Chapter 6 Review - Bond Valuation

10% coupon bond, with semiannual coupons, face value of 1,000, 20 years to maturity, $1,197.93 price. Find the Current yield and YTM.

Current yield = 100 / 1,197.93 = .0835 = 8.35% Capital gain yield = (1,193.68 - 1,197.93) / 1,197.93 = -.0035 = -.35% YTM= 8.35 - .35 = 8%, which the same YTM computed earlier

Bondholders may become _______ _______ when firms default on bond payments

Equity holders

Default risk premium

Extra compensation lenders demand for assuming the risk of default

On a financial calculator, par value/face value equals the

FV

High coupon rate bonds have ____ reinvestment rate risk than low coupon rate bonds

more

A Selling price above par value is called a

premium bond

nominal rate =

real rate + inflation rate

PMT and FV need to have the _____ sign. PV the ______ sign

same & Opposite

Bond rating

tells the investor the risk category that has been assigned to a bond

Coupon

the amount the bondholder receives as interest payments

Bid price

the price a dealer is willing to pay for a security

Ask price

the price at which a dealer or other trader will sell a security

Floating-rate bond (floaters)

-Coupon payments adjustable, -adjustments are tied to interest rate index such as Treasury bill interest rate, -value depends on how coupon payment adjustments are defined, lags behind interest rates -interest rate goes up/down payments stay the same

Treasury bonds

-Pay a fixed rate of interest every six months until they mature. -bought through a bank or broker

Oh Happy Day Properties wants to raise $4 million by selling bonds at par. Comparable bonds in the market have a 6.3% annual coupon, 10 years to maturity, and are selling at 101.7% of par. What coupon rate should Oh Happy Day Properties set on its bonds to sell these at $1000 per bond?

-Solve for I/Y -N = 10; PV=1000x1.017 = -$1,017; PMT=63 (.063x1000); FV=1000 CPT I/Y = 6.0683 rounded to 6.07%

real rate of return

-the nominal rate of return minus the inflation rate -percentage change in buying power

Notes lifetime

1 - 10 years

For Semiannual coupons, to find PMT you...

1. Divide Coupon rate by 2 2. Divide Par value (face value) by new Coupon rate

Debt and Equity legal recourse

Debt - Creditors HAVE legal recourse if interest or principal payments are missed Equity - Dividends are not liability of the firm and stockholders have NO legal recourse if dividends are not paid

Debt and equity voter rights

Debt - Creditors do NOT have voting rights Equity - Common stockholders VOTE for the board of directors and other issues

Debt and Equity tax deductibles

Debt - Interest is considered a cost of doing business and IS tax deductible Equity - Dividends are not considered a cost of doing business and are NOT tax deductible

Debt and equity ownership

Debt - Not an ownership interest Equity - Ownership interest

What is bond relationship with Dividends?

Dividends are paid on preferred/common stock, but not on bonds

T or F Coupon interest rates are usually fixed for many bonds

True

Premium bond with Annual coupons Suppose you are looking at a bond that has a 10% annual coupon and a face value of $1000. There are 20 years to maturity and the yield to maturity is 8%. What is the price of this bond?

Using a calculator: N = 20; I/Y = 8; PMT = 100; FV= 1000; CPT PV = -1,196.36

Yield to maturity formula w/ yields

current yield + capital gain yield

As Interest rates increase, bond prices _________ and vice versa

decrease

Debentures

unsecured bonds

Bond

A financial security that represents a promise to repay a fixed amount of funds over a long term basis (10+) years

Fixed bond rate

A rate that stays as a fixed percentage of the par value

When Computing yield-to-maturity (YTM), _____ is the missing piece of information on the financial calculator

CPT I/Y

Bond pricing equation

C[1-(1/(1+r)^t)/r] + F/(1+r)^t F= Face/par value of bond r= yield to maturity n= no. of periods C= Coupon bond price

Default risk

Chance of debt not getting paid back

Collateral is secured by

Financial securities

Multiple securities

High tax rates will invest to not pay federal taxes, revenue bonds

Suppose a bondholder pays a bond by repurchasing 5% of the bond issue each year. Over 20 years all the bonds are repaid. This is an example of...

Sinking fund

Maturity date

Specific date when principal is repaid

Protective covenants

Limits certain actions during the term of the loan

Low grade bond ratings

Moody's Ba and B S&P BB and B Considered possible that the capacity to pay will degenerate.

Let the Coupon rate = 14% with semiannual (2) coupons; YTM = 16%; Maturity = 7 years; Par value = $1,000

PMT = 70 (look above for formula); N = 14 (7x2); I/Y = 8 (YTM/2); FV = 1,000; CPT PV = -917.56

If given YTM, how to find Interest rate (PMT)?

PMT = YTM/semiannual or annual

Bond value formula #2

PV of annuity + PV of lump sum

Bond value formula

PV of coupons + PV of face value

Types of common bonds

Structured notes, convertible, put bond, CoCo bonds, NoNo bonds,

The discount (increases/decreases) the yield (YTM) to above the coupon rate

increases

Bills lifetime

less than 1 year

Two forms of Interest rate risk

1. Price risk 2. Reinvestment rate risk

Risk characteristics include

1. Subordinated debenture vs Senior debt? 2. Sinking fund vs no Sinking fund 3. Callable bond vs Non-callable bond 4. Short term note vs Long term bond

Discount bond with Annual coupons question Consider a bond with a coupon rate of 10% and annual coupons. The par value is $1,000 and the bond has 5 years to maturity. The yield to maturity is 11%. What is the value of the bond?

