Purchase new car in 5-years. $1000,
end of each 5 years. 6% compounded
annum. How much will you have
after 5-years?
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)^t-1}/r)
PV perpetuity=
C/r (eg. Preferred stock) r=Dividend/ price per share
Growing annuity PV
=C*{(1-((1+g)/(1+r))^t)/(r-g)}
EAR=
{1+(Quoted rate/m)}^m
–
1 or Eff( Nom APR, # periods)
Growing perpetuity PV
=C/(r-g)
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
Interest-only Loans (borrower pays interest each period and pays the entire principle at one point in the future). Yr1-Y(n-1)=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*[1-1/(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=(p1-p0)/p0=(D1-D0)/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 CF-
Project Δnwc
-Project CS
Operating CF=
EBIT(sale-cogs-dep)+dep-tax
CFFA=ocf-ncs-
Δnwc
Cf, cash income
=sales-increase in a/c outflow=cost-change in a/p
After-tax salvage=salvage-T(salvage-book value)
Bv=initial cost-accumulated dep
Straight line
D=(initialcost-salvage)/number of years
Discounted payback:
y0 cf-PV 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
return-R
treasury)*risk