Chapter 7 Finma2

Chapter 7 - The Valuation and Characteristics of Bonds

ValuationA systematic process through which the price at which a security should sell is established - Intrinsic valueTHE BASIS OF VALUE– Real assets (houses, cars) have value due to services they provide– Financial assets (paper) represent rights to future cash flows

Value today is PV

Different opinions about securities’ values come from different assumptions about cash flows and interest rates– Stocks are hardest to value because future dividends and prices are

never guaranteed.

The Basis of Value

Any security’s value is the present value of the cash flows expected from owning it.

– A security should sell for close to that value in financial markets

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The Basis of Value

InvestingUsing a resource to benefit the future rather than for current satisfaction– Putting money to

work to earn more money

– Common types of investments

DebtEquity

ReturnWhat the investor receives for making an investment– 1 year investments

return = $ received / $ invested

– Debt investors receive interest. Equity investors get dividends + price change

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Definition

The rate of return on an investment is the interest rate that equates the present value of its expected cash flows with its current priceReturn is also known as – Yield, or– Interest

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Return On One Year Investment

Return is what the investor receives Can be expressed as a dollar amount or as a rate

Rate of return is what the investor receives divided by what was invested For debt investments: the interest rate

In terms of the time value of money: Invest PV at rate k and receive future cash flows of principal = PV, and interest = kPV at the end of a year, so

FV1 = PV + kPV FV1 = PV(1+k)

PV = FV(1 + k)

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The Basis for Value

Discount Rate The term discounted rate is often used for interest rate

Returns on Longer-Term Investments

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Bonds

Bonds represent a debt relationship in which an issuing company borrows and buyers lend. – A bond issue represents borrowing from many

lenders at one time under a single agreement

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Bond Terminology and Practice

A bond’s term (or maturity) is the time from the present until the principal is returned

A bond’s face (or par) value represents the amount the firm intends to borrow (the principal) at the coupon rate of interest

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Coupon Rates

Coupon Rate – the fixed rate of interest paid by a bond In the past, bonds had “coupons” attached, today they are “registered” Most bonds pay coupon interest semiannual

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Bond Valuation—Basic Ideas

Adjusting to Interest Rate Changes– Bonds are originally sold in the primary market and

trade subsequently among investors in the secondary market.

– Although bonds have fixed coupons, market interest rates constantly change.

– How does a bond paying a fixed interest rate remain salable (secondary market) when interest rates change?

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Bond Valuation—Basic Ideas

Bonds adjust to changing yields by changing their prices – Selling at a Premium – bond price above face value– Selling at a Discount – bond price below face value

Bond prices and interest rates move in opposite directions

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Determining the Price of a Bond

The value (price) of a security is equal to the present value of the cash flows expected from owning it. In bonds, the expected cash flows are predictable.– Interest payments are fixed, occurring at regular

intervals. – Principal is returned along with the last interest

payment.

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Determining the Price of a BondFigure 7-1 Cash Flow Time Line for a Bond

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This bond has 10 years until maturity, a par value of $1,000, and a coupon rate of 10%.?


The Bond Valuation Formula– The price of a bond is the present value of a stream

of interest payments plus the present value of the principal repayment

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k,n

Interest payments are annuities--can usethe present value of an annuity form

Principal repayment is a lump sum in ula:

PMT[PVFA

the futur

]

B PV(princiPV(interest payme pal repaymP +nt ) es nt)

k, n

e--can use the future value formula:FV[PVF ]


Two Interest Rates and One More– Coupon Rate– k - the current market yield on comparable bonds– “Current yield” - annual interest payment divided by

bond’s current price– Not used in valuation– Info for investors

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Figure 7-2 Bond Cash Flow and Valuation Concepts

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Concept Connection Example 7-1 Finding the Price of a Bond

Emory issued a $1,000, 8%, 25-year bond 15 years ago.Comparable bonds are yielding 10% today.

What price will yield 10% to buyers today? What is the bond’s current yield?

Assume the bond pays interest semiannually.


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Must solve for present value of bond’s expected cash flows at today’s interest rate. Use Equation 7.4 :

B k, n k, nP [PVFA ] + [PVFFVM ]P Tk represents the periodic

current market interest rate, or

10% 2 = 5%.

n represents the number of

interest-paying periods until maturity, or

10 years x 2 = 20.

