HW 7
You purchase a bond with an invoice price of $948. The bond has a coupon rate of 5.9 percent, and there are four months to the next semiannual coupon date. Assume a par value of $1,000. What is the clean price of the bond?
Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are four months until the next coupon payment, so two months have passed since the last coupon payment. The accrued interest for the bond is: Accrued interest = $59/2 × 2/6 Accrued interest = $9.83 And we calculate the clean price as: Clean price = Dirty price - Accrued interest Clean price = $948 - 9.83 Clean price = $938.17
You purchase a bond with a coupon rate of 5.3 percent and a clean price of $951. Assume a par value of $1,000. If the next semiannual coupon payment is due in two months, what is the invoice price? (
Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are two months until the next coupon payment, so four months have passed since the last coupon payment. The accrued interest for the bond is: Accrued interest = $53/2 × 4/6 Accrued interest = $17.67 And we calculate the dirty price as: Dirty price = Clean price + Accrued interest Dirty price = $951 + 17.67 Dirty price = $968.67
Locate the Treasury issue in Figure 7.4 maturing in May 2038. Assume a par value of $10,000. Coupon rate: 4.500% Bid price : 128.0625 Today's asked price : 128.1250 Change : .6875 a. What is its coupon rate? b. What is its bid price? c. What was the previous day's asked price?
Bid price = 128.0625 = 128.0625% Bid price = (128.0625/100)($10,000) Bid price = $12,806.25 The previous day's ask price is found by: Previous day's asked price = Today's asked price - Change = 128.1250 - .6875 = 127.4375 The previous day's price in dollars was: Previous day's asked price = 127.4375 = 127.4375% Previous day's asked price = (127.4375/100)($10,000) Previous day's asked price = $12,743.75
Union Local School District has a bond outstanding with a coupon rate of 2.8 percent paid semiannually and 16 years to maturity. The yield to maturity on this bond is 3.4 percent, and the bond has a par value of $5,000. What is the price of the bond?
Calculator Solution: Enter N = 16 X 2 I/Y = 3.4%/2 PV = ? ~ $4,632.12 PMT = $70 FV = $5000
Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of €1,000, 23 years to maturity, and a coupon rate of 3.8 percent paid annually. If the yield to maturity is 4.7 percent, what is the current price of the bond?
Calculator Solution: Enter N = 23 I/Y = 4.7% PV = ? ~ 875.09 euros PMT = 38 euros FV = 1,000 euros
McConnell Corporation has bonds on the market with 14.5 years to maturity, a YTM of 5.3 percent, a par value of $1,000, and a current price of $1,045. The bonds make semiannual payments. What must the coupon rate be on these bonds?
Calculator Solution: Enter N = 29 I/Y = 5.3%/2 PV = $1,405 PMT = ? ~ $28.74 FV = $1,000 $28.74(2)/$1,000 = .0575 or 5.75%
Suppose the following bond quotes for IOU Corporation appear in the financial page of today's newspaper. Assume the bond has semiannual payments, a face value of $2,000 and the current date is April 19, 2018. Company (Ticker): IOU (IOU) Coupon : 5.7 Maturity : Apr, 2034 Last Price : 108.96 Last Yield : ?? EST Vol (000s) : 1,827 a. What is the yield to maturity of the bond? b. What is the current yield?
Calculator Solution: Enter N = 32 I/Y = ? ~ 2.443% PV = $2,179.20 PMT = $114/2 FV = $2000 2.443% × 2 = 4.89% The current yield is the annual coupon payment divided by the bond price, so: Current yield = $114/$2,179.20 Current yield = .0523, or 5.23% a. 4.89% b. 5.23%
West Corp. issued 25-year bonds two years ago at a coupon rate of 5.3 percent. The bonds make semiannual payments. If these bonds currently sell for 105 percent of par value, what is the YTM?
Calculator Solution: Enter N = 46 I/Y = ? ~ 2.467% PV = 1,050 PMT = $53/2 FV = $1,000 2.467% × 2 = 4.93% YTM = 4.93%
Both Bond Sam and Bond Dave have 7.3 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has three years to maturity, whereas Bond Dave has 20 years to maturity. a. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave? b. If rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of Bond Sam and Bond Dave?
Calculator Solution: If both bonds sell at par, the initial YTM on both bonds is the coupon rate, 7.3 percent. If the YTM suddenly rises to 9.3 percent: Enter N = 6 I/Y = 9.3%/2 PV = ? ~ $948.67 PMT = $73/2 FV = $1,000 Percentage change in price of Bond Sam: = ($948.67 - 1,000)/$1,000 = -.0513, or -5.13% Enter N = 40 I/Y = 9.3%/2 PV = ? ~ $819.86 PMT = $73/2 FV = $1,000 Percentage change in price of Bond Dave: = ($819.86 - 1,000)/$1,000 = -.1801, or -18.01% If the YTM suddenly falls to 5.3 percent: Enter N = 6 I/Y = 5.3%/2 PV = ? ~ $1,054.81 PMT = $73/2 FV = $1,000 Percentage change in price of Bond Sam: = ($1,054.81 - 1,000)/$1,000 = .0548, or 5.48% Enter N = 40 I/Y = 5.3%/2 PV = ? ~ $1,244.80 PMT = $73/2 FV = $1,000 Percentage change in price of Bond Dave: = ($1,244.80 - 1,000)/$1,000 = .2448, or 24.48% All else the same, the longer the maturity of a bond, the greater is its price sensitivity to changes in interest rates.
Treasury bills are currently paying 4.7 percent and the inflation rate is 2.2 percent. a. What is the approximate real rate of interest? b. What is the exact real rate?
The approximate relationship between nominal interest rates (R), real interest rates (r), and inflation (h) is: R = r + h Approximate r = .047 - .022 Approximate r = .025, or 2.50% The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is: (1 + R) = (1 + r)(1 + h) (1 + .047) = (1 + r)(1 + .022) r = [(1 + .047)/(1 + .022)] - 1 r = .0245, or 2.45%
Workman Software has 6.4 percent coupon bonds on the market with 18 years to maturity. The bonds make semiannual payments and currently sell for 94.31 percent of par. a. What is the current yield on the bonds? b. What is the YTM? c. What is the effective annual yield?
The current yield is: Current yield = Annual coupon payment/Price Current yield = $64/$943.10 Current yield = .0679, or 6.79% Calculator Solution: Enter N = 36 I/Y = ? ~ 3.480% PV = $943.10 PMT = $64/2 FV = $1000 3.480% X 2 = 6.96% Enter NOM = 6.96% EFF = ? ~ 7.08% C/Y = 2 a. 6.79% b. 6.95% c. 7.10%
Is the yield to maturity on a bond the same thing as the required return? Is YTM the same thing as the coupon rate? Suppose today a 10 percent coupon bond sells at par. Two years from now, the required return on the same bond is 8 percent. a. What is the coupon rate on the bond b. What is the YTM on the bond?
The yield to maturity is the required rate of return on a bond expressed as a nominal annual interest rate. For noncallable bonds, the yield to maturity and required rate of return are interchangeable terms. Unlike YTM and required return, the coupon rate is not a return used as the interest rate in bond cash flow valuation, but is a fixed percentage of par over the life of the bond used to set the coupon payment amount. For the example given, the coupon rate on the bond is still 10 percent, and the YTM is 8 percent. a. 10% b. 8%
