# Chapter 7 - The Valuation and Characteristics of Bonds

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Chapter 7 - The Valuation and Characteristics of Bonds

Valuation A systematic process through which the price at which a security should sell is established - Intrinsic value THE 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

The Basis of Value Investing
Using a resource to benefit the future rather than for current satisfaction Putting money to work to earn more money Common types of investments Debt Equity Return What the investor receives for making an investment 1 year investments return = \$ received / \$ invested Debt investors receive interest. Equity investors get dividends + price change

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 price Return is also known as Yield, or Interest

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)

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

Returns on Longer-Term Investments

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

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

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

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?

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

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.

Determining the Price of a Bond Figure 7-1 Cash Flow Time Line for a Bond
This bond has 10 years until maturity, a par value of \$1,000, and a coupon rate of 10%.?

Determining the Price of a Bond
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

Determining the Price of a Bond
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

Figure 7-2 Bond Cash Flow and Valuation Concepts

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.

Concept Connection Example 7-1 Finding the Price of a Bond
Must solve for present value of bond’s expected cash flows at today’s interest rate. Use Equation 7.4 : k represents the periodic current market interest rate, or 10%  2 = 5% . The payment is 8% x \$1,000, or \$80 annually. However, it is received in the form of \$40 every six months. n represents the number of interest-paying periods until maturity, or 10 years x 2 = 20. The future value is the principal repayment of \$1,000.

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

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

Figure 7.3 Price Progression with Constant Interest Rate

Finding the Yield at a Given Price
Calculate a bond’s yield assuming it is selling at a given price Trial and error – guess a yield – calculate price – compare to price given 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
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%

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.

Figure 7-5 Valuation of a Bond Subject to Call

Valuing the Sure-To-Be-Called Bond
Call Provisions Valuing the Sure-To-Be-Called Bond Requires that two changes be made to bond valuation formula 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 call CP = call price = FV + Call Premium

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.

Concept Connection Example 7-4 Basics: Pricing a “Likely to Be Called” Bond
The bond must yield the current rate of interest in either case.

Concept Connection Example 7-4 Basics: Pricing a “Likely to Be Called” Bond
m = number of periods to call CP = call price = face value + call premium PMT = (.18 x \$1,000) / 2 = \$90 m = 5 x 2 = 10 k = 8% /2 = 4% CP = \$1, (\$1,000) = \$1,180 PB (call) = \$90 [PVFA4,10] + \$1,180 [PVF4,10] = \$90[8.1109] + \$1,000[.6756] = \$ \$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.

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 premium Provision is for the benefit of the bondholder

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 risky In theory riskier loans should be discounted at higher rates leading to lower calculated prices

Convertible Bonds Unsecured bonds exchangeable for a fixed number of shares of stock at the bondholder's discretion Conversion 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 shares Convertibles usually pay lower coupon rates

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

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

Concept Connection Example 7-5 Basics: Investing in Convertible Bonds
The proceeds from selling those shares at the current market price were In addition the bond paid interest during the year of So the total receipts from the bond investment were

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

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

Concept Connection Example 7-5 Basics: Investing in Convertible Bonds
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 stop But dividend payments may start

To Issuing Companies Convertible features are “sweeteners” enabling a risky firm to pay a lower interest rate Viewed as a way to sell equity at a price above market Usually have few or no restrictions To Buyers Offer the chance to participate in stock price appreciation Offer a way to limit risk associated with a stock investment

Forced Conversion A firm may want bonds converted
As stock price rises convertible represents a lost opportunity to sell new equity at a higher price Convertible bonds are always issued with call features which can be used to force conversion Issuers generally call convertibles when stock prices rise to 10-15% above conversion prices

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

Figure 7-6 Value of a Convertible Bond

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 outstanding Thus outstanding convertibles represent a potential to dilution of EPS

Concept Connection Example 7-7 - Dilution
Montgomery 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 Dilution
Diluted 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/bond 40 shares/bond × 2,000 bonds = 80,000 shares New shares outstanding = 1,000, ,000 = 1,080,000 2. Adjust the net income by interest saved: Interest paid on bonds: .08 x \$1,000 x 2,000 = \$160,000 After tax: \$160,000 × (1-.4) = \$96,000 New net income = \$3,000,000 + \$96,000 = \$3,096,000 Diluted EPS: \$3,096,000 ÷ 1,080,000 = \$2.87

Institutional Characteristics of Bonds Kinds of Bonds
Bonds are either bearer or registered Registered, Owners of Record, Transfer Agents Owners of registered bonds are recorded with a transfer agent.

Kinds of Bonds Secured bonds and mortgage bonds Debentures
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

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

Bond Ratings—Table 7.2

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

Controlling Default Risk Bond 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

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

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 pay Improved appearance of financial ratios Not real Led to widespread use of lease financing The leading form of “off balance sheet financing”

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

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

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

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

Leasing from the Perspective of the Lessor
Lessors are usually financial institutions - banks, finance or insurance companies Lease payments are calculated to offer the lessor a given return Lessor holds legal title—can repossess assets if lessee defaults Lessors get better treatment in bankruptcy proceedings than lenders

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

Lease Vs. Buy The 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 sense Leasing is almost always more expensive

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

Short leases transfer the risk of obsolescence to lessors Tax deducting the cost of land Increasing liquidity—the sale and leaseback Tax advantages for marginally profitable companies

Leveraged Leases The 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

Figure 7A-1 Leveraged Leases