chapter 4 1

Chapter 4: The valuation of long-term securities

• Study objectives– Distinctions among valuation concepts– Bond valuation– Preferred stock valuation– Common stock valuation– Rates of Return

chapter 4 2

What does it mean?

• What is a cynic? A man who knows the price of everything and the value of nothing.---Oscar Wilde

chapter 4 3

Why shall we know the valuation of long-term securities?

• Make investment decisions

• Determine the value of the firm

chapter 4 4

Distinctions among valuation concepts

• Liquidation value versus going-concern value– Liquidation value is the amount of money that could be

realized if an asset or a group of assets (e.g., a firm) is sold separately from its operating organization.

– Going-concern value is the amount a firm could be sold for as a continuing operating business

• The computation of liquidation value and going-concern value is very different– As in accounting, the security valuation models that we

will discuss in this chapter will generally assume that we are dealing with going-concern

chapter 4 5

Book value versus market value

• The book value of an asset is the accounting value of the asset---the asset’s cost minus its accumulated depreciation.

• The book value of a firm is equal the dollar difference between the firm’s total assets and its liabilities and preferred stock as listed on its balance sheet– Because book value is based on historic values and

estimations, it may not be accurate after a long period of time

chapter 4 6

Book value versus market value

• In general, the market value of an asset is simply the market price at which the asset (or a similar asset) trades in an open market place.

• For a firm, market value often viewed as being the higher of the firm’s liquidation or going concern value– Market value often outrival book value as to decision

relevance, because market value takes risk, future opportunity, current cash flow in account.

chapter 4 7

Market value versus intrinsic value

• For an actively traded security, the market value would be the last reported price at which the security was traded. – For an inactively traded security, an estimated market price

would be needed

• The intrinsic value of a security is what the price of a security should be if properly priced based on all factors bearing on valuation---assets, earnings, future prospects, management, and so on.– If markets are reasonably efficient and informed, the current

market price of a security should fluctuate closely around its intrinsic value

chapter 4 8

The valuation approach

• The valuation approach taken in this chapter is one of determining a security’s intrinsic value. This value is the present value of the cash flow stream provided to the investor, discounted at a required rate of return appropriate for the risk involved

chapter 4 9

Bond valuation

• A bond is a security that pays a stated amount of interest to the investor, period after period, until it is finally retired by the issuing company– In China, bond interest may not be paid annually, but

until the retirement of the bond

• Face value is the stated value of an asset. In the case of a bond, the face value is usually $1000– The face value is supposed to be paid back to the

bondholders as the principal, no matter what the purchasing price of the bond

chapter 4 10

Bond Valuation

• Coupon rate: the stated rate of interest on a bond; the annual interest payment divided by bond’s face value

• The factors that affect the valuation of bond– Face value

– Coupon rate

– Required rate of return

– Maturity

chapter 4 11

The Model of Bond Valuation

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Perpetual Bonds

• A bond that never matures (rarely exists now)

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chapter 4 13

Bonds with a Finite Maturity

• Typical coupon bonds (limited outstanding period, annually paid interest)

• V=I(PVIFAr,n)+MV(PVIFr,n)

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Example

• The Brothers determines to issue 10000 $1000-par-value bonds with 10% coupons. The bonds will be retired in 9 years. The Brothers decides to issue the bond at $1020. If Mr. White wants to buy the bond and his required rate of return is 8%, should Mr. White buy the bond?

chapter 4 15

Example

• V=$100(PVIFA8%,9)+$1000(PVIF8%,9)=$1124.70

• Because V>P, Mr. White should buy the bond

chapter 4 16

Zero-coupon bond

• A zero-coupon bond is a bond that pays no interest but sells at a deep discount from its face value; it provides compensation to investors in the form of price appreciation

• The interest of a zero-coupon bond is the remainder of the face value less issuing price

• V=MV/(1+r)n

chapter 4 17

Example

• Suppose that Pace Enterprises issues a zero-coupon bond having a 10-year maturity and a $1000 face value. If the investor’s required return is 12%, then

