Transcript Lecture 6 Managerial Finance FINA 6335 Bond and Stock Valuation Ronald F. Singer Present Value of Bonds & Stocks • At this point, we apply the.

Lecture 6
Managerial Finance
FINA 6335
Bond and Stock Valuation
Ronald F. Singer
Present Value of Bonds &
Stocks
• At this point, we apply the concept of
present value developed earlier to price
bonds and stocks.
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 value of the bond is $100,000. (referred to as par)
• PV of coupon annuity = 20
6000
= 58,908
(1 +
t=1
0.08)
• PV of principal
=
100,000
= 21,455
(1 + 0.08)20
• Present Value of Total
• OR
=
80,363
Yield to Maturity
• By Calculator
N = 20
I%YR = 8
PMT = 6,000
FV = 100,000
PV => 80,363.71 or 80.364% of par.
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 IF the
promised payments are all paid.
• It is that interest rate which makes the price of the
bond equal the present value of the promised
payments.
Characteristics of US Bonds
• Promised Payments include Coupon Payments
and Principle (Face Value or Par Value)
• Coupons are quoted as annualized percent of
the Face Value
• Coupons are usually paid semi-annually, at the
month of the maturity date and six months later.
• Principle is usually in $1,000 increments
• Prices are quoted as % of Face Value
• Quote Bond: ATT 7s ‘10
• 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 March 1, 2010.
The semiannual coupon payments are: 4.5% of 100,000 or 4,500.
(As of March 1, 2008)
0
4,500
1
4,500
2
4,500
3
9/08
•
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
4
3/10
104,500
(1+YTM)4
2
• By Calculator
4
-99375
99375.000
4500
4500.000
100000
100000.000
CPT
4.6749
N
4.000
PV
PMT
FV
I/Y
-
Bond Pricing
From Yahoo! Finance (finance.yahoo.com)
Click: Investing>bonds>Bond Center
Type
Corp
Current
Issue
Price Coupon Maturity YTM Yield
ABBOTT 96.38 3.750
3/15/11 4.825 3.891
LABS
Fitch
Rating
AA
18.75 18.75
18.75…………………………1018.75
$963.80
3/08 9/08
3/09
3/11
– Principal: $1,000 (most US Corporate bonds have
$1,000 principal).
– Coupon (Annual): $37.50
– Maturity : March 15, 2011
– Current yield: 3.891%
Current = Coupon = 3.75 = 3.891%
Yield
Price
96.38
Price = ..9638 x 1000 = $963.80
What is the bond's Accrual (we can assume 90 day
quarters) So
Accrual = Coupon (Days from last Coupon/Days in
coupon period)
= (37.5) X (162) = 16.875
2
180
Cash (Dirty) price is = $963.80 + 16.875 = 980.675
Note in this case: YTM > Current Yield > Coupon: Why?
Calculating Bond Price
Suppose we know the appropriate Yield to Maturity
("Discount Rate")
For Example: 5% (NB: Bond Quotes are in simple
interest)
The Bond Value is
P0=  18.75 + 1000
t=1 (1.025)t (1.025)7
P = $960.32 or 96.03 (% of par)
Calculating YTM
• Suppose price was 98 ($980). What is the
yield to maturity?
• N=7
• PV = -98
• PMT = 1.875
• FV = 100
• CPT I% = 2.1862 X 2 = YTM = 4.37
Treasury Bonds, Notes and Bills
Type
Issue
Zero
US Treas
Treas US Treas
Treas US Treas
Current Fitch
Price Coupon Maturity YTM Yield Rating
89.74 0.000
105.03 5.750
100.60 4.125
8/15/10 3.733 0.000
8/15/10 3.912 5.474
8/15/10 3.904 4.100
AAA
AAA
AAA
Valuing Bonds Using Law of One
Price
• Strips: Zero Coupon Treasuries. These
are called “strips” because it is a regular
(coupon) bond with the coupons stripped
away, so that you only have the principal
or face value.
From Yahoo Finance
Strips
Maturity
8/15/08
2/15/09
8/15/09
2/15/10
Price
96.82
95.09
93.44
91.39
Value US Treas 6.50s, 2/15/10
6
.
58/08
0
2/09
8/09
2/10
Value US Treas 6.50s, 2/15/10
3.25
6
.
58/08
0
3.25
2/09
3.25
103.25
8/09
2/10
Value US Treas 6.50s, 2/15/10
To Value this Bond using Zero’s
Date Paid
PV
First coupon
8/15/08 .9682*3.25 = 3.1467
Second coupon
2/15/09 .9509*3.25 = 3.0904
Third coupon
8/15/09 .9344*3.25 = 3.0368
Fourth coupon
+ Principal
YTM = ???
2/15/10
.9139*103.25 =94.3602
103.63
Valuation of Common Stock
• The Annual Expected Return on a share of common stock is
composed of two components:
Dividends and Capital Gains
Expected Returns:
E(R0) = Dollar Return
= E(Div1) + E (P1) - Po
Price
P0
P0
Where
•
P0 = The current per share price
E(Div1) = Expected dividend per share at time 1
E(P1) = Expected price per share at time 1
E(Ro) = Expected Return
E(R0) = expected dividend yield + expected capital gain return
• From Yahoo! Finance
• OCCIDENTAL PET (NYSE:OXY)
• Last Trade:79.16
Trade
Time:11:47AM ET
• Change: 0.46 (0.58%)
Prev Close:78.70
• Open:78.29
1y Target Est:82.73
• Day's Range:78.29 - 79.9152
• wk Range:44.85 - 80.83
• Volume:1,884,459
Avg Vol (3m):7,065,790
• Market Cap:65.36B
P/E (ttm):12.30
• EPS (ttm):6.44
Div & Yield:1.00 (1.30%)
Analysis of OXY
• Yield = Current Quarterly Dividend X 4
Price
P/E Ratio = Most Recent Price
EPS (ttm)
ttm means the “trailing twelve months”
So you can solve for Earning per Share
• Note, we don't observe E(Ro) but we observe prices
and promised payoffs.
