Chapter 7 math
Call Premium A 5.5 percent corporate coupon bond is callable in four years for a call premium of one year of coupon payments. Assuming a par value of $1,000, what is the price paid to the bondholder if the issuer calls the bond? (Assume annual interest payments.)
$1055 principal + call premium = $1,000 + 5.5% x $1,000 = $1,055
TIPS Interest and Par Value A 2½ percent TIPS has an original reference CPI of 170.4. If the current CPI is 205.7, what is the current interest payment and par value of the TIPS? (Assume semi-annual interest payments and $1,000 par value.)
$1207.16, $15.09, respectively par value = 205.7/170.4 x $1,000 = $1,207.16 interest payment = ½ x 2.5% x $1,207.16 = $15.09
Bond Prices and Interest Rate Changes A 6 percent coupon bond with 12 years left to maturity is priced to offer a 6.5 percent yield to maturity. You believe that in one year, the yield to maturity will be 6.25 percent. What is the change in price the bond will experience in dollars? (Assume semi-annual interest payments and $1,000 par value.)
$21.55 Compute the current bond price:N = 24, I = 3.25, PMT = 30, FV = 1000 CPT PV = -958.78 Now compute the price in one year:N = 22, I = 3.125, PMT = 30, FV = 1000 CPT PV = -980.33 So the dollar change in price is:$980.33 - $958.78 = $21.55
Interest Payments Determine the interest payment for the following three bonds: 5½ percent coupon corporate bond (paid semi-annually), 6.45 percent coupon Treasury note, and a corporate zero coupon bond maturing in 10 years. (Assume a $1,000 par value.)
$27.50, $32.25, $0, respectively 5½ percent coupon corporate bond (paid semi-annually): ½ x 5.5% x $1,000 = $27.50 6.45 percent coupon Treasury note: ½ x 6.45% x $1,000 = $32.25 corporate zero coupon bond maturing in 10 years: 0% x $1,000 = $0
TIPS Capital Return Consider a 2.75% TIPS with an issue CPI reference of 184.2. At the beginning of this year, the CPI was 195.4 and was at 200.5 at the end of the year. What was the capital gain of the TIPS in dollars?
$27.69 gain = end of year value - beginning of year value = 200.5/184.2 x $1,000 - 195.4/184.2 x $1,000 = $1,088.49 - $1,060.80 = $27.69
Zero Coupon Bond Price Calculate the price of a zero coupon bond that matures in 10 years if the market interest rate is 6 percent. (Assume semi-annual compounding and $1,000 par value.)
$553.68
Bond Quotes Consider the following three bond quotes; a Treasury note quoted at 87:25, and a corporate bond quoted at 102.42, and a municipal bond quoted at 101.45. If the Treasury and corporate bonds have a par value of $1,000 and the municipal bond has a par value of $5,000, what is the price of these three bonds in dollars?
$877.81, $1024.20, $5072.50, respectively Treasury note at 87:25: (87 + 25/32)% x $1,000 = $877.8125 Corporate bond at 102.42: 102.42% x $1,000 = $1,024.20 Municipal bond at 101.45: 101.45% x $5,000 = $5,072.50
Bond Prices and Interest Rate Changes A 6.75 percent coupon bond with 10 years left to maturity is priced to offer a 6.5 percent yield to maturity. You believe that in one year, the yield to maturity will be 6.65 percent. If this occurs, what would be the total return of the bond in percent? (Assume semi-annual interest payments and $1,000 par value.)
5.5% Compute the current bond price:N = 20, I = 3.25, PMT = 33.75, FV = 1000 CPT PV = -1018.17 Now compute the price in one year:N = 18, I = 3.325, PMT = 33.75, FV = 1000 CPT PV = -1006.69 So the dollar change in price + interest payments are:$1,006.69 - $1,018.17 + $67.50 = $56.02 The percentage return is: $56.02 ÷ $1,018.17 = 5.5%
Current Yield What's the current yield of a 6 percent coupon corporate bond quoted at a price of 101.70?
5.9% 6% ÷ 101.7% = 0.058997 = 5.9%
Taxable Equivalent Yield What's the taxable equivalent yield on a municipal bond with a yield to maturity of 3.9 percent for an investor in the 35 percent marginal tax bracket?
6.00%
Yield to Maturity A 5.75 percent coupon bond with 12 years left to maturity is offered for sale at $978.83. What yield to maturity is the bond offering? (Assume interest payments are paid semi-annually and par value is $1,000.)
6.00% N = 24, PV = -978.83, PMT = 28.75, FV = 1000 CPT I = 3%, YTM = 3% x 2 = 6%
Yield to Call A 7.25 percent coupon bond with 25 years left to maturity can be called in 5 years. The call premium is one year of coupon payments. It is offered for sale at $1066.24. What is the yield to call of the bond? (Assume that interest payments are paid semi-annually and par value is $1,000.)
6.90% N = 10, PV = -1066.24, PMT = 36.25, FV = 1072.50 CPT I = 3.45%, YTC = 3.45% x 2 = 6.90%
Yields of a Bond A 4.5 percent coupon municipal bond has 10 years left to maturity and has a price quote of 97.75. The bond can be called in 4 years. The call premium is one year of coupon payments. What is the bond's taxable equivalent yield for an investor in the 33 percent marginal tax bracket? (Assume interest payments are paid semi-annually and a par value of $5,000.)
7.13% YTM: N = 20, PV = -4887.50, PMT = 112.50, FV = 5000 CPT I = 2.39%, YTM = 2.39% x 2 = 4.78%
Time to Maturity A bond issued by a corporation on June 15, 2007, is scheduled to mature on June 15, 2017. If today is December 16, 2008, what is this bond's time to maturity? (Assume annual interest payments.)
8 years 6 months June 15, 2017 minus December 16, 2008 = 8 years and 6 months
Credit Risk and Yield Rank the following bonds in order from lowest credit risk to highest risk all with the same time to maturity, by their yield to maturity: JM Corporate bond with yield of 12.25 percent, IB Corporate bond with yield of 4.49 percent, TC Corporate bond with yield of 8.76 percent, and B&O Corporate bond with a yield of 5.99 percent.
IB bond, B&O bond, TC bond, JM bond
Compute Bond Price Compute the price of a 4.75 percent coupon bond with 15 years left to maturity and a market interest rate of 6.25 percent. (Assume interest payments are semi-annual and par value is $1,000.) Is this a discount or premium bond?
discount N = 30, I = 3.125, PMT = 23.75, FV = 1000 CPT PV = -855.34 Since this is less than $1,000, it is a discount bond.
Bond Ratings and Prices A corporate bond with a 5.75 percent coupon has 15 years left to maturity. It has had a credit rating of BB and a yield to maturity of 6.25 percent. The firm has recently gotten more financially stable and the rating agency is upgrading the bonds to BBB. The new appropriate discount rate will be 6.00 percent. What will be the change in the bond's price in dollars? (Assume interest payments are paid semi-annually and a par value of $1,000.)
increase $23.72 Compute the current bond price:N = 30, I = 3.125, PMT = 28.75, FV = 1000 CPT PV = -951.78 Now compute the price after the rating change:N = 30, I = 3.00, PMT = 28.75, FV = 1000 CPT PV = -975.50 So the dollar change in price is:$975.50 - $951.78 = $23.72
Comparing Bond Yields A client in the 33 percent marginal tax bracket is comparing a municipal bond that offers a 5 percent yield to maturity and a similar-risk corporate bond that offers a 6.25 percent yield. Which bond will give the client more profit after taxes?
the municipal bond