Transcript Lecture 2 - Bauer College of Business

Lecture 5 & 6 Security
Valuation
Corporate Finance
FINA 4330
Ronald F. Singer
Fall, 2009
Present Value of Bonds &
Stocks
• At this point, we apply the concept of
present value developed earlier to price
bonds and stocks.
• Price of Bond =
Present Value of
Present Value of
+
Coupon Annuity
Principal
Example
Consider a 20 year bond with 6% coupon rate paid annually.
The market interest rate is 8%.
The face (par) value of the bond is $100,000.
• PV of coupon annuity = 20
6000
= 58,908
t
t=1(1 + 0.08)
• PV of principal=
100,000 = 21,455
(1 + 0.08)20
• Present Value of Total
=
80,363
• OR
By Calculator
• 20
•
N
8
I%YR
• 6000
PMT
• 100000
• PV
FV
80,363.71
Yield to Maturity
• YTM: The Annual Yield you would have to earn to
exactly achieve the cash flow promised by the
bond
• It is the internal rate of return of the bond
• It is that interest rate which makes the price of the
bond equal the present value of the promised
payments.
• Consider a bond with principal of $100,000 and a coupon, paid
semiannually, of 9%, selling for 99.375 (This is percent of the face
value), so that the actual price is
100,000 x .99375 = $99,375.
Maturity date is August 31, 2008.
The semiannual coupon payments are: 4.5% of 100,000 or 4,500.
(As of August 25, 2006)
4,500
0
1
2/10
4,500
2
4,500
104,500
3
4
8/11
•
99,375
99,375 = 4500
+
4500
+ 4500
+
(1+YTM)
(1+YTM)2 (1+YTM)3
2
2
2
• The Yield to Maturity is 9.35%.
104,500
(1+YTM)4
2
• By Calculator
4
-99375
4500
100000
ComPuTe
N
PV
PMT
FV
I/Y
x 2 = 9.35
4.000
-99375.000
4500.000
100000.000
4.6749
Corporate Bonds
Yahoo.com
• Bond Center Bond Center > Bond Screener > Bond
Screener Results
• Type Issue Price Coupon(%) Maturity YTM(%) Current
• Yield(%) Fitch Ratings Callable
Sprint 8.375s ’12 (5 payments)
Sprint 8.375s ‘12 “Name of Bond”
– Principal or Par: $1,000 (most US Corporate bonds
have $1,000 principal).
– Coupon (Annual): $83.75 or 8.375% of par
– Maturity : March 15, 2012
– Coupon Payment Dates: March 15, and
September 15 through March 15, 2012 (every 6
months)
– Current yield: 8.292%
Current = Coupon(% of par) = 8.375 = 8.292%
Yield
Price (% of par)
101.00
Actual Price = 101 times 1000 = $1010.00
The Bond's Yield to Maturity?
YTM = 7.961
Note in this case: YTM < Current Yield < Coupon: Why?
Calculation of YTM
Suppose we know the appropriate Yield to Maturity
("Discount Rate")
For Example: 10% (NB: Bond Quotes are in simple
interest)
The Bond Value is
P0= 5 41.875 + 1000
t=1 (1.05)t
(1.05)5
41.875..41.875..41.875………………………
1041.875
└────┴───┴───────┴────┴────────┴───
9/09 3/10 9/10
3/11 9/11
3/12
P0 = PVA(5,10%,41.875) + PV(5,10%,1000) + 41.875
Treasury Yield Curves
• www.bloomberg.com
Stocks
• www.finance.yahoo.com
• SPRINT NXTEL CP (NYSE:S)
Sprint Nextel (S) (8/21/09)
Last Trade: 3.90
Trade Time: Aug 21
Change
0.07 (1.83%)
Prev Close: 3.83
Open:
3.90
1y target Est. 5.35
Range:
3.84-3.93
52 wk Range: 1.35-9.35
Volume:
28,768,634
Avg Vol (3m): 42,768,900
Market Cap:
11.22B
P/E (ttm):
NA
EPS (ttm):
-1.02
DIV & Yield
N/A (N/A)
Sprint Nextel Corp
Current (Annual)
Yield = Dividend
Price
P-E Ratio = Closing Price
Current Earnings
Current =
EPS
Closing Price
P-E Ratio
• Stock Valuation
If we solve for Po, the current value of the stock
Po =
E(Div1) + E (P1)
1 + E(R)
= The Present Value of the Expected Payoffs to the
Stockholder.
This can be thought of as simply the Present Value of
the Dividend plus the price per share that you expect
to receive after a 1 year holding period.