• V=$1000/(1+12%)10=$322

chapter 4 18

Seminal compounding of interest

• Although some bonds (typically those issued in European Markets) make interest payments once a year, most bonds issued in America pay interest twice a year. As a result, it is necessary to modify our bond valuation model

• V=(I/2)(PVIFAr/2,2n)+MV(PVIFr/2,2n), here I is the nominal interest of the bond and n is the years that the bond exists

chapter 4 19

Example

• To illustrate, if the 10% coupon bonds of the U.S. Blivet Corporation have 12 years to maturity and our nominal annual required rate of return is 14%, the value of one $1000-par-value bond is

• V=($50/2)(PVIFA14/2,24)+MV(PVIF14/2,24)=$770.45

• Why V<par value? Because required return>coupon rate

chapter 4 20

Preferred Stock Valuation

• Preferred stock is a type of stock that promises a (usually) fixed dividend, but at the discretion of the directors. It has preference over common stock in the payment of dividends and claims on assets

• Cumulative and noncumulative preferred stock• A cumulative preferred stock is a stock whose divi

dend not paid out is deferred to later years

chapter 4 21

Example

• To illustrate the payment of different types of dividends, the following data from the Boston Lakers Basketball Team will be used. Assume that outstanding stock includes: preferred stock (5%, $10 par value 6000 shares issued and outstanding) $60000, common stock ($5 par value, 8000 shares issued and outstanding) $40000

chapter 4 22

Example

case Preferred dividend feature

Years in arrears

Total dividend

Preferred dividend

Common dividend

1 noncumulative

--- 2000 2000 0

2 noncumulative

--- 4000 3000 1000

3 cumulative 2 7000 7000 0

4 cumulative 2 11000 9000 2000

chapter 4 23

The valuation of preferred stock

• The payment of preferred stock is similar to an annuity, so the valuation model of a preferred stock is :

• Vp=Dp/R

• If Margana Cipher Corporation had a 9%, $100-par-value preferred stock issue outstanding and your required return was 14% on this investment, its value per share to you would be Vp=Dp/R=$64.29

• In China, no listed company has issued preferred stock

chapter 4 24

Common stock valuation

• Common stock is the security that represent the ultimate ownership (and risk) position in a corporation

• The difficult issues of valuation: uncertainty and payment of stock dividend, different risk levels, etc.

chapter 4 25

Are dividends the foundation

• Case 1: hold the stock for a long time

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chapter 4 26

Are dividends the foundation

• Case 2: hold the stock for a short time (e.g., 2 years)

• Note: D1, D2…Dn and P2 are all estimates

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chapter 4 27

A logical question to the models

• The logical question to raise at this time is: why do the stocks of companies that pay no dividends have positive, often quite high, values?

• The answer is: investors expect to sell the stock in the future at a price higher than they paid for it.

• Terminal value depends on the expectations of the marketplace viewed from the terminal point. The ultimate expectation is that the firm will eventually pay dividends, either regular or liquidating, and that future investors will receive a company-provided cash return on their investment

chapter 4 28

Dividend Discount Models

• Constant Growth• Assume that dividends grow at a constant rate. But

in real life, few companies do this. We shall learn this in corporate finance---dividend policy

• Assume that D0 is the present dividend per share and g is the growth rate of dividend, so D1 is (1+g) D0 , D2 is D0 (1+g)2,…Dn is D0 (1+g)n

• According to the valuation model, constant growth stock is valuated as:

chapter 4 29

Constant Growth

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chapter 4 30

Constant Growth• Tip: a common mistake made in using the above

equation is to use, incorrectly, the firm’s most recent annual dividend for the variable D1 instead of the annual dividend expected by the end of the coming year