1. Use the formula Bond value = PV of annuity + PV of lump sum = 100[1 - 1/(1.11)^5]/.11 + 1000/(1.11)^5 (C=Par Value x Coupon Rate) = 369.59 + 593.45 = $963.04 (Calc tip. Input 100(1-1/(1.11))^5) first and then /.11) FIN calc N =5; I/Y = 11; PMT=100; FV = 1000; CPT PV = -963.04

A Microgates Industries bond has a 10 percent coupon rate and a $1,000 face value. Interest is paid semiannually, and the bond has 20 years to maturity. If investors require a 12 percent yield, what is the bond's value? What is the effective annual yield on the bond?

50 => PMT; 40 => N; 6 => I/Y; 1000 => FV; CPT PV = - 849.54 EAR = [1 + APR/m]m - 1 (APR = .06*2)(Interest rate x # of compounding periods) EAR = 1 + .12/2]2 - 1 EAR = .1236 or 12.36%

If YTM < coupon rate, then par value (</>) bond selling price

<

If YTM = coupon rate, then par value __ selling price

=

Premium

A bond sells higher than its par value

Risk-free asset

An asset that has a certain future return - with virtually no possibility of loss

Coupon rate

Annual coupon / face value

Discount

Bond sells lower than its par value

Law of One price

Bonds of similar risk will be priced to yield about the same return, regardless of the coupon rate

Convertible bonds

Bonds that can be converted into common stock at the bondholder's option

over the counter (OTC)

No particular place where buying and selling occur, instead dealers stand ready around the world

Collateral value of assets

Collateral is simply an asset, such as a car or home, that a borrower offers up as a way to qualify for a particular loan

YTM formula

Interest rate x # of periods

Sinking fund bonds

Means of repaying funds early, borrowed through a bond issued, through periodic payments to a trustee who retires part of the issue by purchasing the bonds in the open market

Medium grade bond rating

Moody's A and S&P A - capacity to pay is strong, but more susceptible to changes in circumstances Moody's Baa and S&P BBB - capacity to pay is adequate, adverse conditions will have more impact on the firm's ability to pay

High grade bond ratings

Moody's Aaa and S&P AAA - capacity to pay is extremely strong Moody's Aa and S&P AA - capacity to pay is very strong

Very low grade bond ratings

Moody's C (and below) and S&P C (and below) income bonds with no interest being paid, or in default with principal and interest in arrears

Low coupon rate bonds have _______ price risk than high coupon rate bonds, since most of its value is in the par value

More

Short-term bonds have ______ reinvestment rate risk than long-term bonds

More

Long-term bonds have ______ interest rate risk than short-term bonds, hence are more ______

More & Volatile

For Semiannual coupons, to find N (number of years)

Multiply Maturity by 2

Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1,000. The current price is $928.09.

N = 15; PV = -928.09; FV = 1,000; PMT = 100; CPT I/Y= 11%

Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1,000, instead had 19 years to maturity, also at 4% for 6 months.

N = 38; PMT = 50; FV = 1,000; I/Y = 4%; CPT PV = -1,193.68

YTM with Semiannual Coupons Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1,000, 20 years to maturity and is selling for $1,197.93.

N = 40; PV = -1,197.93; PMT = 50; FV = 1,000; CPT I/Y= 4% (Is this the YTM?) YTM = 4%*2 = 8% N = years to maturity x 2 PMT = coupon rate/2; face value x new coupon rate

Bond Prices: Dufner Co. issued 15-year bonds one year ago at a coupon rate of 4.8 percent. The bonds make semiannual payments. If the YTM on these bonds is 5.3 percent, what is the current dollar price assuming a $1,000 par value?

N= 28 [1 year ago, so 15-1 = 14*2 (semiannual) PMT=24[1,000*4.8% = 48/2] (semiannual) I/Y=2.65% [5.3%/2] (semiannual) FV=1,000 CPT PV = -951.02

If a bond has a zero-coupon rate, does it gain market rate interest?

No

nominal rate of return: inflation: fisher effect equation

R = (approximately) r + h OR (1+nominal R)=(1+real rate r)x(1+expeceted inflation rate h) r = real rate of return h = inflation rate

Yield or Yield to maturity (YTM)

Shows the total return you will receive if you hold the bond to maturity

On a financial calculator, to find the PMT you...

Take the face value and divide it by the annual coupon rate

Price risk

The change in price due to changes in interest rates

Reinvestment rate risk

The uncertainty concerning rates at which cash flows can be reinvested

Par value (face value)

What the security costs to purchase

Public issue

When a company raises funds by selling or issuing its shares to the public through issue of offer document/prospectus

put bond

allows the holder to force the issuer to buy the bond back at a stated price before maturity. The reverse of a call provision

As interest rate increases, the present value ________

decreases

Price selling below par value is called

discount bond

Nominal rates

interest rates or rates of return that have not been adjusted for inflation