Stock Valuation
This relation will hold through time,
therefore,
P1 = E (Div2) + E(P2)
1 + E(R)
Substitute for E(P1 ) in previous equation:
Po = E(Div1) + E(Div2) + E(P2)
1 + E(R)
(1 + E(R))2 (1 + E(R)) 2
The Value of Stock
This relation will hold through time, therefore,
P1 = E (Div2) + E(P2)
1 + E(R)
Substitute for P1
Po =
E(Div1) + E(Div2) +
E(P2)
1 + E(R)
( 1 + E(R))2
( 1 + E(R))2
And:
Po =
E(Div1) +
1 + E(R)
E(Div2) +
( 1 + E(R))2
E(Div3) +
( 1 + E(R))3
E(P3)
( 1 + E(R))3
So in general, we can think of a stock as equal to the
present value of a dividend stream over some time
period plus what you can get for the stock if you sold it
at the end of the time period. That is:
In general, Po = T E (Divt) + E(PT)
t=1 (1 + E(R))t (1 + E(R))T
Or, as the time period gets very large,
Present Value of E(PT)----> 0
And the stock price is the present value of all future
dividends paid to existing stockholders
Po = 
t=1
E (Divt)
(1 + E(R))t
Example: ABC corporation has established a policy of simply
maintaining its real assets and paying all earnings net of (real)
depreciation out as a dividend. Suppose that:
r = 10%
Net Investment = ?
Current Net Earning per Share is 10.
(Ignore Changes in Working Capital)
then:
EPS(1) =
EPS(2) . .=. . EPS(t). = 10
Year
growth
dividends
free cash flow
and:
1
0
10
10
Po =
2
0
10
10
10
.10
3
0
10
10
= 100
....
Now let this firm change its policy:
Let it take the first dividend (the dividend that would have been
paid at time 1) and reinvest it at 10%. then continue the policy of paying
all earnings out as a dividend.
We want to write the value of the firm as the present value of the
dividend stream, the present value of free cash flow and the present
value of Constant Earnings Per Share plus PVGO.
TIME
1
2
3
.....
EPS
10
11
11
DIVIDEND
0
11
11
FCFE
0
11
11
INVESTMENT
10
0
0
Present Value of Dividends 100
Present Value of Free Cash Flow to equity 100
Suppose return on investment were 20%? Suppose it were 5% ?
Capitalized Value of Dividends
Consider the value of the stock (or the per share Price of the
stock)
The basic rule is: The value of the stock is the present value of the
cash flows to the stockholder. This means that it will be the
present value of total dividends (or dividends per share), paid to
current stockholders over the indefinite future
.
That is:
V(o) =  E{ Dividend(t)}
t=1
(1 + r)t
or:
P(0) =

E{ DPS(t) }
t=1
(1 + r)t
This equation represents: The Capitalized Value of Dividends
Capitalized Value of Dividends
The problem is how to make this OPERATIONAL.
That is, how do we use the above result to get at actual valuation?
We can use two general concepts to get at this result: They all involve the
above equation under different forms.
(1) P0 =EPS(1) + PVGO
r
(2) P0 =  (FCFE per Share)t
t=1
(1 + r)t
EPS(1) is the expected Earnings per share over the next period.
PVGO is the "present value of growth opportunities.
r is the "appropriate discount rate
FCFE per share is the Free Cash Flow to Equity per Share that is, the
cash flow available to stockholders after the bondholders are paid off and
after investment plans are met.
Capitalized Dividend Model
Simple versions of the Capitalized Dividend Model
DIV(1) = DIV(2) = . . . = DIV(t) = ...
The firm's dividends are not expected to grow.
essentially, the firm is planning no additional
investments to propel growth. thus:
with investment zero:
DIV(t) = EPS(t) = Free Cash Flow(t)
PVGO = 0
therefore the firm (or stock) value is simply:
P0 = DIV= EPS = FCFE
r
r
r
Constant Growth Model
New let the firm plan to reinvest b of its earnings at a rate of return of i through
the indefinite future. Then annual growth in earnings, dividends, and the
price per share will be a constant equal to:
g = b x i,
b is the “Plowback Ratio” or (1 – “Payout ratio”) or the Net Investment as a
percentage of earnings.
i is th Return on Equity (ROE)
note that: in the special case that Change in Working Capital is zero:
EPS = Would be Free Cash Flow to equity if Net Investment were zero, so
that:
DIV(t) = (1 - b)EPS(t) = Free Cash Flow to Equity(t)
and we can write the valuation formula as:
P0 = DIV(1) = (1-b)EPS(1) = Free Cash Flow to Equity (1)
r-g
r-g
r-g
= EPS(1) + PVGO
r
This value of the firm can be represented by
vo = EPS1 + PVGO:
r
where,
PVGO =  NPV(t)
t=1 (1+r)t
Notice: if the NPV’s of future projects are positive then
the value of the stock, and its price per share will be
higher, given its current earnings and its
capitalization rate
General Equation for Firm
Valuation
• Stock Value can be represented by the PV
of a Dividend Annuity plus the predicted
stock price at the end of the Annuity.
•
DIV
DIV + P(T)