Corporate Finance Bond Valuation

bond

is a long-term contract under which a borrower agrees to make payments of interest and principal on specific dates to the holders of the bond

• Call provision

is valuable to the firm but detrimental to long-term investors A provision in a bond contract that gives the issuer the right to redeem the bonds under specified terms prior to the normal maturity date

rd > coupon rate: fixed-rate bond sells below par;

it is a discount bond.

rd = coupon rate: fixed-rate bond sells at par;

it is a par bond

rd < coupon rate: fixed-rate bond sells above par;

it is a premium bond.

• Once it has been issued

it is an outstanding bond, also called a seasoned issue The prices of outstanding bonds can vary widely from par

price risk

relates to the current market value of the bond portfolio

A company is more likely to call its bonds if they are able to

replace their current high-coupon debt with less expensive financing • Broadly speaking, a bond is more likely to be called if its price is above par • Because a price above par means that the going market interest rate (the yield to maturity) is less than the coupon rate

rd:

the discount rate used to calculate the PV of the cash flows It is NOT the coupon interest rate

Coupon Interest Payment

the number of dollars of interest

N:

the number of periods before the bond matures. N declines over time after the bond has been issued.N is different from the number of years when coupon is paid semi-annually

Original maturity

the number of years to maturity at the time a bond is issued

M:

the par value of the bond. This is the amount paid at maturity

Investment horizon:

the period of time an investor plans to hold a particular investment

Par Value

the stated face value of the bond Commonly $1,000, but could be any multiple of $1,000 • The amount of money the firm borrows and promises to repay on the maturity date

Although some bonds pay interest annually,

the vast majority actually make payments semiannually

Zero-Coupon Bonds:

Bonds that pay no annual interest

By the type of issuers:

Treasury bonds • Municipal bonds • Corporate bonds • Foreign bonds

Coupon Interest Rate:

the stated annual interest rate on a bond

• Credit rating agencies

use both qualitative and quantitative factors to determine the bond ratings • Financial Ratios • Qualitative Factors: indenture, restrictive covenants... • Miscellaneous Qualitative Factors

Refunding operation:

when the interest rates drop, firms could issue new lowyielding securities and retire the high-rate issue to reduce interest expense

A bond's calculated YTM changes

whenever interest rates in the economy change

If you purchase a bond that is callable and the company calls it

you do not have the option of holding it to maturity And you don't earn the YTM

Default risk on Treasuries is zero

but this risk is substantial for lower-grade corporate and municipal bonds

Convertible Bonds:

: bonds that are exchangeable at the option of the holder for the issuing firm's common stock

Annual: Coupon Payment

= Coupon Rate * Par Value

Sinking Fund Provision

A provision that requires the issuer to retire a portion of the bond issue each year • A sinking fund is a mandatory payment. A failure to meet the sinking fund requirement constitutes a default, which may throw the company into bankruptcy Generally, bonds that have a sinking fund are regarded as being safer than those without such a provision - Lower coupon rates when issued

Maturity Date

A specified date on which the par value of a bond must be repaid The bond maturity could range from 10 to 40 years The maturity declines each year after it has been issued

Allied currently has three equally risky issues that will mature in 15 years. All of them have face value of $1,000. Find their current market prices:

Allied's just-issued 15-year bonds have a 10% annual coupon. They were issued at par. • $1,000 (Par Bond) Five years ago, Allied issued 20-year bonds with a 7% annual coupon. (discount bond) Inputs 15 10 70 1,000 N I/YR PV PMT FV Outputs -771.82 Ten years ago, Allied issued 25-year bonds with a 13% annual coupon. Inputs 15 10 130 1,000 N I/YR PV PMT FV Outputs -1,228.18

Floating-Rate Bonds:

Bonds whose interest rate fluctuates with shifts in the general level of interest rates

Fixed-Rate Bonds:

Bonds whose interest rate is fixed for their entire life

Semi-Annual: Coupon Payment =

Coupon Rate / 2 * Par Value

A friend of yours just invested in an outstanding bond with a 5% annual coupon and a remaining maturity of 10 years. The bond has a par value of $1,000 and the market interest rate is currently 7%. How much did your friend pay for the bond? Is it a par, premium, or discount bond?

Inputs 10 7 ($1,000*5%=50) 1,000 N I/YR PV PMT FV Outputs -859.53 Discount bond because − the market price ($859.53) is less than the par value ($1,000) − Or the market rate (7%) is greater than the coupon rate (5%)

Suppose you were offered a 14-year, 10% annual coupon, $1,000 par value bond at a price of $1,494.93. What rate of interest would you earn on your investment if you bought the bond, held it to maturity, and received the promised interest payments and maturity value?

