Principles of Managerial Finance 9th Edition

1
Principles of Managerial Finance9th Edition

• Chapter 7

Bond Stock Valuation
2
Learning Objectives

• Describe the key inputs and basic model used in
  the valuation process.
• Apply the basic bond valuation model to bonds and
  describe the impact of required return and time
  to maturity on bond values.
• Explain yield to maturity (YTM), its calculation,
  and the procedure used to value bonds that pay
  interest semiannually.

3
Learning Objectives

• Understand the concept of market efficiency and
  basic common stock valuation under each of three
  cases zero growth, constant growth, and variable
  growth.
• Discuss the use of book value, liquidation value,
  and price/earnings (PE) multiples to estimate
  common stock values.
• Understand the relationships among financial
  decisions, return, risk, and the firms value.

4
Valuation Fundamentals

• The (market) value of any investment asset is
  simply the present value of expected cash flows.
  
• The interest rate that these cash flows are
  discounted at is called the assets required
  return.
• The required return is a function of the expected
  rate of inflation and the perceived risk of the
  asset.
• Higher perceived risk results in a higher
  required return and lower asset market values.

5
Basic Valuation Model
V0 CF1 CF2 CFn
(1 k)1 (1 k)2
(1 k)n
Where V0 value of the asset at time zero CFt
cash flow expected at the end of year t k
appropriate required return (discount rate) n
relevant time period
6

• Ex1. ??????A?????????300??????,??????12,????????
  
• V0 300(PVIFA12,8) 300/0.122,500
• EX2. ?????????????85,000,??????15,??????
• V085,000PVIF15,542,245
• EX 3. ????????????????????
• 2,000?4,000?0?10,000,??????20,??????
• V02,000PVIF20,14,000PVIF20,210,000PVIF2
  0,49,262

7
What is a Bond?

• A bond is a long-term debt instrument that pays
  the bondholder a specified amount of periodic
  interest over a specified period of time.

(note that a bond debt)
8
General Features of Debt Instruments
Maturity value, face value, par value, future
value

• The bonds principal is the amount borrowed by
  the company and the amount owed to the bond
  holder on the maturity date.
• The bonds maturity date is the time at which a
  bond becomes due and the principal must be
  repaid.
• The bonds coupon rate is the specified interest
  rate (or amount) that must be periodically
  paid.
• The bonds current yield is the annual interest
  (income) divided by the current price of the
  security.

9
General Features of Debt Instruments
?holding period return??

• The bonds yield to maturity is the yield
  (expressed as a compound rate of return) earned
  on a bond from the time it is acquired until the
  maturity date of the bond.
• A yield curve graphically shows the relationship
  between the time to maturity and yield to
  maturity for debt in a given risk class.

