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EQUATION SHEET
Principles of Finance
Exam 2
COST OF MONEY
Dollar return
Yield 

= (Dollar income) +
(Capital gains)
= (Dollar income) + (Ending value – Beginning value)
Dollar return
Dollar income  Capital gains

Beginning value
Beginning value
Dollar income  (Ending value - Beginning value)
Beginning value
Rate of return = r = Risk-free rate + Risk premium = r = rRF + RP
Rate of return = r = rRF + RP = rRF
+ [DRP + LP + MRP]
= [r* + IP] + [DRP + LP + MRP]
rTreasury = rRF + MRP = [r* + IP] + MRP
Yield on an 
n-year bond
rate  Interest rate   Interest rate
Interest
 in Year n   R R 
in Year 1   in Year 2 
1
n
Value of an asset 



CF2
CFn

 Rn
n
CF1


(1 r)1 (1 r)2
2
(1 r)n
n


 (1r)
t1
CFt
t
Valuation Concepts
General valuation model:
V0 PV of CF 


CF1
CFn
(1r )1
 

n

(1r )n
 (1r)
CFt
t1
t
Bond Valuation:
1 - 1 
1 
Bond =V  INT + ... + INT  M = INT  (1+rd )N  + M 

d
1
N
N
Value


(1 + r d)
(1 + r d)
rd
 (1 + r d) 



Vd =
Vd =
INT
1
+ ... +
(1 + YTM )
INT
1
(1 + YT C)
INT
(1 + YTM )
+ ... +
N
INT
N
(1 + YT C)
+
+
M
(1 + YTM )N
Adjust rd, N, and INT if interest is
paid more than once per year.
YTM = Yield to maturity
M
(1 + YT C)N
INT V d1 - V d 0
rd YTM = Bond yield = Current + Capital gains =
+
yield
yield
V d0
V d0
YTC = Yield to call
Stock Valuation:
ˆ
Stock  V Pˆ  D
1

s
0
value
(1 r )1

s
(1 rs )

ˆ
D
t
 (1 r )
t
t1
s
ˆ1
D0 (1 + g) = D
rs - g
rs - g
Constant growth stock: P0 =
Nonconstant growth stock: P0 


ˆ
D

Dˆ 1
(1 rs )
1

Dˆ 2
(1 rs )
2

 
Dˆ (1 gnorm )
; where Pˆn  n
rs  gnorm
(1 rs )
Dˆ n  Pˆn
n

ˆ
ˆ   Pˆ P
D
D
r̂s = Stock yield = Dividend + Capital gains  1  g =  1  +  1 0
yield
yield
 P0   P0
P0
  







Economic EVA EBIT(1 T)   Average cost  Invested 

value added
of funds
capital 
Risk and Rates of Return
Expected rate = rˆ = Pr r + Pr r + ... + Pr r =
11
2 2
nn
of return
n
 Prr
ii
i=1
n
Variance =  2 =
(r - r)ˆ Pr
2
i
i
i=1
n
 (r  r)ˆ Pr
Standard deviation =  =  2 =
2
i
i
i=1
n
 (r  r )
n
Estimated  = s =
r
2
t
r
t=1
n 1
Coefficient of variation = CV =
r1  r2   rn t1

n
n
t
Risk

=
Return rˆ
N
rˆP = w1rˆ1 + w 2rˆ2 + ... + w NrˆN =
 w rˆ
j j
j=1
N
P = w11 + w 22 + ... + wNN =
w 
j j
j=1
Return = Risk-free return + Risk Premium = rRF + RP
RP =
RPInvestment =
rInvestment =
=
=
Return - rRF
RPM x βInvestment
rRF + RPInvestment
rRF + (RPM)βInvestment
rRF + (rM - rRF)βInvestment
Capital asset pricing
model (CAPM)
gnorm = normal, or
constant growth