Lecture 4: Securities Valuation C.L. Mattoli 1 (C) 2008Red Hill Capital Corp. USA.

Lecture 4: Securities Valuation

C.L. Mattoli

1(C) 2008Red Hill Capital Corp.

USA

Intro

This week we look more deeply into interest rates and rates of return.

Last week we talked about discount rates and RRR’s, but how are they determined?

We will also apply our knowledge of time value to the main types of corporate securities: debt and equity securities.

The chapters in the textbook covered this week are 6 & 7.


USA

Valuing Bonds


USA

Intro: Intrinsic Value We learned that the value of anything is its

DFCF value. The value of future cash flows must be brought

back to the present by discounting at some opportunity cost RRR.

The value that we get from discounting cash flows is called the intrinsic value, the value of the estimated future cash flows.

It is the price that we should pay, if we want to earn the RRR that we use to discount the cash flows.


USA

Debt is easy We learned how to value future cash

flows, using the time value concept. Securities, like stocks, bonds,

commercial bills, notes, CD’s, etc., are promises of future cash flows.

Thus, we should be able to value them using discounted future cash flow (DFCF) methods.


USA

Debt is easy Debt securities are the easiest to fit into our

time value scheme since they have contractually-obligated and clearly-stated future payment schedules.

Moreover, the maturity time is also stated and is a finite time.

Of course, the other thing that we will eventually have to worry about is that, just because the cash flows are promised, does not mean that we will get them (risk).


USA

Debt is easy

Stock, on the other hand has no promised cash flows, although it may pay cash dividends, and it has, technically, an infinite life.

In that regard, debt securities are easier to value on DFCF than other securities.


USA

Debt Securities

We discussed several types of bank loans, in the last module, which are an intermediated form of debt.

Then, there are debt securities that are issued by corporations and by governments.

We usually refer to long-term corporate debt securities as corporate bonds, which is a generic name.


USA

Debt Securities

Other names could be debentures or notes.

Indeed, in Australia, debentures are secured debt securities, while the term corporate bond is an unsecured debt security.

In the U.S., on the other hand, debentures are unsecured and bonds are secured.


USA

Debt Securities We use the term bond to describe general

LT corporate debt securities. There are pure discount bonds, like the

pure discount balloon-payment loans that we discussed in the last module.

The other type of bond is a coupon bond, which is like an interest only-loan, but can also be looked at as an annuity plus a discount bond.


USA

What security?

Some loans, intermediated or securitized, are secured by assets.

For example, home mortgage loans are usually secured by the house.

That means that in default, the lender can take possession of the property and sell it to satisfy the loan.

Debt securities can also be secured by specific or general assets of the corporation.


USA

Bond definitions

There is a language for bonds that we began to learn in earlier modules.

Bonds have a maturity (date), which is the final date when total repayment of the debt is due.

Maturity time of most bonds is between 5 and 10 years, although it could be 20 or 30 years, or another number.


USA

Bond definitions

Years to maturity will decrease as time moves on: a 2015 maturity bond will have 7 years to maturity in 2008 and 5 in 2010.

All bonds have a Face Value (FV), which is the amount that will be paid at the end, and is also called par value.

FV is usually multiples of $1,000, although some bonds might have there incremental FV as $100,000 or more.


USA

Bond definitions Bonds that are selling in the market at their

FV are called par value bonds. Most bonds will also pay interest in the form

of coupon interest payments. The coupon rate, %C, the % coupon

interest rate, will be stated on the bond, and you have to find the actual annual dollar coupon payment by multiplying FV by %C. E.g., a $1,000 FV with %C = 8% is $C = %C x FV = 8% x$1,000 = $80/year.


USA

Bond definitions

Usually, coupon payments are made semi-annually, which means, for the above example, $40 coupon interest would be paid out every 6 months for a total of $80/year.

Bonds that pay coupon interest are called coupon bonds or fixed interest bonds.

We show a 4 1/8 % $1,000 FV bond in the next slide.


USA

Picture of a Bond Face Value


USA

Zero-coupon bonds

Although zero-coupon bonds (ZCB’s) are not common, in Australia, they are, in the U.S. and other countries.

As the name says, they pay no coupon interest. The only payment is FV at maturity.

Thus, they sell at a discount to FV and are discount bonds.

Valuation is particularly easy, using DFCF methods.


USA

Zero-coupon bonds We should pay PV for the bond, based on

our own RRR = k. Thus, PV = FV/(1 + k)n where FV is the face value of the bond and n is the number of years to maturity (assuming that you want to) will earn a compound annual return on investment =k

In that regard, if I invest PV, now, and I get FV, in n years, I will earn an annual compound rate of return on investment of k: k = [FV/PV]1/n -1.


