Chapter 7 slides

Principles of Managerial Finance

9th Edition

Chapter 7

Bond & Stock Valuation

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.

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 firm’s value.

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 asset’s 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.

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

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)

General Features of Debt Instruments

• The bond’s principal is the amount borrowed by the

company and the amount owed to the bond holder on

the maturity date.

• The bond’s maturity date is the time at which a bond

becomes due and the principal must be repaid.

• The bond’s coupon rate is the specified interest rate

(or $ amount) that must be periodically paid.

• The bond’s current yield is the annual interest

(income) divided by the current price of the security.

General Features of Debt Instruments

• The bond’s 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 yields for debt in a

given risk class.

Bonds with Maturity Dates

Annual Compounding

B0 = I1 + I2 + … + (In + Pn)

(1+i)1 (1+i)2 (1+i)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 + (100+1,000)

(1+.10)1 (1+i)2 (1+.10)3

Using Excel


are currently 10%.

Coupon Interest ($) 100$ Maturity (periods) 3Face Value ($) 1,000$ Market Interest Rate (%) 10%Market Price ($) ($1,000.00)

Finding the Value of a Bond

Note: the equationfor calculating

price is =PV(rate,nper,pmt,fv)


Annual Compounding



When the coupon rate matches the discount rate, thebond always sellsfor its par value.


Annual Compounding

Using Excel


are currently 10%.

What would happen to the bond’s price if interest rates increased from 10% to 15%?

When the interestrate goes up, the bond price will

always go down.

Coupon Interest ($) 100$ Maturity (periods) 3Face Value ($) 1,000$ Market Interest Rate (%) 15%Market Price ($) ($885.84)



Annual Compounding

Using Excel

What would happen to the bond’s price it had a 15 year maturity rather than a 3 year maturity?

And the longer thematurity, the greater

the price decline.

Coupon Interest ($) 100$ Maturity (periods) 15Face Value ($) 1,000$ Market Interest Rate (%) 15%Market Price ($) ($707.63)



Annual Compounding

Using Excel

What would happen to the original 3 year bond’s price if interest rates dropped from 10% to 5%?

When interest ratesgo down, bond

prices will alwaysgo up.




Annual Compounding

Using Excel

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 thematurity, the greater

the price increase willbe.




Effect of Changes in Interest Rates on Price

$-

$200

$400

$600

$800

$1,000

$1,200

$1,400

$1,600

5% 10% 15%

3 yr bond

15 yr bond

Graphically

As interest rates go up

Bo

nd

pri ces g

o d

ow

n


Semi-Annual Compounding

Using Excel

For the originalexample, divide the 10%

coupon by 2, dividethe 15% discount rate

by 2, and multiply3 years by 2.

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 isslightly larger than the

price of the annual coupon bond (1,136.16)

because the investorreceives payments

sooner.

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.




Semi-Annual Compounding

Using Excel

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

• First, we already have seen that the longer the term to

maturity, the greater is a bond’s volatility

• Second, the riskier a bond, the more variable the

required return will be, resulting in greater price

volatility.

• Finally, the amount of coupon interest also impacts a

bond’s price volatility.

• Specifically, the lower the coupon, the greater will be

the bond’s volatility, because it will be longer before

the investor receives a significant portion of the cash

flow from his or her investment.

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

Interest Price PriceRate 5% Coupon 15% Coupon

0% 1,500$ 2,500$ 10% 693$ 1,307$ 20% 371$ 790$

10 Year Bond


$-

$500

$1,000

$1,500

$2,000

$2,500

$3,000

0% 10% 20%

5% Coupon

15% Coupon

Coupon Effects on Price Volatility

Price Converges on Par at Maturity• It is also important to note that a bond’s price will

approach par value as it approaches the maturity date,

regardless of the interest rate and regardless of the

coupon rate.

Interest Price PriceRate 20 Years 1 Year

0% 3,000$ 1,100$ 10% 1,000$ 1,000$ 20% 513$ 917$

10% Coupon Bond


$-

$500

$1,000

$1,500

$2,000

$2,500

$3,000

$3,500

0% 10% 20%

20 Years

1 Year

Price Converges on Par at Maturity• It is also important to note that a bond’s price will

approach par value as it approaches the maturity date, regardless of the interest rate and regardless of the coupon rate.

