L2ValuationBasics.ppt*
- DCF valuation method
- Super-normal growth model
- Applications: single CF, annuity, perpetuity, uneven CFs, bond, stock, etc.
LECTURE 2 Valuation Basics
(Chapters 4, 6, 7)
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- Amount of cash flows expected
- Risk of the cash flows
- Timing of the cash flow stream
Factors that Determine Value
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DCF Method: General Formula
Finding PVs is discounting. The discount factor i is determined by the cost of capital invested.
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10%
Single Cash Flow
100
0
1
2
3
PV = ?
What’s the PV of $100 due in 3 years if i = 10%?
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Financial Calculator Setup
BGN END
P/Y 1
FORMAT: DEC 4 or larger
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Financial Calculator Solutions
N I/YR PV PMT FV
?
N = 3, I/YR = 10, PMT = 0, FV = 100
CPT, PV
-75.13
/
INPUTS
OUTPUT
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Spreadsheet Solutions
PV(rate, nper, PMT, [fv], [type])
PV(10%, 3, 0, 100, 0) = ($75.13)
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A series of equal payments made at fixed intervals for a specified number of periods.
Ordinary (deferred) annuity: the payments occur at the end of each period.
mortgages, car loans, student loans
Annuity Due: the payments are made at the beginning of each period.
apartment rental, life insurance premiums
Annuity
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Ordinary Annuity
PMT
PMT
PMT
0
1
2
3
i%
PMT
PMT
0
1
2
3
i%
PMT
Annuity Due
Ordinary Annuity vs. Annuity Due
PV
FV
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What’s the PV of a 3-year ordinary annuity of $100 at 10%?
100
100
100
0
1
2
3
10%
90.91
82.64
75.13
248.69
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Financial Calculator Solutions
N I/YR PV PMT FV
?
N = 3, I/YR = 10, PMT = 100, FV = 0
CPT, PV
-248.69
/
INPUTS
OUTPUT
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Spreadsheet Solutions
PV(rate, nper, PMT, [fv], [type])
PV(10%, 3, 100, 0, 0) = ($248.69)
*
Find the PV if the
annuity were an annuity due.
100
100
0
1
2
3
10%
100
*
*
Financial Calculator Solutions
N I/YR PV PMT FV
?
BGN END, N= 3, I/YR = 10, PMT = 100, FV = 0
CPT, PV
-273.55
/
INPUTS
OUTPUT
16
Spreadsheet Solutions
PV(rate, nper, PMT, [fv], [type])
PV(10%, 3, 100, 0, 1) = ($273.55)
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A series of equal payments or payments with constant growth rate made at fixed intervals for unlimited number of periods.
Perpetuity
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What’s the PV of a perpetuity that starts with a
payment $100 at the end of year 1, and the
payments growing at an annual 5% and invested
every year at a rate of 10%?
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Uneven Cash Flow Stream
0
100
1
300
2
300
3
10%
-50
4
90.91
247.93
225.39
-34.15
530.08
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- Input in “CFLO” register:
CF0 = 0
CF1 = 100
CF2 = 300
CF3 = 300
CF4 = -50
- Enter I = 10%, then press NPV button to get NPV = 530.09.
(Here NPV = PV.)
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Keystrokes Explanation
CE/C Clears display
CF
2nd CLR Clears cash flow variables
0 ENTER ↓ Stores the initial cash flow CF0=0
100 ENTER ↓ Stores the first year’s cash flow CF1=100
ENTER ↓ Stores the number of years CF1 is repeated
300 ENTER ↓ Stores CF2=300
2 ENTER ↓ Stores the number of years CF2 is repeated
50 +/- ENTER ↓ Stores CF3=-50
ENTER Stores the number of years CF3 is repeated
2nd QUIT Stores storage of individual cash flows
NPV
10 ENTER ↓ Stores interest rate
CPT Calculate the NPV
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Excel Formula in cell A3:
= NPV (rate, value 1, [value 2] ….)
= NPV (10%, 100, 300, 300, -50)
or = NPV (10%,B2:E2)
A B C D E
1 0 1 2 3 4
2 100 300 300 -50
3 530.09
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Bond Valuation
Key Features of a Bond:
1. Par value: Face amount; paid at maturity. Assume $1,000.
2. Coupon interest rate: Stated interest rate. Multiply by par value to get dollars of interest. Generally fixed.
(More…)
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3. Maturity: Years until bond must be repaid. Declines.
4. Issue date: Date when bond was issued.
5. Default risk: Risk that issuer will not make interest or principal payments.
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What’s the value of a 10-year, 10% coupon bond if kd = 10%?
V
k
k
B
d
d
$100
$1
,
1
000
1
1
10
10
.
.
.
+
$100
1
+
k
d
100
100
10%
100 + 1,000
V = ?
...
= $90.91 + . . . + $38.55 + $385.54
= $1,000.