USA

Zero-coupon bonds You could compound interest more than

once a year, if you wanted to compare your return to other rates of return that are compounded more than once a year.

The interest rate that you use for RRR is often referred to as the yield to maturity (YTM) of the bond or, simply, the yield.

Thus, if you are given a dollar price for the bond, you can figure out the YTM.


USA

Coupon Bonds Coupon bonds have regular coupon interest

payments, so they will pay multiple CF’s over their lives, but they are only slightly more complicated to value.

Our general equation for CF valuation is:

A coupon bond has coupon interest payments, C, every year through maturity, plus a final payment of FV at the maturity time.

k)(1CFk)(1

CFPV in

0iii

in

0i


USA

Coupon Bonds

Since the coupon payments are the same dollar value, paid out in 1 year intervals, it is like an annuity.

The FV payment at maturity is like in the case of a ZCB.

Thus, the value of a coupon bond is like the value of an annuity for n years to maturity plus a ZCB at the end.


USA

Coupon Bonds In fact, sometimes, securities dealers, clip off the

strip of coupon payments, and sell the strip and the ZCB face value portion, separately.

In that manner they create what is called a strip and a ZCB from a coupon bond.

In any event we can value a coupon bond as:

= C[1 – (1+k)– M]/k + FV/(1+k)M

M

M

ttBond k

FV

k

CPV

)1(]

)1([

1

Coupons Face value


USA

ZCB Example Assume that a ZCB has FV= $1,000,

matures in exactly 10 years from now, and your RRR = 6.5% compounded annually (priced to yield 6.5% compounded annually).

Then, the price that you should pay is PV = $1,000/(1+6.5%)10 = $532.73.

Thus, if you invest $532.73, now, and get $1,000, in 10 years, you will have earned a compound annual return of 6.5%


USA

Coupon Bond Example

Take a bond, this time, that has FV = $1,000, k = 6.5%, n = 10 years, compounding is annual, and it pays coupon interest of 7%.

We already valued the FV portion, in the preceding example. Now, we have to value the coupon annuity portion and add it to that.

The coupon interest is C = 7%x$1000 = $70.


USA

Coupon Bond Example Thus, PVcoupon bond =

$70[1 – (1+0.065)-10]/0.065

+ $1000/ (1+0.065)10

= $503.22 + $532.73 = $1035.95

Notice that this price is more than the face value.


USA

Coupon Bond Secrets As you may or may not recall, we showed

that the PV of an interest-only loan was the principal.

Coupon bonds have the same cash flows as an interest-only loan.

The difference is that the discount rate yield might be different, higher or lower, than the coupon interest rate.

If k > C, that means that the RRR is higher than the interest rate that is being paid in the coupon.


USA

Coupon Bond Secrets As a result, an investor will want to be

compensated for the coupon underpayment. There are 2 ways to profit from an investment:

1) income, such as coupon interest, and 2) capital gains, increase in value of investment over the holding period: return = income + cap gain.

Therefore, to make up for the lack of income, an investor will require a capital gain, i.e., he will pay a discount to FV for the bond, and make a capital gain over the maturity period.


USA

Coupon Bond Secrets If k < C, there is excess return from coupons,

and the investor will buy the bond at a premium to face value (PV > face) (premium bond).

The capital loss will take away some return. If k = %C, then, the bond will be priced at

face value (par bonds) PV = %CFV[1 – (1+k)-n]/k +FV(1+k)-n = FV.

Then, as the time to maturity decrease, as time moves forward, the value will approach FV. See next slide.


USA

Coupon Bond Secrets

So, for example, assume the coupon rate is 5% and the RRR =6%

Then, you get 5% cash coupon payments every year, but you need 6% total = RRR

So, maybe you would pay (depending on the maturity) $900 for a $1,000 FV bond.

In that way you will also make $100 = $1,000 – $900, divided up over the years until maturity, to get the extra 1%

(C) 2008Red Hill Capital Corp. USA 29

Bond price as maturity time declines The price of a discount, or premium bond goes

to FV as time goes on and maturity is approached for different coupon rates & k=10%.

Premium bond%C > k

Discount bond%C < k

Par bond%C = k

Excerpt: Investing in the Real World, C. L. Mattoli © 2004-8


USA

Interest Rate Risk We have seen in the last several slides how the

value of a bond changes with varying coupon interest rates, %C, for fixed YTM = RRR = k.

Of course, once a bond is issued, the coupon and FV are fixed (except in the case of variable rate bonds), so, the only variable in the bond equation is the interest rate RRR = k.

Thus, for issued bonds with fixed coupon rates, you can see from the bond value equations that, if k increases, PV decreases; if k decreases, PV increases (PV and k are inversely related).


