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Lesso n 12
CAPITAL BUDGETING
Out line
• Wha t is Cap ita l Bud ge ting?
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Ident ifying t he Re le va nt Cas h F lo ws
Eva lua t io n Tec hniq ues - 3 Met hod s o f Eva lua t ing I nvest me nt P roposa ls
Accept /Rejec t Dec is io n
Net Prese nt Va lue P ro file
Dete r mining W he t her to P urc hase a Mac hine
Wha t Is Cap ita l Bud ge t ing?
•
Capita l Bud get ing:
– Repres e nts a lo ng- ter m inves tme nt dec is io n
– Invo lves the p la nning o f e xpe nd itures fo r a project with a life o f ma ny year s
– Us ua lly req uires a lar ge initia l cas h o utflo w with the e xpec tatio n o f future cas h
inflo ws
– Uses pr ese nt va lue a na lys is
– Emp ha s izes cas h flows rathe r tha n inco me
Ident ifying t he Re le va nt Cas h F lo ws
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Re le va nt cas h flo ws are incre me nt a l cas h flo ws a ttr ib utab le to a p rojec t
Ta x Effe cts
• Deprec iatio n
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Stra ight line :
(Cost- Salva ge va lue )/ life
MACRS :
Cha nges in Net Work ing Cap ita l:
• Is the ca s h flo w d iffere nce betwee n the projected increa se in c urre nt asse ts a nd c urre nt
liab ilit ie s.
Cash F lo w fro m a n I nvest me nt :
• Net cas h flo w fro m the proje ct = pro jec t cas h inflo ws - projec t cas h o utflo w
• Let:
r = Change = inc re me nta l
R = r re ve nue
E = r projec t e xpe nse o t her t ha n depre c ia t io n
D = r deprec ia t io n
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t = ta x ra te
ITC = inve st me nt ta x cred it
I = cost o f new invest me nt
S = sa lva ge va lue or se ll ing pr ice
WC = work ing cap ita l
O = other s
BV = Book va lue = cost - acc umula ted dep.
CGT = cap ita l ga in o r los s ta xes = t (S - BV)
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CFi = (r Ri - r Ei) (1 - ti) + r Di tI + ITCi - Ii + Si - CGTI + WCi + Oi
inflo w if CFi > 0
out flo w if CFi < 0
CF0 = IO = init ia l o ut flo w
Eva lua t io n Tec hniq ues
3 Met hods fo r Eva lua t ing I nve st me nt Propo sa ls
There a re 3 wide ly used me t hods :
• Payback M ethod (P B)
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Inter na l Rate o f Re t ur n ( IRR)
Net Prese nt Va lue (NPV)
The Pa yback Per iod (P BP)
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The pa yback pe r iod is t he le ngt h o f t ime it takes to reco ver t he init ia l o ut flow.
• I f net a nnua l cas h inf low is e ve n or if it is e ve n fo r at leas t the le ngth o f the P BP :
PBP = IO / CF
CF = annua l ca s h inflo w d ur ing t hat pe r iod
• otherwise :
PBP = X + ( Y/CFx +1 )
X=
yea r pr io r to full reco ver y
Y=
the unreco ve red port io n o f t he IO b y t he e nd o f year X
Accept, Re ject, & Ra nk
• Accept if the project’s PBP is le ss tha n the req uired P BP, Rejec t othe rwise.
•
Ra nk accord ing to t he s hor tes t accep tab le P BP.
Ad va nta ge s o f PBP :
1. Hed ge a ga inst unce rta int y b y ignor ing cas h flows a fte r t he P BP.
2. It co uld be used wit h o t her met hods.
3. Simp le to use.
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4. It give s more att e nt io n to liq uid it y.
5. Project s wit h s ho rter o utco me ha ve mo re fa vo rab le e ffec t in t he s hor t r un o n EPS = CS
pr ices.
Disad va nta ges :
1. No cons ide rat io n o f ca s h flo ws a fter P BP.
2. Time va lue is no t take n into acco unt.
3. It might lead to s e lec t io n o f les s des irab le p rojec ts.
4. It might lead to s e lec t io n o f wro ng p rojec ts.
Net Prese nt Va lue (NPV)
Prese nt va lue o f fut ure ne t cas h inf low d isco unt ed at a n app ropr iate d isco unt rate (t he
cost o f cap ita l k) less t he init ia l o ut flo w.
N PV =
n
3 CFt / (1 + K)t - IO
t=1
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N PV =
n
3 (CFt ) (PVIF t ,k ) - IO
t=1
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I f CF is e ve n:
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NPV = (CF 1 th ro ugh n ) (PVIFA n ,k ) - IO
I f CF is e ve n e xcep t la st yea r
NPV = (CF1 th ro ugh n -1 ) (PVIFA (n -1), k ) + (CF n ) (PVIF n ,k ) - IO
Accept a nd Re ject :
Accept if NPV > 0
Rejec t if NPV < 0
Ra nk ing: Ra nk accord ing to t he highes t accep tab le NPV.