+
+
+
+
0
1
2
10
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10 10 100 1000
N I/YR PV PMT FV
-1,000
The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10:
INPUTS
OUTPUT
$ 614.46
385.54
$1,000.00
PV annuity
PV maturity value
Value of bond
=
=
=
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10 13 100 1000
N I/YR PV PMT FV
-837.21
When kd rises, above the coupon rate, the bond’s value falls below par, so it sells at a discount.
What would happen if expected inflation rose by 3%, causing k = 13%?
INPUTS
OUTPUT
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What would happen if inflation fell, and kd declined to 7%?
10 7 100 1000
N I/YR PV PMT FV
-1,210.71
If coupon rate > kd, price rises above par, and bond sells at a premium.
INPUTS
OUTPUT
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Semiannual Bonds
1. Multiply years by 2 to get periods = 2n.
2. Divide nominal rate by 2 to get periodic rate = kd/2.
3. Divide annual INT by 2 to get PMT = INT/2.
2n kd/2 OK INT/2 OK
N I/YR PV PMT FV
INPUTS
OUTPUT
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2(10) 13/2 100/2
20 6.5 50 1000
N I/YR PV PMT FV
-834.72
Find the value of 10-year, 10% coupon,
semiannual bond if kd = 13%.
INPUTS
OUTPUT
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Different Approaches:
- Dividend growth model
- Using the multiples of comparable firms
- Free cash flow method
- CAPM (for public firms only)
Common Stock Valuation
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Stock Value = PV of Dividends
We apply our present value formula to dividends, with P-hat0 as today’s price of a share of stock, and the D’s equal to the dividend per share, to obtain the following equation:
The dividends can grow either at a constant rate (from negative to zero to positive), or a non-constant rate. When they grow at a constant rate, the above equation becomes:
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What happens if g > ks?
- If ks< g, get negative stock price, which is nonsense.
- We can’t use model unless (1) g ks and (2) g is expected to be constant forever. Because g must be a long-term growth rate, it cannot be ks.
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What’s the stock’s market value?
D0 = 2.00, ks = 13%, g = 6%.
Constant growth model:
= = $30.29.
0.13 - 0.06
$2.12
$2.12
0.07
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The value of Gordon’s Model
- The role of risk (ks), growth, and cash-flows is obvious.
- When: ks , g , or CFs (dividends) , then the stock price is greater.
- When: ks , g , or CFs (dividends) , then the stock price is lower.
- We can see that stock value is due largely to long-term growth, not short-term results.
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Super-Normal Growth Model
- Use this approach when short-term growth is greater than ks.
Consider an example for a firm which has:
- D0 = $2.40, and k = 12%,
- dividend growth at 25% for 4 years, and
- dividend growth at 5% per year forever
after the initial 4 years.
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Super-Normal Growth Model
Note that D1 = $3.00 and k = 12%
Dividends grow at 25% for 4 years, and then at 5% per year forever.
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Super-Normal Growth (Contd).
First, find the value of the stock at the end of the super-normal growth period (t = 4):
Note: The discount timing for the continuing value of $87.89 is t = 4.
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- PV of a series of cash flows (single cash flow, annuity, perpetuity, uneven cash flows)
- Bond valuation: annual or semi-annual compounding
- Stock valuation using dividend growth model: constant growth, super-normal growth
Lecture Highlights
(
)
(
)
(
)
i
+
1
CF
...
i
+
1
CF
i
+
1
CF
CF
=
PV
n
n
2
2
1
0
0
+
+
+
+
(
)
13
.
75
10%
+
1
100
=
PV
3
=
(
)
(
)
(
)
248.69
13
.
75
64
.
82
91
.
90
10%
+
1
100
10%
+
1
100
10%
+
1
100
=
PV
3
2
=
+
+
=
+
+
(
)
(
)
273.55
64
.
82
91
.
90
100
10%
+
1
100
10%
+
1
100
100
=
PV
2
=
+
+
=
+
+
CF
=
PV
1
0
g
i
-
2000
%
5
%
10
100
=
CF
=
PV
1
0
=
-
-
g
i
(
)
(
)
(
)
(
)
530.08
15
.
34
39
.
225
93
.
247
91
.
90
10%
+
1
50
-
10%
+
1
300
10%
+
1
300
10%
+
1
100
=
PV
4
3
2
=
-
+
+
=
+
+
+
ssss
k
D
k
D
k
D
k
D
P
1
. . .
111
ˆ
3
3
2
2
1
1
0
gk
D
P
s
1
0
ˆ
$
.
P
D
k
g
g
s
0
1
=
-
>
requires
k
s
(
)
$
P
D
g
k
g
D
k
g
s
s
0
0
1
1
=
+
-
=
-
1523.6$)05.1(8594.5$
8594.5$)25.1(6875.4$
6875.4$)25.1(75.3$
75.3$)25.1(00.3$
$3.00)$2.40(1.25D
5
4
3
2
1
D
D
D
D
891.87$
05.012.0
1523.6$
5
4
gk
D
P
58.68$
1
89.87$86.5$
1
69.4$
1
75.3$
1
00.3$
4321
0
kkkk
P
