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```					                                        AK/ADMS 3530.03 Finance
Midterm Exam Formula Sheet

Time Value of Money
Future Value
FV = Investment  1  r 
t
PV =
1  r t
C                                                                            C1
PV of a perpetuity =                                            PV of a growing perpetuity =
r                                                                           rg

1      1      
PV of an annuity = C             t 
 r r(1  r )                                                   (1  r ) t  1 
FV of an annuity = C                  
 1  (1  r )  t                                                                  r         
= C                               (easier to calculate)
       r          
1      1      
Annuity factor =            t 
 r r(1  r ) 
C1   1  g  
t

PV of a growing annuity =       1                                            1  (1  r )  t 
r  g  1 r  
                                             =                   
       r          
(lower version is easier to calculate)
PV of an annuity due = (1+r)  (PV of an annuity)
FV of an annuity due = (1+r)  (FV of an annuity)
1  Nominal rate
1 + Real rate =
1  Inflationrate

APR = Period Rate  m                          

EAR = 1  Period Rate   1                   
m
 where m = number of periods per year
1               
Period Rate = (1  EAR ) m  1                 



1
Bonds and Stocks
1      1       Face Value
Price of a bond = PV (Coupons) + PV (Face Value) = C             t 

 r r(1  r )     (1  r ) t

Annual coupon payment
Current yield =
Bond price
Yield to maturity (YTM) = interest rate for which the present value of the bond’s
payments equals the price
The approximate formula for the yield to maturity:
(face value - current price)
Annual coupon payment 
years to maturity
YTM 
(face value  current price)
2
Income  Capital gain or loss
Rate of return =
Initial price

Dividend payment
Dividend yield =
Stock price

Sustainable growth rate: g = ROE  Plowback ratio
DIV 1   DIV 2            DIV H          PH
Dividend Discount Model: P0                     ...             
1  r (1  r ) 2
(1  r ) H
(1  r ) H
where H is the horizon date, and PH is the expected price of the stock at date H
DIV1
P0 
,
Constant-Growth Dividend Discount Model:     rg
where DIV1  DIV0  (1  g )

DIV 1             DIV1 P1  P0
Expected Rate of Return Formula: r            g, or r      
P0                P0     P0

2

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