10
Bonds with Maturity Dates
Annual Compounding
B0 I1 I2 (In
Pn) (1i)1 (1i)2
(1i)n
For example, find the price of a 10 coupon bond
with three years to maturity if market interest
rates are currently 10.
B0 100 100 (1001,000)
(1.10)1 (1.10)2
(1.10)3
100
100
1001000
0
1
2
3
11
Bonds with Maturity Dates
Annual Compounding
Using Excel
For example, find the price of a 10 coupon bond
with three years to maturity if market interest
rates are currently 10.
Note the equation for calculating price is
PV(rate,nper,pmt,fv)
0.1 3 100 1000
12
Bonds with Maturity Dates
Annual Compounding
Using Excel
For example, find the price of a 10 coupon bond
with three years to maturity if market interest
rates are currently 10.
When the coupon rate matches the discount rate,
the bond always sells for its par value.
Sell at par
13
Bonds with Maturity Dates
Annual Compounding
Using Excel
What would happen to the bonds price if interest
rates increased from 10 to 15?
Why different? (1) economic condition changed
(2) firms risk changed
When the interest rate goes up, the bond price
will always go down.
Sell at a discount
14
Bonds with Maturity Dates
Annual Compounding
Using Excel
What would happen to the bonds price it had a 15
year maturity rather than a 3 year maturity?
And the longer the maturity, the greater the
price decline.
15
Bonds with Maturity Dates
Annual Compounding
Using Excel
What would happen to the original 3 year bonds
price if interest rates dropped from 10 to 5?
When interest rates go down, bond prices will
always go up.
Sell at a premium
16
Bonds with Maturity Dates
Annual Compounding
Using Excel
What if we considered a similar bond, but with a
15 year maturity rather than a 3 year maturity?
And the longer the maturity, the greater the
price increase will be.
17
Graphically
10 coupon bond, ??1,000
??????,??????,????
15-year bond
Bond prices go down
As interest rates go up
18
Bonds with Maturity Dates
Semi-Annual Compounding
Using Excel
If we had the same bond, but with semi-annual
coupon payments, we would have to divide the 10
coupon rate by two, divided the discount rate by
two, and multiply n by two.
For the original example, divide the 10 coupon
by 2, divide the 5 discount rate by 2, and
multiply 3 years by 2.
19
Bonds with Maturity Dates
Semi-Annual Compounding
?4?????? ?EAR(1i/3)3-1
Using Excel
??????? NoteEAR(1i/2)2-1
If we had the same bond, but with semi-annual
coupon payments, we would have to divide the 10
coupon rate by two, divided the discount rate by
two, and multiply n by two.
Thus, the value is slightly larger than the price
of the annual coupon bond (1,136.16) because the
investor receives payments sooner.
20
Coupon Effects on Price Volatility
??????????

• The amount of bond price volatility depends on
  three basic factors
• length of time to maturity
• risk
• amount of coupon interest paid by the bond

changes in the bond price for a given change
in required return
Required return, discount rate, expected return,
yield to maturity, market interest rate

• First, we already have seen that the longer the
  term to maturity, the greater is a bonds
  volatility
• Second, the higher the market interest rate, the
  lower the price volatility.

21
Coupon Effects on Price Volatility

• The amount of bond price volatility depends on
  three basic factors
• length of time to maturity
• risk
• amount of coupon interest paid by the bond

• Finally, the amount of coupon interest also
  impacts a bonds price volatility.
• Specifically, the lower the coupon, the greater
  will be the bonds volatility, because it will be
  longer before the investor receives a significant
  portion of the cash flow from his or her
  investment.

22
Coupon Effects on Price Volatility
(1)???53.8 (2)???47.7 ??5coupon bond???????
(2)
(1)
?????????,?????????
15 coupon bond
5 coupon bond
??YTM(????)??????????
5
23
Price Converges on Par at Maturity

• It is also important to note that a bonds price
  will approach par value as it approaches the
  maturity date, regardless of the interest rate
  and regardless of the coupon rate.

24
Price Converges on Par at Maturity

• It is also important to note that a bonds price
  will approach par value as it approaches the
  maturity date, regardless of the interest rate
  and regardless of the coupon rate.

25
Yields

• The Current Yield measures the annual return to
  an investor based on the current price.

Current Annual Coupon Interest Yield
Current Market Price
For example, a 10 coupon bond which is currently
selling at 1,150 would have a current yield of
Current 100 8.7 Yield
1,150
26
Yields
??bond price,????YTM

• The yield to maturity measures the compound
  annual return to an investor and considers all
  bond cash flows. It is essentially the bonds
  IRR based on the current price.

PV I1 I2 (In
Pn) (1i)1 (1i)2
(1i)n
Notice that this is the same equation we saw
earlier when we solved for price. The only
difference then is that we are solving for a
different unknown. In this case, we know the
market price but are solving for return.
27
Yields

• The yield to maturity measures the compound
  annual return to an investor and considers all
  bond cash flows. It is essentially the bonds
  IRR based on the current price.