USA

Interest Rate Risk Interest rates (RRR’s), demanded in the

market, can change. In other words, as economic variables, like

inflation, GDP, and supply/demand for money, change, investors will change their RRR’s for securities.

Thus, we look at sensitivity of bond prices, i.e., how and how much they change in relation to changes in the RRR YTM interest rate variable.


USA

Interest Rate Risk

This is commonly referred to as interest rate risk since an upward change in RRR will result in a downward change in bond prices.

How much a bond’s price will change for a given change in RRR depends on both the coupon and the time to maturity.

In fact, we can make some general observations:


USA

Interest Rate Risk

1. The longer the maturity time, the more sensitive will be the price to rate changes, ceteris paribus (all else held fixed).

2. The higher the coupon rate the less sensitive will be the price to rate changes.

The first fact is responsible for a normal upward sloping term structure of interest rates, the dependence of RRR on time to maturity, as we shall discuss.


USA

Interest Rate Risk

Basically, the longer the maturity, the more payments, and the further out the payment, the more it will be affected by a change in rates since the value of each payment has a factor (1+k)-n.

Moreover, the final payment has a factor of (1+k)-M.


USA

Interest Rate Risk

When coupons are small versus RRR, the final payment becomes more important, and the total value of the bond will be more greatly affected, the smaller the coupons.

We show some dependences in the tables, below.

See, also, the chart in the textbook, figure 6.2 on page 159.


USA

Bond Sensitivity

Decreasing Rate Sensitivity with Increasing Coupon

Principal= 1000 1000 1000 1000 1000 1000

YTM rate= 10% 9.5% 10% 9.5% 10% 9.5%

Maturity= 20 20 20 20 20 20Cpn rate= 20% 20% 30% 30% 40% 40%PV= 1851.36 1925.30 2702.71 2806.54 3554.07 3687.78%Chg Pr 3.994 3.8415 3.7621

Table 3.5.1

Excerpt: Investing in the Real World, C. L. Mattoli © 2004-8


USA

Bond sensitivityDollar Value of 20-year Maturity $1,000 FV Bond

under Variation of YTM and Coupon RatesCoupon Rate $45 $50 $55 $60 $65 $70 $75

YTM4.5% 1000 1065 1130 1195 1260 1325 13905.0% 938 1000 1062 1125 1187 1249 13125.5% 880 940 1000 1060 1119 1179 12396.0% 828 885 943 1000 1057 1115 11726.5% 780 835 890 945 1000 1055 11107.0% 735 788 841 894 947 1000 10537.5% 694 745 796 847 898 949 1000

Table 1Excerpt: Investing in the Real World, C. L. Mattoli © 2004-8


USA

Bond SensitivityPercentage Change in Price , Varying YTM (Read:

Columns) for Fixed Coupon RateCoupon Rate $45 $50 $55 $60 $65 $70 $75

YTM5.0% -6.20% -6.10% -6.02% -5.86% -5.79% -5.74% -5.61%

5.5% -6.18% -6.00% -5.84% -5.78% -5.73% -5.60% -5.56%

6.0% -5.91% -5.85% -5.70% -5.66% -5.54% -5.43% -5.41%

6.5% -5.80% -5.65% -5.62% -5.50% -5.39% -5.38% -5.29%

7.0% -5.77% -5.63% -5.51% -5.40% -5.30% -5.21% -5.14%

7.5% -5.58% -5.46% -5.35% -5.26% -5.17% -5.10% -5.03%

Cumulative -35.4% -34.7% -34.0% -33.4% -32.9% -32.5% -32.0%



USA

Bond SensitivityPercentage Change in Price , Varying Coupon

(Read: Rows) for Fixed YTM Rate

Coupon Rate $50 $55 $60 $65 $70 $75Cumulativ

eYTM

4.5% 6.50% 6.10% 5.75% 5.44% 5.16% 4.91% 27.4%5.0% 6.61% 6.20% 5.93% 5.51% 5.22% 5.04% 27.9%5.5% 6.82% 6.38% 6.00% 5.57% 5.36% 5.09% 28.4%6.0% 6.88% 6.55% 6.04% 5.70% 5.49% 5.11% 28.9%6.5% 7.05% 6.59% 6.18% 5.82% 5.50% 5.21% 29.3%7.0% 7.21% 6.73% 6.30% 5.93% 5.60% 5.30% 29.9%7.5% 7.35% 6.85% 6.41% 6.02% 5.68% 5.37% 30.3%



USA

Rate risk, a closer look First of all, note that if RRR rates go up, the

price of the bond goes down, and vise versa. On the other hand, if rates go up, the opportunity

rate for reinvesting intermediate coupon cash flows increases, also.