If we solve for Po, the current value of the stock
Po = E(Div1) + E (P1)
1 + E(R)
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
In general, Po = T E (Divt) + E(PT)
t=1 (1 + E(R))t (1 + E(R))T
You can think of E(PT) as a liquidating dividend equal to
the value of firm's assets at time T.
As T ----> 00,
Present Value of E(PT)----> 0
And the stock price is the present value of all future
dividends paid to existing stockholders
Po = 00 E (Divt)
t=1 (1 + E(r))t What happened to capital gain?
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) =
or:
oo
 E{ Dividend(t)}
t=1
(1 + r)t
P(0) =  E{ DPS(t) }
t=1
(1 + r)t
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) P = EPS1 + PVGO
r
(2) P =  (Free Cash Flow per Share(t))
t=1
(1 + r)t
EPS1 is the expected earnings per share over the next period.
PVGO is the "present value of growth opportunities.
r is the "appropriate discount rate
Free Cash Flow per Share 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
r
r
Constant Growth Model
Next suppose that the firm plans to reinvest b of its earnings at a
rate of return of i throughout the indefinite future. Then growth
will be a constant level of:
g = b x i,
b is the “plowback” or “retention” rate, and 1-b is the dividend
payout.
and, g is the constant growth rate in dividends, earnings, earnings
per share, and the stock price
note that under simplifying assumptions:
DIV(t) = (1 - b)Earnings(t) – DWC +DEP
= Free Cash Flow to Stockholders(t).
Total Payout Model
• Sometimes firms substitute share
repurchase for dividends. Under those
circumstances we can think of the cash
flow to stockholders, as the sum of
Dividends plus share repurchases. Then,
the Total payout model would be the
present value of future dividends and
repurchases, and the share price is simply
that present value per CURRENT
outstanding shares.
Constant Growth Model
Lets assume that DWC +DEP = 0, and there are
no interest payments, for simplicity, so that
(EPS) = Cash Flow from Operations per share.
we can write the valuation formula as:
P0 = DIV(1) = (1-b)EPS(1) = Free Cash Flow(1)
r-g
r-g
r-g
= EPS(1) + PVGO
r
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.
Assume, Change in working capital is 0 throughout:
suppose that: r = 10%
Net Investment = ?
Current Net Earning per Share is 10.
then:
EPS(1) =
EPS(2) . .=. . EPS(t). = 10
Year
growth
dividends
free cash flow
Thus:
Po =
1
10
0.10
0
10
10
= 100
2
3
0
10
10
0
10
10
....
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
.....
earnings
10
dividends
0
free cash
flow
investment
Present Value of Dividends
Present Value of Free Cash Flow
Present Value of current Earnings plus Present Value of growth
opportunities. Suppose return on investment were 20%? Suppose it were
5% ?
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
.....
earnings
10
11
11
dividends
0
11
11 ……….
free cash
0
11
11
flow
investment
10
0
Present Value of Dividends
Present Value of Free Cash Flow
Present Value of current Earnings plus Present Value of growth
opportunities. Suppose return on investment were 20%? Suppose it were
5% ?
This value of the firm can be represented by
Po = EPS1 + PVGO:
r
where,
PVGO =  NPV(t)
t=1 (1+r)t
Notice: if the NPV of future projects is positive
then the value of the stock, and its price per
share will be higher, given its current earnings
and its capitalization rate
Free Cash Flow Model
Free Cash Flow = EBIT(1-t) +Depreciation
- CapExp – DWC
Then the Value of the Firm, V = PV of FCF
And Equity value = V – Debt + Cash
P = (Equity value)/(Shares outstanding)
Discounted Free Cash Flow Model
• Approach: Determine the (present) value
of the total cash flow to all Security
holders, and then subtract the value of all
securities other than equity to get the
Equity Value of the firm.
•
Cash Flow to all Security Holders
• The Cash flow to all security holders is the
firm’s Free Cash Flow. So!
• Free Cash Flow = EBIT(1-t) +Depreciation
– Capital Expenditures – Increase in
Working Capital
A Simple Example
• Assume Free Cash Flow grows at a constant
rate over time. Historically this has been 8%
Suppose we have the following data:
• Earnings = 5.2 million
• EBIT = 10 million
• Depreciation = 2 million
• Interest = 3 million
• Increase in Working capital is .5 million
• Capital Expenditures is 3 million
• Legal tax rate is 35%
Free Cash Flow
• FCF = EBIT(1-t) + Depreciation –Increase
in WC – CapEx
•
= 10(1-.35) + 2 - .5 + 3
= 6.5 + 2 -.5 + 3 = 11
If this will grow at 8% per year, and the cost
of capital is 15%, then the
The value of the firm is: 11 = 157.15 m
.07
Estimating Growth
•
•
•
•
•
•
•
Can use historical averages or:
Dividends = 8 million
Return on Assets = 20%
Dividend Payout = 6/11 = 54.55%
Retention Rate(b) = 1-.5455 = .4545
Since ROA (i) = 20%
g = b X i = .2 X .4545 = 9.09%, so
• V=
11
(.15-.0909)
= $186.12M
The Discount Rate
• We are using the Cash Flow to all security
holders, and we want to know what the
appropriate rate to discount that cash flow.
• We will see that the appropriate discount
rate is the WACC, which is the average
return required by all security holders
having a claim to that cash flow.
• More about this later