Inputs 14 -1,494.93 100 1,000 N I/YR PV PMT FV Outputs 5 This rate is called the bond's yield to maturity (YTM)

Suppose you were offered a 14-year, 10% annual coupon, $1,000 par value bond at a price of $1,494.93. This bond is callable 9 years after the issue date and the call price is $1,100. What is the yield to maturity (YTM)?

Inputs 14 -1,494.93 100 1000 N I/YR PV PMT FV Outputs 5

You have just purchased an outstanding 15-year bond with a par value of $1,000 for $1,145.68. Its annual coupon payment is $75. What is the bond's yield to maturity?

Inputs 15 -1,145.68 75 1,000 N I/YR PV PMT FV Outputs 6

A 15-year fixed-rate bond with par value of $1,000, coupon rate 10%, and coupons are paid annually. Assume the discount rate is 10%. What is the bond price today?

Inputs 15 10 100 1,000 N I/YR PV PMT FV Outputs -1,000

What is the price for a 15-year, 10% semiannual coupon bond with par value of $1,000, if the current nominal rate is 5%?

Inputs 15*2=30 5/2=2.5 10%*1000/2=50 1,000 N I/YR PV PMT FV Outputs -1,523.26

You have just purchased an outstanding noncallable, 15-year bond with a par value of $1,000. Assume that this bond pays interest of 7.5%, with semiannual compounding. If the going (nominal) annual rate is 6%, what price did you pay for this bond?

Inputs 15*2=30 6/2=3 7.5%*1000/2=37.5 1,000 N I/YR PV PMT FV Outputs -1,147.00

• Halley Enterprises's bonds currently sell for $975. They have a 7-year maturity, an annual coupon of $90, and a par value of $1,000. What is their yield to maturity?

Inputs 7 -$975 $90 1,000 N I/YR PV PMT FV Outputs 9.51

Now, assume that this bond is callable in 7 years at a price of $1,075. What is the bond's YTC? If the yield curve remains flat at its current level during this time period, would you expect to earn the YTM or YTC?

Inputs 7 -1,145.68 75 1,075 N I/YR PV PMT FV Outputs 5.81 This bond sells at a premium, so interest rate is less than the coupon rate. If the yield curve remained flat at current level, you would expect the firm to call the bond and issue new bonds at lower interest rate

A bond that matures in 8 years has a par value of $1,000 and an annual coupon payment of $70; its market interest rate is 9%. What is its price?

Inputs 8 9 70 1,000 N I/YR PV PMT FV Outputs -889.30

Suppose you were offered a 14-year, 10% annual coupon, $1,000 par value bond at a price of $1,494.93. This bond is callable 9 years after the issue date and the call price is $1,100. What is the yield to call (YTC)?

Inputs 9 -1,494.93 100 1,100 N I/YR PV PMT FV Outputs 4.21

Various Types of Corporate Bonds

Mortgage bond: a bond backed by real estates assets • Debentures: a long-term bond that is not secured by a mortgage on specific property • Subordinated Debentures: bonds having a claim on assets only after the senior debt has been paid in full in the event of liquidation

A bond that has just been issued is known as a new issue

Newly issued bonds generally sell at prices very close to par

call premium

The issuer must pay the bondholders an amount greater than the par value

Yield to Call (YTC)

The rate of return earned on a bond when it is called before its maturity date

Price (Interest Rate) Risk:

The risk of a decline in a bond's price due to an increase in interest rates • Rising rates cause losses to bondholders Price risk is higher on bonds that have long maturities among bonds with similar coupons

Reinvestment Risk:

The risk that a decline in interest rates will lead to a decline in income from a bond portfolio When bonds mature, bondholders have to replace bonds with high coupon rate with bonds with low coupon rate

yield to maturity

YTM is the return that investors will receive if all of the promised payments are made YTM equals the expected rate of return only when • The probability of default is zero • The bond cannot be redeemed early

When a coupon bond is issued, the coupon is generally set

at a level that causes the bond's market price to equal its par value

Until the 1970s, most bonds were

beautifully engraved pieces of paper and their key terms, including their face values, were spelled out on the bonds

INT:

dollar value of interest paid every period

Short investment horizon:

holding long-term bonds leads to more price risk

• Long investment horizon:

holding short-term bonds leads to more reinvestment risk

• If the issuer defaults

investors will receive less than the promised return