Thus, an interest rate rise diminishes current value, while increasing future opportunity, and vice versa.

If nothing else changes, in the future, there will actually be a point in time, in the future, at which the increased reinvestment rate will overcome the initial loss in value.


USA

Finding the YTM If you know the price of a bond in the

market, you should be able to determine the market’s RRR=YTM,

The form of the general bond equation is not directly solvable for YTM, containing terms of 1/k, 1/k(1+k)n, and 1/(1+k)n.

Financial calculators and spreadsheet programs have functions to solve for YTM.

Otherwise, solution involves trial and error.


USA

Finding the YTM For example, if a 10% coupon bond is selling

above par, you might start with a guess of YTM = 9%. Then, you put that into the equation, solve for price and see, if it is larger or smaller than the market price.

If it is smaller, then, you need to increase your guess to, say, 9.5%, and try again.

You would continue this procedure until you are very close to the actual market price and resulting YTM.


USA

Characteristics of Debt


USA

Debt vs. Equity The real difference between debt and

equity is that, if a debt obligation is not repaid, either interest or principal, creditors can sue the corporation and could put it into bankruptcy, requiring liquidation or reorganization of the firm.

Equity represents a residual ownership of the firm, after all creditors are paid, but it has no obligatory payments.


USA

Debt vs. Equity On the other hand, debt usually has a limited

cash flow stream, interest payments and principal, while there is no limit on the rewards of owning equity.

Moreover, interest on debt is a tax-deductible expense of the corporation, while dividends are paid from after-tax money, although, in Australia, the double taxation can be removed

Corporations like the leverage that debt offers for enhancing returns, but they do not like the fact that, if they cannot make payments, it can result in bankruptcy.


USA

Debt vs. Equity As a result, so-called hybrid securities that

have features of both debt and equity, although legally debt, have been created over the years to soften the hard edges of debt.

Thus, there are things, like perpetual bonds, which have an infinite life, like equity, and convertible bonds, which start out as debt but may be converted to equity at a future date.

Should a perpetual bond that makes payments, only if the corporation has income, be classified as debt or equity? Questions, like that, are for the courts and tax authorities to decide.


USA

The Indenture or Trust Deed Bondholders need protection since the

corporate agents represent the shareholders and they use debt to enhance shareholder value.

The Indenture (trust deed) lays out all of the specific obligations between the corporation and the creditors for a debt obligation, in a legal document that is several hundred pages long.

A trustee, usually a bank, acts to represent and protect the debt holders and to manage the sinking fund, if there is one (see below).


USA

Trust Deed Contents The trust deed contains the following basic

contents:

1. Basic description of terms.

2. Total amount issued.

3. Specification of assets to be used as security, if any.

4. Arrangements for repayment.

5. Call provisions, if any.

6. Protective covenants.


USA

Terms Corporate bonds have faces values that

represent the principal amount. If the corporation issues $1 million in $1,000

FV bonds, it will issue 1,000 bond certificates of $1,000 each.

The recorded accounting par value is usually the same as face value, and we use the terms interchangeably.

Bonds are usually registered, and the company’s registrar keeps track of ownership for payment and other purposes.


USA

Terms Before the electronic age, coupons were

actually contained in a strip across the bottom of the bond certificate, and they needed to be clipped off and sent in for payment.

Now, many companies are moving to electronic payment of interest and principal.

Bonds can also be issued in bearer form, not registered, and evidenced by the certificate, only, with no record of ownership.

Bearer bonds are much less common, today.


USA

Security & Seniority Bonds may be secured by assets,

specified as collateral, or by a mortgage on a real property.

Otherwise, it might be unsecured. Seniority tells the position of creditors in

liquidations. The secured debtors get paid first, and holders of subordinated debentures or unsecured notes will be in the back of the line. All debt is senior to equity.


USA

Repayment, Sinking Funds and Calls The indenture will specify two dates per year,

usually, for payment of semi-annual coupon interest.

Repayment of the principal is due for certain by the maturity date, but there are bond provisions that can lead to earlier repayment.

Sinking fund bonds make provision for a pool of money, kept by the trustee, accumulated to repay a certain portion of the issue in years prior to maturity, e.g., in the 11, 12, 13, 14, and 15th year of a 15-year bond.


USA

Repayment, Sinking Funds and Calls The sinking fund might be used to buy in

bonds in the market or to liquidate specific bonds, through, e.g., a lottery.

That kind of provision changes the value of the bond, since the actual maturity might be different. It provides, in theory, more security for the lender.

Bond call provisions, on the other hand, are for the borrowers benefit.


USA

Repayment, Sinking Funds and Calls They allow the borrower to call away the

bonds from holders at specified prices at specified points in the future, although callability usually kicks in only after a certain amount of time.