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

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

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.

PV = I1 + I2 + … + (In + Pn)

(1+i)1 (1+i)2 (1+i)n

Yields

Using Excel

For Example, suppose we wished to determine the YTM on the following bond.

Market Price ($) ($1,000.00)Coupon Interest ($) 100$ Maturity (periods) 10Face Value ($) 1,000$ Market Interest Rate (%) ?

Finding Yield to Maturity

Yields• The yield to maturity measures the compound annual

return to an investor and considers all bond cash flows. It is essentially the bond’s IRR based on the current price.

Period Cash Flow0 ($1,000.00)

Market Price ($) ($1,000.00) 1 100$ Coupon Interest ($) 100$ 2 100$ Maturity (periods) 10 3 100$ Face Value ($) 1,000$ 4 100$ Market Interest Rate (%) 10% 5 100$

6 100$ 7 100$ 8 100$ 9 100$ 10 1,100$

Finding Yield to Maturity

To compute the yield on this bondwe simply listedall of the bond cash flows in a

column andcomputed the

IRR =IRR(d10:d20)



Using Excel

• 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 bond’s coupon

rate.

• For premium bonds, the current yield > YTM.

• For discount bonds, the current yield < YTM.



• 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.

Market Price ($) ($1,000.00)Coupon Interest ($) 100$ Maturity (periods) 10Face Value ($) 1,000$ Call Premium 100$ Market Interest Rate (%) ?

Finding Yield to Call

Yields

Period Cash Flow0 ($1,000.00)

Market Price ($) ($1,000.00) 1 100$ Coupon Interest ($) 100$ 2 100$ Maturity (periods) 10 3 100$ Face Value ($) 1,000$ 4 100$ Call Premium 100$ 5 100$ Market Interest Rate (%) 11% 6 100$

7 100$ 8 100$ 9 100$ 10 1,200$

Finding Yield to Call

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.

Risk and Yield Fluctuations

S&P Bond Yield toBond Issue Rating MaturityAT&T, 7 3/4, 07 AA 7.08%Seagram & Sons, 8 5/8, 07 AA 7.16%Long Island Lighting, 7 1/2, 07 BB+ 9.23%Inland Steel, 9.9, 07 BB- 9.64%

Bond Ratings and Yields for Bonds Maturing in 2007

Moody's Aaa versus Baa Yield Spread

5%

7%

9%

11%

13%

15%

17%

1965 1970 1975 1980 1985 1990 1995 2000 Year

Aaa

Baa

Risk and Yield Fluctuations

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.

Common Stock ValuationStock Returns are derived from both dividends and capital gains, where the capital gain results from the appreciation of the stock’s market price.due to the growth in the firm’s earnings. Mathematically, the

expected return may be expressed as follows:

E(r) = D/P + g

For example, if the firm’s $1 dividend on a $25 stock is expected to grow at 7%, the expected

return is:

E(r) = 1/25 + .07 = 11%

Stock Valuation Models

The Basic Stock Valuation Equation

)1(...

)1(

2

)1( 211

k

D

k

D

k

DPO

• 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.


The Zero Growth Model

1. Zero Growth (Constant Dividend) Model

A. Solving for Price: V = D/k, where D = dividend and k = required return

What would an investor be willing to pay for a stock if she expected to receivea dividend of $2.50 each year indefinitely and her required return is 15%?

D 2.50$ k 15.00%V? 16.67$



Using Excel

B. Solving for Return: k = D/V

What rate of return would an investor expect if the current price of a stockis $119 and she expected the firm to pay a constant dividend of $4/year?

V 119.00$ D 4.00$ k? 3.4%



Using Excel

• The constant dividend growth model assumes that the

stock will pay dividends that grow at a constant rate

each year -- year after year.


developed a spreadsheet tutorial using Excel




The Constant Growth Model

1. Constant Growth Model

A. Solving for Price: V = D0(1+g)/k-g = D1/(k-g) , where D0 = current dividend, k = required return,and g = growth rate

What would an investor be willing to pay for a stock if she just received adividend of $2.50, her required return is 15%, and she expected dividnedsto grow at a rate of 5% per year.

