equation list (booth and cleary 3rd edition) comm 308

8/12/2019 Equation List (Booth and Cleary 3rd Edition) Comm 308

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Equation List - Comm 308 - Booth-Cleary TextIMPORTANT: Some equations on this list will not be providedon your exam or quiz crib sheet as you are expected to know them.

You are also responsible for any variations on these or other relationships that have been taught to you but do not appear on this list.

5.2Future Value ofPV

0: FV

n=PV

0(1+ k)

n

will not be on exam crib sheetReason: Simple transformation of 5.3

5.3

Present value (compound interest): PV0 =

FVn

(1+ k

)

n

5.4

Future value (ordinary annuity): FVn = PMT

1+ k( )n

1

k

5.5

Present Value of an annuity:PVn

=PMT

k1

1

1 + k( )n

5.6

Future value (annuity due): FVn = PMT

1+ k( )n

1

k

1+ k( )

will not be on exam crib sheet

Reason: Student should be able to get the future value of annuity due using their understanding of

timeline and future value of simple annuity(5.4)

5.7

Present value (Annuity due): PV0 =PMT

k1

1

1+ k( )n

1+ k( )


Reason: Student should be able to get the present value of annuity due using their understanding of

timeline and present value of simple annuity(5.5)

5.8 Present value of perpetuity: PV0 =

PMT

k

5.9Effective annual rate: k= 1+

QR

m

m

1will not be on exam crib sheet

Reason: Student should be able to use 5.11 to get the answer.

5.10 Effective rate with continuous compounding: k =eQR 1

5.11 Effective period rate (for any period f): k= 1+QR

m

m

f

1

5A-2 Present value of growing perpetuity: PV0

=PMT

01+g( )

kg

=PMT

1

kg

5A-4 Present value of growing annuity:PV0 =

PMT1

kg1

1+g

1+ k

n

6.1Bond valuation: B =

I

kb

11

1+ kb( )

n

+F

1

1+ kb( )

n


Reason: Student should be able to use timeline and 5.5 and 5.3 to get the answer.


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7.10 Share price with growth opportunities:P0 =

EPS1

kc

+PVGO

7.11 Growth rate:g = b*ROE

8.1

1

0

Income yield CF

P=


Reason: Should be able to see from 8.3.

8.2Capital gain (loss) yield =

P1

P0

P0 will not be on exam crib sheet

Reason: Should be able to see from 8.3

8.3 Total return = Income yield + Capital gain (loss) yield =CF

1

P0

+

P1P

0

P0

8.4 Arithmetic average (AM)1

n

j

i

r

n

=

=


Reason: Student should know this

8.5 Geometric average (GM) = 1+ r1( ) 1+ r2( ) 1+ r3( ) 1+ rn( )

1n 1= 1+ r

i( )

i=1

n

1

n

1

8.6 Expected return:ER= ri* Prob

i(

i=1

n

8.7Standard Deviation for individual returns: Ex-post

( )2

1

1

n

i

i

r r

n

=

=

8.8 Standard Deviation for individual returns: Ex-ante ( )( )2

1

Probn

i i

i

r ER

=

=

8.9 Expected portfolio return:ERp= w

i*ER

i(i=1

n

9.10

( )P B A B

ER ER w ER ER= + will not be on exam crib sheet

Reason: Should be able to see from 8.9

8.11 Portfolio standard deviation: P

= wA

( )2

A

( )2

+ wB

( )2

B

( )2

+ 2 wA

( ) wB

( )COVA,B( )

8.12 Covariance of returns: COVAB

= Probi(r

A,i r

a)

i=1

n

(rB,i rb )

8.13Correlation coefficient of returns:

AB =

COVAB

A

B will not be on exam crib sheet

Reason: Simple transformation of 8.14

8.14 Covariance of returns: COVAB

=AB

A

B

8.15Standard Deviation two-securit ortfolio : = w

2

2

+ w2

2

+ 2 w w


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12.9S = C - P + PV(X) Will not be on exam crib sheet.

Reason: Simple transformation of 12.5

13.1 NPV =CF

1

1+ k( )1+

CF2

1+ k( )2 +

CF3

1+ k( )3 ++

CFn

1+ k( )nCF

0 =

CFt

1+ k( )t

t=1

n

CF0

13.2

CF1

1+ IRR( )1+

CF2

1+ IRR( )2 +

CF3

1+ IRR( )3 ++

CFn

1+ IRR( )n =CF

0

or,CF

t

1+IRR( )t

t=1

n

=CF0

Will not be on exam crib sheet.

Reason: Should be able to see this from definition of IRR and 13.1

13.3 PI =PV(Cashinflows)

PV(Cashoutflows)

13.4

( )

11

1n

Project NPVEANPV

k

k

=

+


Reason: Should be able to use the definition of EANPV and preset value of annuity (5.5) to get the

answer.

14.1 Initial cash outlay: CF0 = C

0+ NWC

0+OC

14.2 Annual After-Tax Cash flows: CFt = CFBTt 1T( )+CCAt T( )

14.4 Ending Cash flows (ignoring tax implications): ECFn = SV

n+ NWC

n

14.5 Net present value: NPV =PV Annual CFs( )+PV ECFn( )CF0

14.6 PV(Operating Cash Flows)=CFBT 1 T( )

k1

1

1+ k( )n

14.7

Present value of CCA Tax shield (ignoring CCA recapture and Terminal loss)

PV(CCA Tax Shield) =(C

0)(d)(T)

d+ k*

1+ 0.5k( )1+ k( )

(SVn)(d)(T)

d+ k*

1

1+ k( )n

20.8

Weighted average Cost of Capital (WACC):

Ka =ROIIC

V

=

KeS+K

d(1T)D

V

= Ke

S

V

+ Kd(1T)

D

V

20.9 WACC= Ke

S

V+K

p

P

V+K

i

D

V, Where: K

i =K

d(1T)

20.1

0Market value: S =P

0 n

20.1

1

p

p

p

DP

k=


Reason: Same as 7.2


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equation list (booth and cleary 3rd edition) comm 308

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