Companies will generally exercise their call rights if interest rates have declined substantially since issue, and they look to refinance.


USA

Protective Covenants

Over time, bond holders have found that they need protection, and features have been added to indentures.

Protective covenants restrict the company, in some way, in its actions, actions, which might affect its ability to pay off a debt.

There are negative and positive covenants.


USA

Protective Covenants

An example of a negative covenant is restricting the amount of dividends paid out or pledging assets to new lenders.

Positive covenants are things, like keeping working capital above a certain level and keeping collateral in good condition.

By these means bond holders are able to get greater protection.


USA

Creditworthiness: Bond Ratings Several Wall Street firms, Standard &

Poor’s (S&P) and Moody’s, and another firm, Fitch’s, rate bond debt for creditworthiness.

Indeed, often, companies pay those firms to provide a rating before issue and maintain ratings.

Bond ratings are concerned with probability of default and the protection that the bond holders have, in the event of a default.


USA

Creditworthiness: Bond Ratings The rating systems start at a high credit

rating of AAA (S&P and Fitch) and Aaa (Moody’s); next AA, etc., down to D for default.

BBB and above are referred to investment grade, while bonds with ratings below that are referred to as junk bonds.

There are also smaller notches, using + and – signs.


USA

Creditworthiness: Bond Ratings Rating services are important because they

provide everyone with information about likelihood of default, which many people would not be able to reckon on their own.

What a rating actually affects is the RRR that people will require to buy the bond. High rating, AAA, means less risk of default, so RRR will be less for AAA than for AA, etc.

Ratings are continually reviewed and might be revised upward or downward.


USA

Creditworthiness: Bond Ratings Indeed, revisions will have a substantial

impact on the existing bond price. Thus, for example, if a rating is changed from

AAA down to AA, the bond has been re-rated as riskier, the RRR will go up, and the price will go down (inverse relation between RRR and price).

They replace the credit valuation services that a bank uses when it intermediates between a portfolio of savings funds and a portfolio of loans.


USA

Types of bonds We have already mentioned several types of

bonds. Bonds are issued by governments, in the

form of coupon bonds or inflation-adjusted, which adjust the principal for inflation.

With those indexed bonds, the principal is adjusted for inflation and the coupon percentage is applied to the new principal.

We consider the bonds of larger stable governments as default free, and we sometimes call them riskless.


USA

Types of bonds For ZCB’s the implicit interest is

determined for tax purposes by amortizing the loan, with interest the difference between beginning and ending year values.

Floating rate bonds provide for adjustment of the coupon rate according to a change in a benchmark index, like the BAB rate.

Other types of bonds are available and are created on an ongoing basis.


USA

Bond Markets


USA

Bonds in Australia The corporate bond market developed

in Australia, only in the late 1980’s. For one, the population is not large,

only about 20 million, versus companies that are relatively large.

Regulation regarding borrowing from the public also hindered development.


USA

Bonds in Australia

For years, Australian companies had to issue debt in foreign and Euro markets.

By now, though, the market has issued over $40 billion in bonds.

Most issues have maturities of 15 years or less, although some have maturities as long as 100 years and even infinite maturity (perpetual bonds).


USA

Trading Venues Bonds are mostly traded OTC, i.e., using

dealer networks, and there are some traded on the ASX, too.

Thus, there is a lack of transparency in bond trading: it’s difficult to know the range of prices and the volume traded in a day.

Representative numbers are published in the newspaper, as shown in the book, and on line.

Although total bond trading exceeds stock trading, not all bonds are even traded every day.


USA

Trading Venues Prices for bonds from brokers might be

given as either a dollar amount or in terms of the YTM.

In addition to the YTM of a bond, we also talk about a bond’s current yield, which is the annual coupon divided by closing price.

See page 177 in the textbook for the kind of information about daily bond prices contained in the press.


USA

Interest Rates


USA

Intro You can find bond yields in the market place,

but what really determines those rates. Government bonds, representing a zero-

default Interest rate, provide a floor on value for interest rates on bonds, since they are the least risky bond.

Indeed, there will be a risk-structure of rates, based on a scale, like S&P’s, with riskier bonds demanding a higher RRR than the less risky.

We shall examine some other factors that go into interest rates.


USA

The Fisher Effect A person gives up current consumption to

save money. If he is going to be induced to lend his

money to someone else to buy something that they would otherwise have to forego, now, he will want not to lose the purchasing power of his money.

Thus, inflation should be a component of all interest rates.


USA

The Fisher Effect The Fisher Effect says that, in fact,

interest rates are comprised of an inflation part, to counter inflation, plus a real rate of interest for the rental of money = nominal rate.

