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Purchase new car in 5years. $1000,
end of each 5 years. 6% compounded
annum. How much will you have
after 5years?
N=5 PMT= 1000 PV=0 FV=?
FV= 5637
If asks for beginning switch to begin
mode.
PV=CF/I
EQUATIONS
Future value of multiple cash flows:
NPV( Discount rate,yr0 CF, {CF1,CF2,CF3}, {FreqCF1, Freq cf2})* (1+Discount rate)^years
Annuity Present value(pay equal payments
) PV= C*([1{1/(1+r)^t}]/r); Fv=C*({(1+r)^t1}/r)
PV perpetuity=
C/r (eg. Preferred stock) r=Dividend/ price per share
Growing annuity PV
=C*{(1((1+g)/(1+r))^t)/(rg)}
EAR=
{1+(Quoted rate/m)}^m – 1 or Eff( Nom APR, # periods)
Growing perpetuity PV
=C/(rg)
APR:
Nom(Eff, # periods) =Interest rate per period* # or periods per year
Irr(Yr0 CF or pv, {CF1,CF2,,,CFN})
to calculate interest with uneven cash flow
Continuous Compounding:
EAR=e^q 1
Interestonly Loans (borrower pays interest each period and pays the entire principle at one point in the future). Yr1Y(n1)=C*r, Yn=C*r+C
Coupon rate
=annual coupon/face value
Current yield
=a bond’s annual coupon*Fv/price=pmt/pv
Price of bond:
PV percentage of face value
Bond value=
C*[11/(1+r)^t]/r+F/(1+r)^t=PV coupons +PV face amount
PMT>PV+ FV 1000> PV
Yield to maturity(YTM)
use TVM solver
1+R(nominal rate)=(1+r(real rate))*(1+h(inflation)) R≈r+h
PMT:
bond value FV:1000 to get PV.
Po=D1/(1+R)+ D2/(1+R)^2 + D3/(1+R)^3…
Po: current price of stock
P1:price in one period
D1:cash dividend paid at the end of the period
Perpetuity: Po=(D1+P1)/(1+R)
Equity: ownership, vote, div not cost not tax dedu, div not liability no legal source, cannot bankrupt no debt
P: value of stock
D:dividend
R:required return
Zero Growth: Po=D/R
Do:dividend JUST paid,
g: growth rate
Constant Growth:Dt=Do*(1+g)^t
R=Dividend yield+Capital
gain yield=D1/Po + g=Do(1+g)/Po where
g=(p1p0)/p0=(D1D0)/D0
Dividen
d
Growth
Model:
Po=Do(
1+g)/(R
g)paid
or
=D1/(R
g) PV0
=C1/(R
g)=Co(1
+g)/(R
g)
Noncon
stant
growth:
npv(R,C
Fo,{Cf1,
cf2,,,(CF
n+Pn)})
Pn=Dn*
(1
+g)/(R
g)
Project total CF
=Projected operating CFProject ΔnwcProject CS
Operating CF=
EBIT(salecogsdep)+deptax
CFFA=ocfncsΔnwc
Cf, cash income
=salesincrease in a/c outflow=costchange in a/p
Aftertax salvage=salvageT(salvagebook value)
Bv=initial costaccumulated dep
Straight line
D=(initialcostsalvage)/number of years
Discounted payback:
y0 cfPV of yr1,year1 –year2,…. Npv(discount rate, cf0,{…}
Profitability Index=pv/initial cost
Crossover:
Mirr:
R(return)=r(ri
skfree)+r(risk
premium)*bet
a=r(treasury)+
(R expected
returnR
treasury)*risk
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 Fall '11
 WHITE
 Finance

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