The payment is 8% x $1,000, or $80 annually. However, it is received in the

form of $40 every six months.

The future value is the principal repayment of

$1,000.


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Substituting :

B 5%, 20 5%, 20P $40[PVFA ] + $1,000[PVF ]

$40[12.4622] + $1,000[0.3769]$498.49 $376.90$875.39

This is the price at which the bond must sell

to yield 10%. It is selling at a discount

because the current interest rate

is above the coupon rate.

The bond’s current yield is

$80 $875.39, or 9.14%.

Maturity Risk Revisited

Related to the term of the debt– Longer term bond prices fluctuate more in response

to changes in interest rates than shorter term bonds– AKA price risk and interest rate risk

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Table 7-1 Price Changes at Different Terms Due to an Interest Rate Increase from 8% to 10%

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Figure 7.3 Price Progression with Constant Interest Rate

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Finding the Yield at a Given Price

Calculate a bond’s yield assuming it is selling at a given priceTrial and error – guess a yield – calculate price – compare to price given

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B , n k, nkP PMT PVFA + FV PVF Involves solving for k, which is more complicated because it

involves both an annuity and a FV

Use trial and error to solve for k, or use a financial

calculator.

Concept Connection Example 7-3 Finding the Yield at a Price

Benson issued a $1,000, 8%, 30-year bond 14 years ago. – Bond is now selling for $718. – What is yield to an investor buying it today? – Semiannual interest.

Concept Connection Example 7-3 Finding the Yield at a Price

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As interest rates rise, bond prices fall, so yield must be above 8%. Guess 10% and apply Equation 7.4

Next guess must be lower to drive price further down.Answer is just below 12%

B k, n k, n

5, 32 5, 32

P PMT PVFA + FV PVF

$40 PVFA + $1,000 PVF

$40 15.8027 + $1,000 0.2099

$842.01

Call Provisions

If interest rates fall, a firm may wish to retire old, high interest bonds by “refinancing” with new, lower interest debt– To ensure ability to refinance, issuers make bonds

‘callable’– Investors don’t like calls – lose high interest – Issuers and investors compromise – Call provisions usually have

A call premium– Extra money paid if called

Period of call protection– Guaranteed not to call for a number of years.

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Figure 7-5 Valuation of a Bond Subject to Call

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Call Provisions

Valuing the Sure-To-Be-Called Bond– Requires that two changes be made to bond

valuation formula

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nB k, k, nP PMT[PVFA ] + [PVFFV ]

n now represents the

number of periods until the bond is likely to be

called.

The future value becomes the call price (face value

plus call premium).

Call Provisions

The new formula becomes PB = PMT[PVFAk,m] + CP[PVFk,m]Where

m = time to callCP = call price = FV + Call Premium

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Concept Connection Example 7-4 Basics: Pricing a “Likely to Be Called” Bond

Northern issued a $1,000, 25-year bond 5 years ago.

Call provision: Can call after 10 years with the payment of one additional year’s interest at coupon rate.

Coupon rate is 18%. Market rate is now 8%.

What is the bond worth today?

Interest payments are semiannual.


The bond must yield the current rate of interest in either case.


]CP[PVF]PMT[PVFA(call)P mk,mk,B m = number of periods to callCP = call price = face value + call premium

PMT = (.18 x $1,000) / 2 = $90m = 5 x 2 = 10k = 8% /2 = 4%CP = $1,000 + .18($1,000) = $1,180

PB (call) = $90 [PVFA4,10] + $1,180 [PVF4,10] = $90[8.1109] + $1,000[.6756] = $729.98 + $797.21 = $1,527.19

The Refunding Decision

When current interest rates fall below the bond’s coupon rate, a firm must decide whether to call in the issue– Compare interest savings to cost of making call:

Call premium Flotation costs –Broker fees, printing costs, etc.

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Dangerous Bonds with Surprising Calls

Bonds can have obscure call features buried in their contract terms.

