Part Three by jrskeirwta

VIEWS: 0 PAGES: 35

• pg 1
```									  Part Three

Valuation
Outline of Valuation

   Discounted Cash Flow Analysis

   Valuation Model

   Risk and Return
Type of Cash Flow
   A lump sum

        \$0      \$0         \$100     \$0

   An annuity of \$100:
 \$0       \$100    \$100    \$100

   An uneven cash flow stream
 (\$50)      \$100      \$75        \$50

Future Value
   Find the FV of \$100 left for 3 years in an
account paying 10 percent annual
interest:

 FV = PV(1 + k)" = PV(FVIFk n)
 = \$100(1.10)3
 = \$100(1.3310) = \$133.10.
Present Value
 Find   the PV of \$100 to be received in 3
years if the appropriate interest rate is
10 percent:
n
 PV = FVn/(1 + k)
 = \$100(1/1.10)3 =\$100(0.7513) =
\$75.13.
Annuities
 Ordinary   Annuity:

   PV   \$100     \$100   \$100 FV

 Annuity   Due

 \$100   \$100     \$100    FV
 PV
Future Value of an Annuity
(Time Line Approach)

   0   \$100      \$100           \$100
                                \$110

10%

\$121

   \$331
Future Value of an Annuity
(Formula Approach)
 FVAn   = PMT(FVIFA)
 = \$100(3.3100) = \$331.
 If the annuity is an annuity due,
then :
 FVAn(Annuity due) = FVAn(1 + k)
 =\$331(1.10)= \$364.10
Present Value of an Annuity
(Time Line Approach)
   0    \$100    \$100      \$100

10%

\$ 90.91
 82.64 ——————
 75.13—————————
 \$248.68
Present Value of an Annuity
(Formula Approach)
 PVA= PMT(PVIFA k,n) = \$100(2.4869)
= \$248.69.

 The present value of an annuity due is
PVA(Annuity due) = PVA(1 + k)
 = \$248.69(1.10) = \$273.56.
Uneven Cash Flow Stream
   0    \$100   \$300   \$300   \$(50)
    10%

 90.91
 247.93
 225.39
 (34.15)
 \$530.08
Finding the Interest Rate
\$100(1 + x)3 = \$125.97
 \$100(FVIF k,3) = \$125.97
 FVIF k,3 = 1.2597
 Look at Table of Future Value for K. The
1.2597 is at Row 3 in the 8% column.
Therefore,
 k = 8%.
General Valuation Model
   The value of any asset can be found as
the present value of its expected future
cash flows, CFi, discounted at the rate k:

   V=    CF 1     +     CF2     +     CF3

        (1 +k)1       (1 +k)2       (1 +k)n•
Bond Valuation
V=l(PVIFA     + M(PVIF k,n)
k,n)

=\$100(PVIFA 10%,10) +
\$1,000(PVIF 10%,10)
=\$614.46 + \$385.54
=\$1,000.
Yield to Maturity of Bond
   Par value = \$1,000
   Current price = \$887
   Annual coupon = \$100
   Term to maturity = 10 years
     0       1      2 ……… 9         10
 -\$887 \$100      \$100 \$100 \$100 \$1,000
   \$887 = \$1oo(PVIFA ytm,10) + \$1,ooo(PVIFytm, 10)
   YTM = 12%.
Current Yield of Bond


                     Annual coupon payment
Current yield =
                        Current price
General Stock Valuation Model
             D1
P0   =
         ks – g

    D0(1+g)
=
    kg - g
Value of Perpetuity

           PMT
V   =
             k
                 \$2
    =                 =   \$12.50.
             0.16
Supernormal Growth

   \$2.000 \$2.600   \$3.380   \$4.394   \$4.658


   g = 30% g = 30% g = 30% g = 6% g = 6%
 PV of Supernormal Dividends
 PV D1 = \$2.600/(1.16)1 = \$2.241
 PV Ds2= \$3.380/(1.16)2 = \$2.512
 PV D3 = \$4.394/(1.16)3 = \$2.815
 \$7.568
 Stock Price at t = 3

p =    D4        =    \$4.658     =   \$4.658 = \$46.58
      ks -   g       0.16-0.06       0.10
 PV of P3
 \$46.58 / (1.16) = \$29.84
 Value of Stock
 Po = \$7.57 + \$29.84 = \$37.41.
Concept of Risk

 Risk
refers to the possibility that
some unfavorable event will occur

 Investment risk is associated with
the probability of low or negative
returns on an investment.
Probability Distribution
(payoff Matrix)

Rate of Return
Demand
Comapany Company
for the Probability
A        B
products
Strong          0.3        100       20
Normal          0.4         15       15
Weak            0.3        -70       10
Probability of Distribution
Probability of
Probability of
Co.B
Co.A

-70                    100   Rate of Return        10 15 20
15
Probability   Density
Expected Rate of Return
Expected rate   of return
n
ˆ
k       i 1
pi ki

= .3(100%)+.4(15%)+.3(-70)
= 15%

ˆ
Deviation  kj  k
Variance and Standard Deviation
n
Variance       2
  ( Ki  K ) Pi
2

i 1

n
Std   Deviation            (K
i 1
i    K ) Pi
2

The smaller the standard deviation, the
lower the risk associated with the event.
Coefficient of Variation
 The coefficient of variation shows the
risk per unit of return and a better
measure for evaluation risk in situation
where investments have substantially
different expected returns.

Coefficien of Deviation  CV 
t
ˆ
K
Portfolio Return
ˆp
Portfolio Re turn  K
ˆ              ˆ
ˆ  W K  ....... W K
 W1 K1   2 2            n n
n
 Wi K i
ˆ
i 1
Portfolio Risk

 The   risk of a portfolio depends not
only on the standard deviation of
the individual stocks, but also on
the correlation between the stocks.
Portfolio Risk
m     n
     W W 
j 1 k 1
j   k   jk

j , k  rj , kjk
When R = -1
Year    stock A % Stock B % Portfolio AB %
1992        40       -10           15
1993       -10        40           15
1994        35        -5           15
1995        -5        35           15
1996        15        15           15
Average
15        15           15
return
standard
22.6       22.6           0
deviation
When r = +1
Year    stock A % Stock B % Portfolio AB %
1992       -10       -10          -10
1993        40        40           40
1994        -5        -5           -5
1995        35        35           35
1996        15        15           15
Average
15        15           15
return
standard
22.6       22.6        22.6
deviation
When +1 > r > -1
Year    stock A % Stock B % Portfolio AB %
1992        40        28           34
1993       -10        20            5
1994        35        41           38
1995        -5       -17          -11
1996        15        3             9
Average
15        15           15
return
standard
22.6       22.6        20.6
deviation
Classification of Risk
 Total   risk can be separated into two
parts:

 Market risk

 Company-specific risk
Effects of Portfolio Size on Risk

```
To top