• g can never be larger than r, why?• Suppose that LKN, Inc.’s dividend per share at

t=1 is expected to be $4, that it is expected to grow at a 6% rate forever, and that the appropriate discount rate is 14%. The value of one share of LKN stock would be V=$4/(0.14-0.06)=$50

chapter 4 31

Conversion to an earnings multiplier approach

• Assume that a company retains a constant proportion of its earnings each year; call it b, then (1-b)=D1/E1, D1=E1(1-b), V=(1-b)E1/(r-g), V/E1=(1-b)/(r-g), (1-b)/(r-g) is called earnings multiplier (EM). V=E1(EM)

• Why we should know earnings multiplier? Because it bring together value and earnings of a stock

chapter 4 32

No Growth

• Assume that dividends will be maintained at their current level forever ( a kind of dividend policy)

• V=D1/r==D0/r. like a preferred stock

chapter 4 33

Growth phases• Firms may exhibit above-normal growth for a

number of years (g may even be larger than r during this phase), but eventually the growth rate will taper off.

• Assume that dividends per share are expected to grow at f compound rate for m years and thereafter at g, the valuation model is:

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chapter 4 34

Example

• If dividends per share are expected to grow at 10% compound rate for 5 years and thereafter at 6%, the required rate is 14%, how to value the stock?

chapter 4 35

Example

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chapter 4 36

Rates of Return

• If we replace intrinsic value in our valuation equations with the market price (p0) of the security, we can then solve for the market required rate of return.

• This rate, which sets the discounted value of the expected cash inflows equal to the security’s current market price, is also referred to as the security’s market yield

chapter 4 37

Rate of return

• It is important to recognize that only when the intrinsic value of a security to an investor equals the security’s market value (price) would the investor’s required rate of return equal the security’s (market) yield

• Market yields serve an essential function by allowing us to compare, on a uniform basis, securities that differ in cash flow provided, maturities, and current prices

chapter 4 38

Yield to maturity (YTM) on bonds

• Yield to maturity (YTM) is the expected rate of return on a bond if bought at its current market price and held to maturity; it is also known as the bond’s internal rate of return (IRR)

• Mathematically, it is the discount rate that equates the present value of all expected interest payments and the payment of principal (face value) at maturity with the bond’s current market price

chapter 4 39

Yield to maturity

• The difficult issue is: it is not a linear function, more complex

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chapter 4 40

Interpolation---Example

• Consider a $1000-par-value bond with the following characteristics: a current market price of $761; 12 years until maturity, and 8% coupon rate (with interest paid annually)

• Suppose we start with a 10% discount rate and calculate the present value of the bond’s expected future cash flows. V=$80(PVIFA10%.12)+$1000(PVIF10%.12)=$684.12>761, so YTM>10%

chapter 4 41

Interpolation---Example

• Try a 15% discount rate

• V=$80(PVIFA15%.12)+$1000(PVIF15%.12)=$620.68<761, so YTM<15%

• X/0.05=(864.12-761)/(864.12-620.68)

• X=0.0212

• YTM=X+10%=12.12%

• It is important to keep in mind that interpolation gives only an approximation of the exact percentage; the relationship between the two discount rate is not linear with respect to present value

chapter 4 42

Behavior of bond price

• When the market required rate of return is more than the stated coupon rate, the price of the bond will be less than its face value---bond discount

• When the market required rate of return is less than the stated coupon rate, the price of the bond will be more than its face value---bond premium

• When the market required rate of return equals the stated coupon rate, the price of the bond will equal its face value---selling at par

chapter 4 43

Behavior of bond price

• If interest rates rise so that the market required rate of return increases, the bond’s price will fall. If interest rates fall, the bond’s price will increase

• For a given change in market required return, the price of a bond will change by a greater amount, the longer its maturity

• Bond price volatility is inversely related to coupon rate

• Figure 4-1 relation between bond price and market required rate of return

chapter 4 44

YTM and Semiannual Compounding

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chapter 4 45

Yield on preferred stock and common stock

• P0=Dp/r

• P0=D1/(r-g)