– Most common type – a sinking fund provision – requires an issuer to call in and retire a fixed percentage of the issue each year

– Generally no call premiumProvision is for the benefit of the bondholder

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Risky Issues

Sometimes bonds sell for a price far below what valuation techniques suggest– Issuing company may be in financial trouble

Buying the bond is very riskyIn theory riskier loans should be discounted at higher rates leading to lower calculated prices

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Convertible Bonds

Unsecured bonds exchangeable for a fixed number of shares of stock at the bondholder's discretionConversion ratio - the number of shares of stock received for each bond

Conversion price - the implied stock price if bond is converted into a certain number of sharesConvertibles usually pay lower coupon rates

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exchanged sharesratio conversion price conversionvalue par s bond'

Concept Connection Example 7-5 Basics: Investing in Convertible Bonds

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Harry Jenson purchased one of Algo Corp.’s 9%, 25-year convertible bonds at its $1,000 par value a year ago when the company’s common stock was selling for $20. Similar bonds without a conversion feature returned 12% at the time. The bond is convertible into stock at a price of $25. The stock is now selling for $29. Algo pays no dividends.

Notice that this bond’s coupon rate was set below the market rate for nonconvertible issues.


a. Harry exercised the conversion feature today and immediately sold the stock he received. Calculate the total return on his investment.b. What would Harry’s return have been if he had invested $1,000 in Algo’s stock instead of the bond?


price conversionvalue par exchanged shares

$25$1,000 shares 40

The proceeds from selling those shares at the current market price were

1,160 $ $29x 40

In addition the bond paid interest during the year of

$90 .09x $1,000

So the total receipts from the bond investment were

1,250 $ $90 $1,160


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Notice that the convertible enabled Harry to participate in some but not all of the rapid price appreciation of Algo’s stock.Also notice that had the stock price fallen, an investment in it would have had a negative return, but the convertible would have returned the 9% coupon rate.

Convertible Bonds

Effect of Conversion on Financial Statements and Cash Flow– An accounting entry removes the value of

convertible bonds from long-term debt placing it into equity as if new shares were sold

– No immediate cash flow impact, but ongoing cash flow implications exist

Interest payments stopBut dividend payments may start

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Advantages of Convertible Bonds

To Issuing Companies

Convertible features are “sweeteners” enabling a risky firm to pay a lower interest rateViewed as a way to sell equity at a price above marketUsually have few or no restrictions

To Buyers

Offer the chance to participate in stock price appreciationOffer a way to limit risk associated with a stock investment

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Forced Conversion

A firm may want bonds converted – As stock price rises convertible represents a lost

opportunity to sell new equity at a higher priceConvertible bonds are always issued with call features which can be used to force conversionIssuers generally call convertibles when stock prices rise to 10-15% above conversion prices

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Valuing (Pricing) Convertibles

A convertible’s price can depend on either– its value as a traditional bond or – the market value of the stock into which it can be

converted

A convertible is always worth at least the larger of its value as a bond or as stock

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Figure 7-6 Value of a Convertible Bond

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Effect on Earnings Per Share—Diluted EPS

Upon conversion convertible bonds cause dilution in EPS– EPS drops due to the increase in the number of

shares of stock outstandingThus outstanding convertibles represent a potential to dilution of EPS

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Concept Connection Example 7-7 - DilutionMontgomery Inc. Issued two thousand $1,000, 8% coupon convertible bonds three years ago. Each bond is convertible into stock at $25 per share. All of the Bonds remain outstanding, i.e., none have converted.Last year net income was $3 million. One million shares stock were outstanding for the entire year, and the firm’s marginal tax rate was 40%. Calculate Montgomery’s basic and diluted EPS for the year.

Solution:

Basic EPS net income ÷ number of shares $3,000,000 ÷ 1,000,000 = $3.00.

Concept Connection Example 7-7 DilutionDiluted EPS Assumes all bonds are converted at beginning of year. 1. Add the number of newly converted shares to denominator.2. Adjust net income for after tax effect of interest saved.

1. Shares exchanged:Par ÷ Conversion price = $1,000 ÷ $25 = 40 shares/bond40 shares/bond × 2,000 bonds = 80,000 sharesNew shares outstanding = 1,000,000 + 80,000 = 1,080,000

2. Adjust the net income by interest saved:Interest paid on bonds: .08 x $1,000 x 2,000 = $160,000After tax: $160,000 × (1-.4) = $96,000New net income = $3,000,000 + $96,000 = $3,096,000

Diluted EPS: $3,096,000 ÷ 1,080,000 = $2.87

Institutional Characteristics of BondsKinds of Bonds

Bonds are either bearer or registered

Registered, Owners of Record, Transfer Agents

Owners of registered bonds are recorded with a transfer agent.

