ACC501 Formulas

7/21/2019 ACC501 Formulas

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BUISNESS FINANCE FORMULAS 1-22

The Balance Sheet Identityis:

Assets Liabilities + Stockholders Equity

Net Worin! Ca"ital # C$rrent A%%et% & C$rrent Lia'ilitie%

NWC > 0 he! Curre!t Assets > Curre!t Liabilities NWC " 0 he! Curre!t Assets " Curre!t Liabilities NWC # 0 he! Curre!t Assets # Curre!t Liabilities

The Inco(e State(ent

$e%e!ue E&'e!ses (!co)e

A)era!e )%* Mar!inal Ta+ Rate%

Su''ose a Cor'oratio! has a ta&able i!co)e o* ,00-000. So the /a& calculatio! ill be: 0-000 & 12 # 3-004 3-000 0-0005 & ,2 # 6-,04 100-000 3-0005 & 782 # 9-004 ,00-000 100-0005 & 72 # 7-000 # 61-,0

;ur total ta& is 61-,0

A%era


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e"reciation a% a Ta+ Shield

Cor"oration A Cor"oration B

Ear!i!


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Curre!t Assets (!%e!toryuick $atio # ????????????????????????????????????

Curre!t Liabilities

Ca%h Ratio

CashCash $atio # ???????????????????????

Curre!t Liabilities

Total e't Ratio

/otal Assets /otal Equity/otal ebt $atio # ????????????????????????????????????

/otal Assets

Total e't Ratio

ebtEquity ratio # /otal ebt = /otal Equity

Equity ulti'lier # /otal Assets = /otal Equity

Intere%t Co)era!e Ratio

Also k!o! as /i)es (!terest Ear!ed 4/(E5 ratio- re*ers to the ability o* the *ir) to

co%er is i!terest obli


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(* e k!o sales ere tur!ed o%er 7., ti)es duri!< the year- e ca! calculate easily

ho lo!< it took to tur!o%er o! a%era


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Net i!co)e$etur! o! Assets # ????????????????????

/otal Assets

Ret$rn on E6$ity$etur! o! equity 4$;E5 is a )easure o* ho the stockholders *ared duri!< the year.

Net i!co)e$etur! o! Equity # ????????????????????

/otal Equity Earnin!% 5er Share

Net i!co)eEDS # ???????????????????????????

Shares ;utsta!di! si)'le i!terest

Compound interest.

( # D & rt

F$t$re 3al$e

BH # D 41 + rt5

(! the o!e?'eriod case- the *or)ula *orFV ca! be ritte! as:

FV # CM 41 + r5

Where C is cash *lo today 4ti)e Jero5 a!d r is the a''ro'riate i!terest rate.Ge!eraliJi!< the *uture %alue o* a! i!%est)e!t o%er )a!y 'eriods:

FV # C M 41 +

r5t

Where

C0 is cash *lo at date 0-r is the a''ro'riate i!terest rate- a!dt is the !u)ber o* 'eriods o%er hich the cash is i!%ested./he e&'ressio! 41 + r5 t is thefuture value interest factor.

5re%ent 3al$e

BHDH # ???????????????? 41+rt5

(! the o!e?'eriod case- the *or)ula *orPV ca! be ritte! as:

1

1

CPV

r=

+


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Where

C1 is cash *lo at date 1 a!dr is the a''ro'riate i!terest rate or discou!t rate

Ge!eral *or)ula *or calculati!< 'rese!t %alue o* C cash *lo i! t'eriods ti)e is:

( )1

1

1 t

PV Cr

=

+

1 =41 + r)t is used to discou!t a *uture cash *lo- so it is called the discount factor ;r

present value interest factor (PVIF rt!- Calculati!< the 'rese!t %alue o* a *uture cash *lo to deter)i!e its orth today is

co))o!ly called discounted cash flow ("CF! valuation

5re%ent 3al$e )%* F$t$re 3al$e

What e called the 'rese!t %alue *actor is ust the reci'rocal o* the *uture %alue *actor.

Buture %alue *actor # 41 + r5t

Drese!t %alue *actor # 1=41 + r5t

(* e let BHt sta!d *or the *uture %alue a*ter t 'eriods- the! the relatio!shi' betee! the*uture %alue a!d the 'rese!t %alue is:

DH & 41 + r5t # BHtDH # BHt = 41 + r5t # BHt & O1= 41 + r5tP

/his is also k!o! as basic 'rese!t %alue equatio!.