Using Excel
For Example, suppose we wished to determine the
YTM on the following bond.
28
Yields

• The yield to maturity measures the compound
  annual return to an investor and considers all
  bond cash flows. It is essentially the bonds
  IRR based on the current price.

Using Excel
To compute the yield on this bond we simply
listed all of the bond cash flows in a column
and computed the IRR
IRR(d10d20)
29
Yields

• The yield to maturity measures the compound
  annual return to an investor and considers all
  bond cash flows. It is essentially the bonds
  IRR based on the current price.

• Note that the yield to maturity will only be
  equal if the bond is selling for its face value
  (1,000).
• And that rate will be the same as the bonds
  coupon rate.
• For premium bonds, the coupon interest rate gt
  YTM.
• For discount bonds, the coupon interest rate lt
  YTM.

Bond price gt face value
Bond price lt face value
30
Yields

• The yield to call is the yield earned on a
  callable bond.
• To calculate the yield to call, simply substitute
  the call date for the maturity date plus the call
  premium if there is one.

For Example, suppose we wished to determine the
yield to call (YTC) on the following bond where
the call premium is equal to one year extra
coupon interest.
???callable bond??10????call
31
Yields

• The yield to call is the yield earned on a
  callable bond.
• To calculate the yield to call, simply substitute
  the call date for the maturity date plus the call
  premium if there is one.

Yield to call
32
Risk and Yield Fluctuations
33
Risk and Yield Fluctuations
34
The Reinvestment Rate Assumption

• It is important to note that the computation of
  the YTM implicitly assumes that interest rates
  are reinvested at the YTM.
• In other words, if the bond pays a 100 coupon
  and the YTM is 8, the calculation assumes that
  all of the 100 coupons are invested at that
  rate.
• If market interest rates fall, however, the
  investor may be forced to reinvest at something
  less than 8, resulting a a realized YTM which is
  less than promised.
• Of course, if rates rise, coupons may be
  reinvested at a higher rate resulting in a higher
  realized YTM.

Interest rate risk price risk
reinvestment risk
35
???????(holding period return) ????????10,??1000
,???????,?????????10,???YTM10,?????1000???????
??????????11,?HPR? B1 100/1.111100/(1.11)2
983 HPR (B1-B0I1) / B0 (983-1000100) / 1000
0.083 HPR (B1-B0)/B0I1/B0 expected capital
gain return
current yield HPR?YTM
36
Common Stock Valuation
Stock Returns are derived from both dividends and
capital gains, where the capital gain results
from the appreciation of the stocks market
price.due to the growth in the firms earnings.
Mathematically, the expected return may be
expressed as follows
Expected return on stock
E(r) D1/P0 g
Expected 1 dividend in year one
For example, if the firm expects to pay 1
dividend in first year on a 25 stock and the
dividend is expected to grow at 7, the expected
return is
E(r) 1/25 .07 11
37
Stock Valuation Models
The Basic Stock Valuation Equation
38
Stock Valuation Models
The Zero Growth Model

• The zero dividend growth model assumes that the
  stock will pay the same dividend each year, year
  after year.
• For assistance and illustration purposes, I have
  developed a spreadsheet tutorial on Excel.
• A non-functional excerpt from the spreadsheet
  appears on the following slide.

39
Stock Valuation Models
The Zero Growth Model
Using Excel
40
Stock Valuation Models
The Zero Growth Model
??preferred stock???
Using Excel
41
Stock Valuation Models
The Constant Growth Model

• The constant dividend growth model assumes that
  the stock will pay dividends that grow at a
  constant rate each year -- year after year.
• For assistance and illustration purposes, I have
  developed a spreadsheet tutorial using Excel
• A non-functional excerpt from the spreadsheet
  appears on the following slide.