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Kinds of Bonds

Secured bonds and mortgage bonds– Backed by specific assets - collateral

Debentures– Unsecured bonds - riskier

Subordinated debentures– Lower in payment priority than senior debt

Junk bonds– Risky companies - high interest rates

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Bond Ratings—Assessing Default Risk

Bonds are assigned quality ratings reflecting their probability of default.– Higher ratings mean lower default probability – Higher rated bonds pay lower interest rates

Bond rating agencies (Moody’s, S&P) evaluate bonds (and issuers), and assign a ratings

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Bond Ratings—Table 7.2

Figure 7-7 Yield Differentials between High- and Low-Quality Bonds

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Controlling Default RiskBond Indentures

Bond indentures attempt to prevent borrowing firms from becoming riskier after bonds issued– restrictive covenants – limit activities and payouts

Safety also provided by sinking funds– Provide money for repayment of bond principal

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Appendix 7-A - Lease Financing

A lease is a contract giving one party (lessee) the right to use an asset owned by another (lessor) for a periodic payment– Individuals usually lease houses, apartments, and

automobiles– Companies lease equipment and real estate

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Leasing and Financial Statements

Originally leasing allowed use without ownership– Lease payments recognized as income statement

expenses, but– No impact on balance sheets

No recognition of ownership or obligation to payImproved appearance of financial ratios– Not real

Led to widespread use of lease financing– The leading form of “off balance sheet financing”

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Misleading Results

Off balance sheet financing makes financial statements misleading– Missed lease payments can cause failure just like

a missed interest payment on debt– Not showing leases on the balance sheet can

mislead investors into thinking a firm is stronger than it is

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FASB 13 Redefines Ownership

1970s: Concerns about leasing led to FASB 13– Prior to FASB 13 an asset was owned for financial

statement purposes by whoever held title Regardless of who used it

– FASB 13 redefined ownership for financial reporting purposes in economic terms

– FASB 13 stated that the real owner of an asset is whoever enjoys its benefits and bears its risks and responsibilities

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Operating and Capital (Financing) Leases

Under FASB 13 lessees must capitalize financing leases– Puts the value of leased assets and the liability for

payments on the balance sheet– Long term leases for high value assets

Operating leases can still be listed off the balance sheet– Short term leases for lower value items

Rules must be met for a lease to be classified as an operating lease

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Financial Statement Presentation of Leases by Lessees

Operating leases– Recognize rent expense– No balance sheet entries

Financing (Capital) leases– Recognize asset and lease obligation on balance

sheet– Recognize depreciation expense for asset– Amortize lease obligation like a loan

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Leasing from the Perspective of the Lessor

Lessors are usually financial institutions - banks, finance or insurance companiesLease payments are calculated to offer the lessor a given returnLessor holds legal title—can repossess assets if lessee defaultsLessors get better treatment in bankruptcy proceedings than lenders

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Residual Values

Residual value—the value of asset at the end of the lease Makes lease pricing and return calculations more complexImportant negotiating points between lessee and lessor

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Lease Vs. BuyThe Lessee’s Perspective

Broad financing possibilities– Equity– Debt—available through bonds or banks– Leasing—available through leasing companies

Conduct a lease vs. buy comparison– Choose the lowest cost option in a present value

senseLeasing is almost always more expensive

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The Advantages of Leasing

Lessors usually require no down payment, lenders want significant money downLessor’s restrictions less stringent than lenders’Easier credit with manufacturers/lessors

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The Advantages of Leasing

Short leases transfer the risk of obsolescence to lessorsTax deducting the cost of landIncreasing liquidity—the sale and leasebackTax advantages for marginally profitable companies

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Leveraged LeasesThe ability to depreciate assets reduces taxes– Government shares the cost of ownership

Unprofitable firms lose this benefit as they pay no tax – But can get some benefits with a Leveraged Lease

In a leveraged lease, a profitable lessor buys equipment financing a portion with borrowed money (hence a leveraged lease) – Leveraged Lessor receives the tax benefits of ownership

Lessor shares those tax benefits with the lessee through lower lease payments– Lessee’s savings can be very substantial

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Figure 7A-1 Leveraged Leases

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Chapter 7 Finma2

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