D0 2.50$

k 15.00%g 5.00%V? 26.25$

Valuation(Note: The tables below have been written using formulas which allow you to alter the information or assumptions.)



Using Excel

B. Solving for Return: k = D0(1+g)/V + g = D1/V + g

What is my expected return on a stock that costs $26.50, just paid adividend of $2.50, and has an expected growth rate of 5%?

D0 2.50$

V 26.25$ g 5.00%k? 15.00%



Using Excel

• 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.


developed a spreadsheet tutorial available under the

heading “Course Materials” on Course Web-Page.




Variable Growth Model

1. Non-Constant Growth Model

A. Solving for Price: This model involves the computation of year-to-year dividends whichare then dicounted at the investors required rate of return.

What would an investor be willing to pay for a stock if she just received adividend of $2.50, her required return is 15%, and she expected dividnedsto grow at a rate of 10% per year for the first two years, and then at a rate of5% thereafter.

Valuation(Note: The tables below have been written using formulas

which allow you to alter the informatins or assumptions.)



Using Excel

Step 1: Compute the expected dividends during the first growth period.

g 10.0%

D0 2.50$

D1 2.75$

D2 3.03$





Step 2: Compute the Estimated Value of the stock at the end of year 2using the Constant Growth Model

D2 3.03$

k 15.00%g 5.00%

V2? 31.76$




Step 3: Compute the Present Value of all expected cash flows to find the price of the stock today.

Cash PV atFlow 15%

1 D1 2.75$ 2.39$

2 D2 3.03$ 2.29$

3 V2? 31.76$ 20.88$

V0 ? 25.56$



Other Approaches to Stock Valuation

• Book value per share is the amount per share that

would be received if all the firm’s 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 firm’s

earnings potential and lacks any true relationship to

the firm’s value in the marketplace.

Book Value


• Liquidation value per share is the actual amount per

share of common stock to be received if al of the firm’s

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

firm’s assets.

• However, it still fails to consider the earning power of

those assets.

Liquidation Value


• 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 stock’s earnings are $5.00/share, the estimated

value of the stock would be P = 15*5 = $75/share.

Valuation 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

Other Approaches to Stock ValuationWeaknesses of Using P/E Ratios

• Valuation equations measure the stock value at a

point in time based on expected return and risk.

• Any decisions of the financial manager that affect

these variables can cause the value of the firm to

change as shown in Figure 8.3 below.

Decision Making and Common Stock Value

• Changes in expected dividends or dividend growth

can have a profound impact on the value of a stock.


Changes in Dividends or Dividend Growth

D0 2.00$ 2.50$ 3.00$ 2.00$ 2.00$ 2.00$

g 3.0% 3.0% 3.0% 3.0% 6.0% 9.0%

D1 2.06$ 2.58$ 3.09$ 2.06$ 2.12$ 2.18$

kS 10.0% 10.0% 10.0% 10.0% 10.0% 10.0%

P 29.43$ 36.79$ 44.14$ 29.43$ 53.00$ 218.00$

Price Sensitivity to Changes in Dividends and Dividend Growth(Using the Constant Growth Model)




Changes in Risk and Required Return

D0 2.00$ 2.00$ 2.00$ 2.00$ 2.00$ 2.00$

g 3.0% 3.0% 3.0% 3.0% 3.0% 3.0%

D1 2.06$ 2.06$ 2.06$ 2.06$ 2.06$ 2.06$

kS 5.0% 7.5% 10.0% 12.5% 15.0% 17.5%

P 103.00$ 45.78$ 29.43$ 21.68$ 17.17$ 14.21$

Price Sensitivity to Changes Risk (Required Return)(Using the Constant Growth Model)




Changes in Risk and Required Return

D0 2.00$ 2.50$ 3.00$ 2.00$ 2.50$ 3.00$

g 3.0% 6.0% 9.0% 3.0% 6.0% 9.0%

D1 2.06$ 2.65$ 3.27$ 2.06$ 2.65$ 3.27$

kS 5.0% 7.5% 10.0% 12.5% 15.0% 17.5%

P 103.00$ 176.67$ 327.00$ 21.68$ 29.44$ 38.47$

Price Sensitivity to Changes in Both Dividends and Required Return(Using the Constant Growth Model)

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