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