exam solution 5 fundamentals of corporate finance, 4th edition brealey

School of Administrative Studies
Atkinson Faculty of Liberal and Professional Studies
York University
Toronto, Ontario, Canada
ADMS 3530.03 Finance

Midterm Formula Sheet
Time Value of Money
FV = Investment × (1 + r )

PV of a perpetuity =

PV =

n

C
r

Future Value

(1 + r )n

PV of a growing perpetuity =

1

1
PV of an annuity = C ×  −
n 
 r r (1 + r ) 

1 − (1 + r ) − n 
= C×

r



 (1 + r ) n − 1
FV of an annuity = C × 

r



(easier to calculate)

1

1
Annuity factor =  −
n 
 r r (1 + r ) 

 1 + g n 
C
PV (Growing Annuity) =
× 1 − 
 
r − g   1 + r  

FV (Growing Annuity) =

[

C
n
n
× (1 + r ) − (1 + g )
r−g

]

1 − (1 + r ) − n 
= 

r



(lower version is easier to calculate)

PV (Annuity Due) = PV(Simple Annuity) × (1+r)
FV (Annuity Due) = FV (Simple Annuity) × (1+r)
1 + Real rate =

1 + Nomimal rate
1 + Inflation rate

APR = Period Rate × m

EAR = (1 + Period Rate ) − 1
m

1

Period Rate = (1 + EAR ) m − 1




 where m = number of periods per year




1

C
r−g


Bonds and Stocks

Price of a bond = PV (Coupons) + PV (Face Value)
1
 Face Value
1
= C× −
+
n 

(1 + r ) n
 r r (1 + r ) 

Current yield =

Annual Coupon payment
Bond price

Rate of return =

Income + Capital gain or loss
Initial price

Dividend yield =

Dividend payment
Stock price

Sustainable growth rate: g = ROE × Plowback ratio

Dividend Discount Model: P0 =

DIVH
PH
DIV1
DIV2
+
+... +
+
2

H
1 + r (1 + r )
(1 + r )
(1 + r ) H

where H is the horizon date, and PH is the expected price of the stock at date H

Constant-Growth Dividend Discount Model: P0 =
Expected Return Formula: r =

DIV1
+g
P0

DIV1
r−g

r=

or

2

DIV1 P1 − P0
+
P0
P0