The equation relating them is 1+R = (1+r)(1+h), using the notation in the textbook, so as not to confuse you, where R is the nominal rate, r is the real rate, and h is the rate of inflation.


USA

The Fisher Effect Sometimes it is given in approximate form as:

R ≈ r + h where the symbol “≈” means approximately equal to.

Surprisingly, real rates of return have been around several percent for many years.

To give an example, assume inflation is 10%/year, i.e., general prices of goods and services in the economy increase by 10% per year, and assume that real interest is 2%. Then, R = (1+2%)(1+10%) – 1 = 12.2%.


USA

The Fisher Effect

All that says, really, is that, first, the person wants to earn money on his money.

He wants 2% more buying power per year for renting out his money of PV(1+r)n.

He also wants his original money to have the same buying power to begin with or PV(1+h)n.

So, he really wants to get PV(1+r)n(1+h)n total.


USA

Term Structure As we mentioned, earlier on, there will be

a component to rates that depends on the term to maturity. This is known as the term structure of rates.

Usually, the term structure is an upward sloping line that demands a higher and higher rate as the term to maturity increases, given the same risk class, i.e., government bonds.


USA

Term Structure

That is easy to understand since the longer that you wait to get paid, the more chance there is for something bad to happen.

One of the things that can happen is a change in interest rates, in general, and, as we saw earlier, and the longer the term to maturity, the more sensitive the bond price to rate changes.


USA

Term Structure On the other hand, if expectations of

inflation are for a drop in the rate of inflation, short-term rates might be higher than the longer-term, resulting in a downward sloping term structure.

A humped structure means people believe in inflation in the near term but it is expected to subside in the later future.

See the text pp.185-6 for some pictures.


USA

In the end A true term structure curve is found from

pure discount bonds, as one-payment instruments are the only ones with a certain annual return: PV = FV/(1+kn)n

The term yield curve is reserved for term structure curves calculated with coupon bonds.

We take the term structure curve for government default-free bonds as the basic time value of money.


USA

In the end

All interest rates will include a real rate and inflation, as components. However, expected inflation is more important than actual inflation.

Usually, because interest rate increases with increasing term to maturity, there is a larger and larger risk premium as term gets larger.


USA

In the end

On top of that structure is a default risk structure, adding incremental RRR as default risk increases, although those premiums may also vary with the term.

Final considerations in interest rates are taxability (interest on some government bonds or bonds of state governments might be totally or partial tax free, e.g.) and liquidity of the market for the bond.


USA

Term & Risk structure of Interest Rates


Ordinary Share Valuation


USA

Intro Equity will, in general, be more difficult to

value than debt, using DFCF methods. Equity has a potentially infinite life. It also has no promised cash flows, except,

perhaps, sale of the shares at the end of a holding period. So predicting an infinite stream of undetermined cash flows will make valuing shares difficult.

Finally, there is no easy measure for RRR’s, like in the bond markets.


USA

Cash Flows If we sold a bond before maturity, we will

have earned some coupon interest and we will make a capital gain or loss on the sale.

Similarly, we can make a return on a stock investment from income = dividends plus a capital gain/loss on sale of the shares.

Assume that you go to buy shares of XYZ Co., today. You expect to be able to sell them in one year for $10/share, and during the year holding period, you will get $1 dividend, and your RRR = 20%.


USA

Cash Flows Then, the price that you should pay

for the shares is PV = CF/(1+r) ($10+$1)/(1+20%) = $9.17.

Thus, you pay that price, get those future CF’s and you will earn a 20% return on initial investment.

We can put this in equation form as P0 = (D1 +P1)/(1+k).


USA

Cash Flows Of course, each such future price will

come from a similar equation: P1 = (D2+P2)/(1+k); Pn = (Dn+1 + Pn+1)/(1+k).

That leads to further equations: P0 = D1/(1+k) + D2/(1+k)2 + … + P n/(1+k)n and, an infinite dividend discount model:

10 )1(t

tt

k

DP


USA

Special Cases Growth companies are newer fast-growing

companies that do not pay dividends, but plough back all of their profits into internal growth.

Of course, they will probably pay dividends some day, after their growth opportunities have diminished.

We can consider the case of no growth in dividends, so that D n = D0 for all time. Then, we have a perpetuity cash flow and P = D/k.

That is a good way to model preferred shares.


USA

Special Cases Another special case that results in a

compact reduced equation is constant dividend growth.

In the constant dividend growth model (CDGM), also called the Gordon Model, dividends grow by g % per year, so Dn+1 = Dn(1+g).

Then the value equation becomes P0 = D1/(k – g).

Dividend growth is actually sometimes a corporate goal.


