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MGT231 REFERENCE FORMULA SHEET
Interest rates:
EAR = (1+ QR/m)m - 1 k = (1+EAR)1/f - 1 k = (1 + QR/m)m / f - 1
1 + Nominal rate = (1 + Real rate) ( 1 + inflation)
Time value of money:
FV =  tr 1PV PV =  tr1
Value Future
PV of a perpetuity = r
C
PV of a growing perpetuity = gr
C1

PV of annuity = 






 trr
C
)1(
11 = 




 

r
rC
t)1(1
FV of annuity = 




 
r
1)r1(C
t

PV of growing annuity =
















t
1
r1
g11
gr
C


Bond valuation:
Price of a Bond = tt )r1(
Value Face
)r1(r
1
r
1C








 = 






 trr
C
)1(
11 +  tr1
Value Face
If f is the m-year forward rate in n years, then: (1 + rn)n(1 + mfn)m = (1 + rm + n)m + n
Dividend discount model:
Price of a share = H
H
H
H
2
21
0 )r1(
P
)r1(
DIV
...
)r1(
DIV
r1
DIV
P








g = ROE x b
No-Growth Dividend Discount Model:
r
DIV
P 10 
Constant-Growth Dividend Discount Model: ,DIV10 gr
P


Expected Rate of Return Formula:
0
01
0
1
0
1
P
PP
P
DIV
g
P
DIV
r

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Capital Budgeting
Present value of CCA tax shield with the half-year rule = 




















 t
cc
)r1(
1
dr
SdT
r1
r5.01
dr
CdT
Risk and Return and Cost of Capital
Arithmetic average: mean = ∑ ௔೔
೙
೔సభ
௡
Standard Deviation of Realized (ex-post) returns (of a sample):
Portfolio standard deviation ))()((2)()()()( ,
2222
BSBSBBSSp COVwwww  
Correlation:
BS
SB
SB
r

 )(Cov
Minimum Variance Portfolio:
i
i RFER

ratio Sharpe
The capital asset pricing model (CAPM):
)( fmAfA rrrr  
Beta of stock j: .
m
jm,j
j 

  or .
)r,r(cov
2
m
mj
j 
 
Beta of a portfolio: βP = w1β1 + w2β2 + … wnβn
)()(Prob anteEx 2
1
i ii
n
i
ERr  


ௌ஻ = ෍ ௜
௡
௜ୀଵ
(ௌ,௜ − ̅௦)(஻,௜ − ̅஻)
஻ =
ௌ ଶ − (ௌ, ஻൯
ௌ ଶ + ஻ ଶ − 2(ௌ, ஻)
ௌ஻ =
1
− 1
෍(ௌ,௜ − ̅௦)
௡
௜ୀଵ
(஻,௜ − ̅஻)
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Note: When comparing an I/S
variable (i.e. a “flow” variable) to a
Balance Sheet variable (i.e. a
“snapshot”) variable, you should
take an average of the opening and
closing snapshot (B/S) balances
Source: Ross et al. Fundamentals of Corporate Finance. McGraw Hill.