FRL CH 7 Bonds and Bond Valuation
Nominal interest rate
quoted rate of interest, change in actual number of dollars
The after-tax returns on Corporate bonds versus
A taxable bond has a yield of 8%, and a municipal bond has a yield of 6%. If you are in a 40% tax bracket, which bond do you prefer? 8%(1 - .4) = 4.8% The after-tax return on the corporate bond is 4.8%, compared to a 6% return on the municipal At what tax rate would you be indifferent between the two bonds? 8%(1 - T) = 6% T = 25%
Repayment (Sinking Fund) Provision
Bond without sinking fund: company has to come up with substantial cash at maturity to retire debt, and this is riskier than systematic retirement of debt through time
Bond values with annual coupon
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? Using the formula: B = PV of annuity + PV of lump sum B = 100[1 - 1/(1.11)5] / .11 + 1,000 / (1.11)5 B = 369.59 + 593.45 = 963.04 Using the calculator: N = 5; I/Y = 11; PMT = 100; FV = 1,000 CPT PV = -963.04
discount bond
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? Using the formula: B = PV of annuity + PV of lump sum B = 100[1 - 1/(1.11)5] / .11 + 1,000 / (1.11)5 B = 369.59 + 593.45 = 963.04 Using the calculator: N = 5; I/Y = 11; PMT = 100; FV = 1,000 CPT PV = -963.04
Bond indenture
Contract between the company and the bondholders that includes The basic terms of the bonds The total amount of bonds issued A description of property used as security, if applicable Sinking fund provisions Call provisions Details of protective covenants
semiannual coupon payment
Coupon rate = 14%, semiannual coupons YTM = 16% Maturity = 7 years Par value = $1,000 Or PMT = 70; N = 14; I/Y = 8; FV = 1,000; CPT PV = -917.56
the fisher effect
The Fisher Effect defines the relationship between real rates, nominal rates, and inflation (1 + R) = (1 + r)(1 + h), where R = nominal rate r = real rate h = expected inflation rate Approximation R = r + h
Types of Bonds
High Grade 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 Medium Grade 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 Low Grade Moody's Ba and B S&P BB and B Considered possible that the capacity to pay will degenerate. Very Low Grade 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
Bond Prices: Relationship Between Coupon and Yield
If YTM = coupon rate, then par value = bond price If YTM > coupon rate, then par value > bond price Why? The discount provides yield above coupon rate Price below par value, called a discount bond If YTM < coupon rate, then par value < bond price Why? Higher coupon rate causes value above par Price above par value, called a premium bond
YTM ("bond yields")
If YTM = coupon rate, then par value = bond price If YTM > coupon rate, then par value > bond price Why? The discount provides yield above coupon rate Price below par value, called a discount bond If YTM < coupon rate, then par value < bond price Why? Higher coupon rate causes value above par Price above par value, called a premium bond Yield to Maturity (YTM) is the rate implied by the current bond price Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity If you have a financial calculator, enter N, PV, PMT, and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign)
Expected inflation rate
If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate? R = (1.1)(1.08) - 1 = .188 = 18.8% Approximation: R = 10% + 8% = 18% Because the real return and expected inflation are relatively high, there is significant difference between the actual Fisher Effect and the approximation.
Zero Coupon Bonds
Make no periodic interest payments (coupon rate = 0%) The entire yield-to-maturity comes from the difference between the purchase price and the par value Cannot sell for more than par value Sometimes called zeroes, deep discount bonds, or original issue discount bonds (OIDs) Treasury Bills and principal-only Treasury strips are good examples of zeroes
Meaning of par value, coupon interest rate, maturity, current yield and YTM
Par value (face value)- the principal amount of a bond that is repaid at the end of the term. Coupon rate - annual coupon divided by the face value of the bond. Coupon payment - The stated interest payment made on the bond. Maturity date - the specified date on which the principal amount of the bond is paid. Yield or Yield to maturity (required return, market rate) - the rate required in the market on the bond.
Changes in market interest rate (required return) and bond values.
Price Risk Change in price due to changes in interest rates Long-term bonds have more price risk than short-term bonds Low coupon rate bonds have more price risk than high coupon rate bonds Reinvestment Rate Risk Uncertainty concerning rates at which cash flows can be reinvested Short-term bonds have more reinvestment rate risk than long-term bonds High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds
premium bond
Suppose you are reviewing 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 the formula: B = PV of annuity + PV of lump sum B = 100[1 - 1/(1.08)20] / .08 + 1000 / (1.08)20 B = 981.81 + 214.55 = 1196.36 Using the calculator: N = 20; I/Y = 8; PMT = 100; FV = 1000 CPT PV = -1,196.36
The term structure of interest rates and the yield curve
Term structure is the relationship between time to maturity and yields, all else equal It is important to recognize that we pull out the effect of default risk, different coupons, etc. Yield curve - graphical representation of the term structure Normal - upward-sloping; long-term yields are higher than short-term yields Inverted - downward-sloping; long-term yields are lower than short-term yields
Federal Government Bonds, State and Local Government Bonds ("Munis"), and Corporate Bonds
Treasury Securities Federal government debt T-bills - pure discount bonds with original maturity of one year or less T-notes - coupon debt with original maturity between one and ten years T-bonds - coupon debt with original maturity greater than ten years Municipal Securities Debt of state and local governments Varying degrees of default risk, rated similar to corporate debt Interest received is tax-exempt at the federal level
Discount Interest Bonds/Bills
With such a loan, the borrower receives money today and repays a single lump sum at some time in the future.
Bond Definition
a debt security usually issued by a corporation or government entity.
Interest Only Bonds
calls for the borrower to pay interest each period and to repay the entire principal (the original loan amount) at some point in the future.
Real interest rate
change in purchasing power
Amortizing Bonds
lender may require the borrower to repay parts of the loan amount over time.
