FORMULA SHEET
Time value of money:
C
FV = C × (1 + 𝑟)𝑡
PV of a perpetuity =
PV = (1+𝑟)𝑡
𝐶
𝐶1
PV of a growing perpetuity =
𝑟
1−(1+𝑟)−𝑡
𝐶
1
𝑟
(1+𝑟)𝑡
PV of annuity = × [1 −
PV of growing annuity =
𝐶1
𝑟−𝑔
Interest rates:
1+ EAR = (1+ APR/k)k
r = (1+ EAR)k/f-1
] =𝐶×[
× [1 − (
𝑟
]
𝑟−𝑔
FV of annuity = 𝐶 × [
(1+𝑟)𝑡 −1
𝑟
1+𝑟
)]
with k the number of compounding periods; APR=Annual percentage rate=quoted rate
with f the number of payments within a year
Bond valuation:
1
1
𝑟
𝑟(1+𝑟)𝑡
Price of a Bond = 𝐶 × [ −
]+
Face Value
𝐶
=
(1+𝑟)𝑡
𝑟
× [1 −
1
(1+𝑟)𝑡
] +
Future Value
(1+𝑟)𝑡
1 + Nominal rate = (1 + Real rate) ( 1 + inflation)
If f is the m-year forward rate in n years, then: (1 + rn)n(1 + f)m = (1 + rm + n)m + n
Dividend discount model:
Price of a share = 𝑃0 =
]
1+𝑔 𝑡
DIV1
1+𝑟
+
DIV2
(1+𝑟)2
+. . . +
DIV𝑇
(1+𝑟)𝑇
DIV1
No-Growth Dividend Discount Model: 𝑃0 =
+
DIV1
𝑃0
g = ROE x b
𝑟
Constant-Growth Dividend Discount Model: 𝑃0 =
Expected Rate of Return Formula: 𝑟 =
𝑃𝑇
(1+𝑟)𝑇
DIV1
𝑟−𝑔
,
+ 𝑔 𝑜𝑟 𝑟 =
𝐷𝐼𝑉1
1
𝑃0
+
𝑃1 −𝑃0
𝑃0