USA

Special Cases We could also make a multi-stage model

with growth rates, e.g., different for different periods of the corporation’s lifecycle.

Again, equations don’t know what time it is. The CDGM gives a value 1 year before the first dividend.

Note, also, that the equation does not work, if g ≥ k, and be careful to see, if in a problem you are give D0 or D1.


USA

90

Constant Growth Model Example What is the value of a share with an

expected growth rate of 2% pa is the last dividend was 15c, dividends are paid semi-annually, and your required return is 6%/year?

58.7$01.003.0

)01.1(15.0

1

P

gk

DP

(C) 2008Red Hill Capital Corp. USA

91

Dividend Model again

Value each of the following two shares, if your required return is 15%:

Share A pays semi-annual dividends. The last dividend was 20c and the expected growth rate is 3%/year.

Share B pays annual dividends. The last dividend was 30c. Dividends are expected to grow at 4% for the next 3 years, then 1% forever after that


92

Solutions For A, we have to convert to semi-annual. The

growth rate, annual, is 3%, so semi-annual growth is 3%/2 =1.5%; annual discount is 15%, so, semi-annual is 15%/2=7.5%. It is still an infinite sum of discounted future CF’s with constant growth, the equation does not know that we are using annual or semi-annual, but we can still use it, so, the answer is

38.3$015.0075.0

)015.1(20.00

10

P

gk

DP


93

Solutions For the B shares, everything is annual, but we

have two stages of growth: one for 3 years, and another for the rest of all time, so:

Putting the numbers into the final equation…

)1()1(

)1(

)1(

)1()1(

)1()1(

3

2

2

3

03

10

8

4

3

10

10

/)(

)1(11

231)1(

rgrggD

r

gD

r

gDr

gDD

eet

eer

P

et

t

tt

t

tt

t

tt

e

n


94

Solutions need a starting point, so I assume the next dividend

is paid tomorrow. Then,

33.2$)15.1(/)01.15(.

)01.1()04.1(30.0

)15.1(

)04.1(30.0

)15.1(

)04.1(30.0

)15.1(

)04.1(30.0

/)(

)1(11

33

3

3

2

2

1

3

2

2

3

03

10 )1(

)1(

)1(

)1(

rgr

ggD

r

gD e

etV

et

t

e


95

Activity solutionTime line. The constant growth starts in the 4th year,

so if we use the CDGM starting with year 4 to infinity, it will give a value for those cash flows, but the value will be one year before the CDG, or year 3, and we have to discount it back 3 more years to present value. Thus, the second term, above.

CGDM D4 D5

0 1 2 3 4 … 5


RRR for Equities Take the CDGM and turn it inside out to get k

= D1/P0 + g. That says that the RRR for a stock is

composed of the dividend yield = D1/P0, based on current price for future dividend, plus the dividend growth rate.

Remember that, in general, rate of return = (income + cap gain)/Initial Investment = inc/II + %ΔP.

The first part of that equation is in the form inc/II = dividend yield = D/P.


USA

RRR for Equities Now, take a closer look at the CDGM. P0 =

D1/(k – g). Similarly, P1, 1 year from now, will be predicted by the CDGM to be P1 = D2/(k – g).

Examining both equations, we can write P1 = D2/(k-g) = (1+g)D1/(k-g) = (1+g)P0.

Thus, implicit in the CDGM is that share price will also grow at the growth rate, g.

Given that, our first equation is k = dividend yield + cap gain percentage rate yield.


USA

Beyond dividend models We might object to discounting dividends and

forgetting about the growth in the company and consequent growth in share price.

It is argued that if you look closely at the dividend discount model, the growth in dividends will be the same as the growth in share price, so the company’s growth from RE is accounted for, partially, in the model.

However, it is really another cash flow number that we should discount.


USA

Beyond dividend models A company will need to earn a certain amount

just to replace equipment as it becomes scrap. On the other hand, earnings are not all of the

cash flow, so some sort of free cash flow number has been suggested to bridge the gap.

Thus, we should add depreciation and other non-cash charges, adjust for WC investment and take out capital spending.

Then, we would use something like IV = FCF0(1+g)/(RRR – g)


USA

Share Characteristics


USA

Preference (Preferred) Shares The reason that preference shares (pfd)

might be preferred by people is that the dividend on preferred, usually a fixed annual amount, must be paid before dividends can be paid on the common shares.

Also, in liquidation, the preferred shareholders must be paid before the common shareholders.


USA

Preference (Preferred) Shares Voting rights for preferred shares will be

limited to votes involving the shares or there might be no voting rights (see an example in table 7.2 in the text).

