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝐸𝑞𝑢𝑖𝑡𝑦 =
𝐵𝑜𝑜𝑘 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 + 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝐸𝑥𝑝𝑒𝑛𝑠𝑒
𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝐴𝑠𝑠𝑒𝑡𝑠 =
𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠
𝑆ℎ𝑎𝑟𝑒 𝑃𝑟𝑖𝑐𝑒
𝑃𝑟𝑖𝑐𝑒 − 𝑡𝑜 − 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑅𝑎𝑡𝑖𝑜 =
𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑃𝑒𝑟 𝑆ℎ𝑎𝑟𝑒
𝐴𝑐𝑐𝑜𝑢𝑛𝑡𝑠 𝑅𝑒𝑐𝑒𝑖𝑣𝑎𝑏𝑙𝑒
𝐴𝑐𝑐𝑜𝑢𝑛𝑡𝑠 𝑅𝑒𝑐𝑒𝑖𝑣𝑎𝑏𝑙𝑒 𝐷𝑎𝑦𝑠 =
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐷𝑎𝑖𝑙𝑦 𝑆𝑎𝑙𝑒𝑠
𝐶𝑜𝑠𝑡 𝑜𝑓 𝐺𝑜𝑜𝑑𝑠 𝑆𝑜𝑙𝑑
𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦 𝑇𝑢𝑟𝑛𝑜𝑣𝑒𝑟 =
𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦
𝑆𝑎𝑙𝑒𝑠
𝐹𝑖𝑥𝑒𝑑 𝐴𝑠𝑠𝑒𝑡 𝑇𝑢𝑟𝑛𝑜𝑣𝑒𝑟 =
𝐹𝑖𝑥𝑒𝑑 𝐴𝑠𝑠𝑒𝑡𝑠
𝑆𝑎𝑙𝑒𝑠
𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠 𝑇𝑢𝑟𝑛𝑜𝑣𝑒𝑟 =
𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