Ad va nta ge s :
1. It pa ys a tte nt io n to t ime va lue o f mo ne y
2. Cons ide r a ll cas h flo w
3. Leads to ma xim izing t he va lue o f t he fir m
Disad va nta ges :
1. Not eas ily unde rstood
2. Does not pa y att e nt io n to t he re invest me nt rate o f ret ur n b y ass uming it to be eq ua l to
K.
3
Inter na l Rate o f Re t ur n ( IRR)
IRR is t hat d isco unt ra te ( intere st ra te) t hat eq uates t he PV o f net c as h inflo w a nd t he
init ia l o ut flow.
n
3 CF f / (1 + IRR)t = IO
t=1
Also
n
3 CFt (PVIFt , IRR) = IO
t=1
Or
IRR is t hat d isco unt ra te ( intere st ra te) t hat p rod uces a ze ro NPV.
N PV =
n
3 CFt / (1 + IRR)t - IO = 0
t=1
Or
N PV =
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n
3 CFt / (PVIFt , IRR) - IO = 0
t=1
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Eve n Cas h inflo w:
(CFt ) PVIFA n ,IRR - IO = 0
Solve for P VIFA n ,IRR = IO / CFt and find I RR
I f PVIF A n ,IRR can not b e loca ted in t he tab le, appro xima te I RR as fo llo ws :
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IRR = iL + { [ ( P VIFA n ,L - PVIFA n , IRR) / (PVIFA n ,L - PVIFA n ,H ] (iH - iL) }
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I f cas h inflo w is une ve n appro xima te I RR as fo llo ws :
1. Find a d isco unt ra te i L t hat will res ult in po s it ive NPV (NPVL)
2. Find a d isco unt ra te iH t ha t wil l res ult in ne gat ive NPV (NPV H)
3. App ly t he fo llowing
IRR = iL + { [NPVL - / (NPVL- NPVH) ] (i H - iL) }
Accept & Rejec t :
Accept if I RR > K
Rejec t if I RR < K
Ra nk ing :
Ra nk accord ing to t he highe st acc eptab le I RR.
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•
4
Ad va nta ge s
Same as NPV p lus it is ea s ie r to under sta nd e xc ept t hat it ma y no t le ad to ma ximizing
the va lue o f t he fir m.
Disad va nta ges
1. May p rod uce mult ip le IRR.
2. May p rod uce ima gina r y numbe r.
3. Does not pa y att e nt io n to t he re invest me nt rate o f ret ur n b y ass uming it to be eq ua l to
IRR.
4. May se lec t pro ject wit h les s NPV.
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Pro fit ab ilit y I nde x (PI )
The ra t io o f PV o f ne t cas h inf low to init ia l o ut flo w.
PI = PV o f ca s h inflow / IO.
- ORn
PI = [ 3 CFf / (1+K)t ]/ IO
t=1
• If cash inflo w is e ve n:
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PI = (CFn ) PVIFA n , k / IO
Accept & Rejec t :
Accept if PI > 1
Rejec t if PI < 1
Ra nk ing :
Ra nk ing ba sed o n t he highes t acceptab le PI.
Acco unt ing Ra te o f Re t ur n ( ARR)
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ARR = a ver a ge a nnua l p ro fit a fter ta xes / [ ( I + S) / 2 )]
I = cost o f t he invest me nt
S = sa lva ge va lue
The ma in ad va nta ge is s imp le. Howe ve r, it does no t take into acco unt t ime va lue o f
mo ne y a nd it ma y lead to wro ng s e lec t io n or t he less des irab le.
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Net Prese nt Va lue P ro file
A grap h o f t he NPV o f a p rojec t at d iffe re nt d isco unt ra tes s ho ws t he NPV at 3
diffe re nt po ints :
– A zero d isco unt rate
– The nor ma l d isco unt rate (or cos t o f cap ita l)
– The I RR
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Allo ws a n e as y wa y to vis ua lize whe t her o r not a n inves t me nt s ho uld be unde rtake n
Capita l Rat io ning
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Capita l rat io ning is t he res ult o f li mit ed funds a va ilab le fo r inves t me nts
Mat he ma t ic a l Approac h to Cap ita l Rat io ning
• Maximize Tota l NPV
• Subje ct to Bud ge t co ns tra ints
NPV and I RR
• in case o f a ccept- reject a ll give the s a me a ns wer
• in case o f ra nk ing o r mutua lly e xc lus ive pro jects :
mo st t imes wil l give t he sa me a ns wer. Howe ve r, t he y ma y give co nflict ing a ns wers. I f
a conflic t e xists, b ase dec is io n o n NPV.
Mult ip le Rate s o f Ret ur n
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n
3CFt / (1 + IRR)t = IO
t=1
Notice t his eq uat io n is a po lyno mia l o f de gr ee n. There fo re n d iffere nt roo ts, or
so lut io ns to t he eq uat io n ma y e xis t.
6
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