They will have a stated liquidation value, and dividends are sometimes given in $-amounts or in terms of %-of-par value. For example, a 10% $100 par value pfd would have an annual dividend of 10%x$100 = $10/year.


USA

Preference (Preferred) Shares Dividends might be cumulative or non-

cumulative. If they are cumulative, then, if payment

cannot be made in any one year, it will cumulate to the next year. For non-cumulative, if it can’t be paid, tough luck.

However, remember that pfd dividends must be paid before dividends can be paid on common shares.


USA

Preference (Preferred) Shares Sometimes preferred will have a limited

life: it is redeemable preferred. There might even be a sinking fund for retiring the issue.

A non-redeemable preferred is valued as a perpetuity; redeemable preferred would be valued like a coupon bond.


USA

Preference (Preferred) Shares That is why many people say that

preferred capital is much like debt capital. It has fixed payments and can have a liquidating final payment.

The real difference is for legal and tax purposes. Dividends non-payment does not lead to default, and pfd dividends are treated as dividend for tax purposes.


USA

Common Ordinary Shares

Common equity has the residual right to assets and income.

Common shareholders have 1 vote per share.

All companies hold an annual vote for directors. In Australia, there is straight voting whereby all directors are elected at one time.

Another possibility is staggered voting wherein part, say 1/3 of the board, is elected each year.


USA

Common Ordinary Shares Although in some countries, in Europe, and in

China, separate voting classes of stock are legal, they are not legal in the U.S. or Australia.

Shareholders also have the right to vote on matters of great importance to the company, such as merger of the firm into another.

Dividend decisions are made at board meetings, and the board declares a dividend to be paid at a certain future date with a given dollar amount.


USA

Common Ordinary Shares

In Australia, one means of raising more equity capital is through a rights issue.

In a rights issue, existing shareholders are given the right to buy more shares, in the new offering, in proportion to their current ownership of shares, e.g., if they own 10%, they get the right to buy 10% of the new issue.


USA

Stock Markets


USA

Intro Markets serve 2 important functions. Primary

markets are for issuing securities, i.e., hooking up people who need money with people who have money.

Secondary markets support the primary markets by providing a means to re-sell already-issued securities, rather than hold them til term or for forever.

Markets are especially important for equity, as there is really no alternative, except to walk the streets. At least, for debt, there are also banks and other financial institutions as alternatives.


USA

Brokers and Dealers An important thing to understand is that a

broker in stocks (or any thing else) just gets paid commissions to execute buy and sell orders. They are facilitators for trading.

Dealers, on the other hand, maintain an inventory of stocks (or bonds, or whatever), maintains a bid, the price he will buy at, and an ask (offer), the price that he will sell at.


USA

Brokers and Dealers

Dealers make money on the bid-ask spread by, at least, in theory, selling at a high price and buying at a lower one.

Markets comprised of dealer networks are called OTC (over the counter) markets, and part of the stock market, especially for shares of smaller companies, is an OTC market.


USA

Bid & Ask (Offer) In markets there are bid and ask prices. If you want to buy stock at $50, you enter a bid, the

price you want to buy at. If someone wants to sell at that price there will be a

transaction, if not, none. An ask or offer is the price someone is willing to sell

at. Transactions occur only when there is a matching

bid and ask. For example, if you bid $50 for 1000 shares, and

someone comes into sell at offer $50 for 20,000. He will sell you 1000 at $50.


The ASX

As opposed to OTC, the ASX is an exchange market with one best bid and offer for each share, as opposed to multiple bids and asks in a dealer network.

Members of the exchange are the only ones to execute orders for trading on the exchange.

Thus, when you call your broker, he calls his floor broker, and the floor broker member executes the trade.


USA

The ASX

The ASX used to be owned by its members, but it converted to a stock company and sold shares, originally to its members.

The ASX also has the roll of monitoring the companies listed on it.

Since the ASX, itself, has listed shares, it is regulated by the ASIC.


USA

The ASX Orders are executed by an electronic system

called Stock Exchange Automated Trading System (SEATS), so there is no actual trading floor, like the NYSE.

The ASX’s job is to manage the order flow from customers to buy and sell stocks.

The ASX maintains auction markets with bids and asks throughout the trading day. When bid matches ask, there is a transaction, a trade, a buy and a sell.


USA

The ASX

There is agent trading, executing orders for customer, or principal trading, by the actual members for their own accounts.

There are about 1700 companies listed for trading on the ASX.

See the book for the kind of information about the daily share trading market in financial newspapers.


USA

End


USA

Date post:	01-Jan-2016
Category:	Documents
Upload:	vernon-arnold
View:	218 times
Download:	0 times

Lecture 4: Securities Valuation C.L. Mattoli 1 (C) 2008Red Hill Capital Corp. USA.

Documents