( )0BH 1 t

C r= +

Findin! the N$('er o, 5eriod%4 R$le o, 82

Bor reaso!able rates o* retur!- the ti)e it takes to double the )o!ey- is


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II* F$t$re )al$e o, C dollar% in)e%ted at r "ercent "er "eriod ,or t "eriod%4

BHt # CQ 41 + r5t/he ter) 41 + r5t is called the *uture %alue *actor.

III* 5re%ent )al$e o, C to 'e recei)ed in t "eriod% at r "ercent "er "eriod4

DH # C=41 + r5t/he ter) 1=41 + r5t is called thepresent value factor.

I3* The 'a%ic "re%ent )al$e e6$ation !i)in! the relation%hi" 'et.een "re%ent and

,$t$re

)al$e i%4

DH # BHt= 41 + r5t

5re%ent 3al$e ,or Ann$ity ca%h ,lo.%

Bor a!!uity calculatio!- e use a %ariatio! o* 'rese!t %alue equatio!.

/he 'rese!t %alue o* a! a!!uity o* C dollars 'er 'eriod *or t 'eriods he! i!terest

rate is r is:

DH# C &41 ? Drese!t %alue *actor5=r # C &O1 ? 1=41 + r5t P=rWhereC # Deriodic 'ay)e!t or a!!uityr # rate o* i!terest

t # !u)ber o* 'eriods/he ter) i! the 'are!thesis is calledpresent value interest factor of an annuity4DH(BA5.

DH(BA # 41 Drese!t %alue *actor5=r

F$t$re 3al$e ,or Ann$itie%

BH # C 4Buture %alue *actor ? 15=r # C O41 + r5t ? 1P=r

Ordinary Ann$ity4-

DH# C RO 1?1=41+i5!P= iT41+i5

Ann$itie% $e4-

DH # C RO 1?1=41+i5!P= iT

5er"et$itie%


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/he 'rese!t %alue o* 'er'etuity is:

Der'etuity DH # C = r

S$((ary o, Ann$ity and 5er"et$ity

I* Sy('ol%

DH # Drese!t %alue- hat *uture cash *los bri!< todayBHt # Buture %alue- hat cash *los are orth i! the *uturer # (!terest rate- rate o* retur!- or discou!t rate 'er 'eriodt # Nu)ber o* ti)e 'eriodsC # Cash a)ou!t

II* F3 o, C "er "eriod ,or t "eriod% at r "ercent "er "eriod4

BHt # C O41 + r5t ? 1P = r

III* 53 o, C "er "eriod ,or t "eriod% at r "ercent "er "eriod4DH # C 41 ? O1= 41 + r5tP5 = r

I3* 53 o, "er"et$ity o, C "er "eriod4

DH # C = r

E,,ecti)e Ann$al Rate%

(* a rate is quoted as 102 co)'ou!ded se)ia!!ually- the! hat this )ea!s is that

the i!%est)e!t actually 'ays 2 e%ery si& )o!ths.(s 2 e%ery si& )o!ths thesa)e thi!< as 102 'er yearK

1 & 1.10 # 1.101 & 1.0, # 1.10,

102 co)'ou!ded se)ia!!ually is equi%ale!t to 10.,2 co)'ou!ded a!!ually.

10.,2 is called e**ecti%e a!!ual rate 4EA$5

E,,ecti)e Ann$al Rate%

EA$ is co)'uted i! three ste's

i%ide the quoted rate by the !u)ber o* ti)es the i!terest is co)'ou!ded

Add 1 a!d raise it to the 'oer o* !u)ber o* ti)es the i!terest is co)'ou!ded.

Subtract 1SoEA$ # 41 + uoted rate = )5) 1

Where m is the number of times the interest is compounded

Ann$al 5ercenta!e Rate%


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A ty'ical credit card a


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h # the i!*latio! rateV Accordi!< to the Bisher E**ect:1 + $ # 41 + r5 Q41 + h5

$earra!


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V Alter!ati%ely- e ca! say that the 'rice o* stock today is equal to the 'rese!t %alue o* allo* *uture di%ide!ds.

( ) ( ) ( ) ( )71 , 8

1 , 7 8

1 1 1 1

DD D D

R R R R= + + +

+ + + +

9ero 7ro.th Stoc%

A share o* co))o! stock i! a co)'a!y ith a co!sta!t di%ide!d is ter)ed as Jero

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ACC501 Formulas