42
Stock Valuation Models
The Constant Growth Model
Using Excel
43
Stock Valuation Models
The Constant Growth Model
Using Excel
expected first year dividend yield
???g,??????k?????????,????????????(??CAPM????
),

???????,k ???????????,???????????????,?????????
???
?????????????????????????,??????,??
??? ,??????????,???????????????,??????,??
k ?? ???
44
Stock Valuation Models
Variable Growth Model

• The non-constant dividend growth model assumes
  that the stock will pay dividends that grow at
  one rate during one period, and at another rate
  in another year or thereafter.
• For assistance and illustration purposes, I have
  developed a spreadsheet tutorial available under
  the heading Course Materials on Course
  Web-Page.
• A non-functional excerpt from the spreadsheet
  appears on the following slide.

45
Stock Valuation Models
Variable Growth Model
Using Excel
46
Stock Valuation Models
Variable Growth Model
2.5(110)1
2.5(110)2
47
Stock Valuation Models
Variable Growth Model
2.75
3.03
0
1
2
3
4
V2
V0
48
Stock Valuation Models
Variable Growth Model
49
??????????????? (free cash flow discounted model)

• (1) FCFs (EBIT-Int)(1-T) Dep - CE - ?NWC RP
  New Debt
• (2) FCFB Int (1-T) RP - New Debt
• (3) FCFA EBIT(1-T) Dep CE - ?NWC
• EBIT (1-T) - ?NFA ?NWC
• NoteCE ???? (capital expenditure)
• ?PPE ( property, plant,
  equipment)
• ?GFA (?????????????)
• RP??????? (principal repayment)
• ?NFA ????????????
• NWC (CA Cash - marketable
  security) - (CL - Long- term
• Debt matured in one
  year)
• (?) ???? ? FCFs,t / (1Ks )t / number of
  shares
• (?) ???? ? FCFA,t / (1KA)t -B / number of
  shares
• KA WACC KSS / (BS) KB(1-T)B
  / (BS)

50
Other Approaches to Stock Valuation
Book Value

• Book value per share is the amount per share that
  would be received if all the firms assets were
  sold for their exact book value and if the
  proceeds remaining after paying all liabilities
  were divided among common stockholders.
• This method lacks sophistication and its reliance
  on historical balance sheet data ignores the
  firms earnings potential and lacks any true
  relationship to the firms value in the
  marketplace.

51
Other Approaches to Stock Valuation
Liquidation Value

• Liquidation value per share is the actual amount
  per share of common stock to be received if al of
  the firms assets were sold for their market
  values, liabilities were paid, and any remaining
  funds were divided among common stockholders.
• This measure is more realistic than book value
  because it is based on current market values of
  the firms assets.
• However, it still fails to consider the earning
  power of those assets.

52
Other Approaches to Stock Valuation
Valuation Using P/E Ratios

• Some stocks pay no dividends. Using P/E ratios
  are one way to evaluate a stock under these
  circumstances.
• The model may be written as
• P (m)(EPS)
• where m the estimated P/E multiple.

For example, if the estimated P/E is 15, and a
stocks earnings are 5.00/share, the estimated
value of the stock would be P 155 75/share.
53
Other Approaches to Stock Valuation
Weaknesses of Using P/E Ratios

• Determining the appropriate P/E ratio.
• Possible Solution use the industry average P/E
  ratio
• Determining the appropriate definition of
  earnings.
• Possible Solution adjust EPS for extraordinary
  items
• Determining estimated future earnings
• forecasting future earnings is extremely difficult

54
Decision Making and Common Stock Value

• Valuation equations measure the stock value at a
  point in time based on expected return and risk.

55
Decision Making and Common Stock Value
Changes in Dividends or Dividend Growth

• Changes in expected dividends or dividend growth
  can have a profound impact on the value of a
  stock.

56
Decision Making and Common Stock Value
Changes in Risk and Required Return

• Changes in risk or required return can have a
  profound impact on the value of a stock.

??ks??,p??,?
,??????????????????, ks??,?????????
57
Decision Making and Common Stock Value
Changes in Risk and Required Return

• Combined effect