Bond Valuation Problems and Solutions

Chapter 6 Review: Bond Valuation Problems

1. Coupon Rate Calculation

   A $1,000 face value bond is currently quoted at 100.8. The bond pays semiannual payments of $22.50 each and matures in six years. What is the coupon rate?

   Coupon rate = ($22.50 × 2) / $1,000 = 0.0450, or 4.50 percent

2. Current Price of a Bond

   A $1,000 face value bond currently has a yield to maturity of 8.22 percent. The bond matures in five years and pays interest semiannually. The coupon rate is 7.5 percent. What is the current price of this bond?

   FV = 1000; PMT = 75/2 = 37.5; N = 5 x 2 = 10; I/Y = 8.22 / 2 = 4.11 => PV = 970.96

3. Determining Coupon Rate

   A six-year, semiannual coupon bond is selling for $991.38. The bond has a face value of $1,000 and a yield to maturity of 9.19 percent. What is the coupon rate?

   PV = -991.38; N = 6 x 2 = 12; FV = 1000; I/Y = 9.19 / 2 = 4.595 => PMT = $45.00

   Coupon rate = (2 × $45.00) / $1,000 = 0.0900, or 9.00 percent

4. Calculating Yield to Maturity (YTM)

   The 6 percent semiannual coupon bonds of IPO, Inc., are selling for $1,087. The bonds have a face value of $1,000 and mature in 11 years. What is the yield to maturity?

   PMT = 60 / 2 = 30; FV = 1000; N = 11 x 2 = 22; PV = -1,087 => I/Y = 2.48% => YTM = 2.48% x 2 = 4.96%

5. Current Yield Calculation

   National Distributors has $1,000 face value bonds outstanding with a market price of $1,013. The bonds pay interest semiannually, mature in 11 years, and have a yield to maturity of 6.87 percent. What is the current yield?

   FV = 1000; PV = -1013; N = 11 x 2 = 22; I/Y = 6.87 / 2 = 3.435 => PMT = 35.20 => C = 35.20 x 2 = 70.40. Current Yield = 70.40 / 1,013 = 6.95%

6. Determining Coupon Rates

   Barnes Enterprises has bonds on the market making annual payments, with 12 years to maturity, a par value of $1,000, and a price of $963. At this price, the bonds yield 6.14 percent. What must the coupon rate be on the bonds?

   Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows:

   P = $963 = C(PVIFA_6.14%,12) + $1,000(PVIF_6.14%,12)

   Solving for the coupon payment, we get:

   C = $56.95

   The coupon payment is the coupon rate times par value. Using this relationship, we get:

   Coupon rate = $56.95 / $1,000

   Coupon rate = 0.0570, or 5.70%

   5.

   Enter

   12

   6.14%

   ±$963

   $1,000

   N

   I/Y

   PV

   PMT

   FV

   Solve for

   $56.95

7. Bond Yields: Calculating YTM

   Stein Co. issued 15-year bonds two years ago at a coupon rate of 5.4 percent. The bonds make semiannual payments. If these bonds currently sell for 94 percent of par value, what is the YTM?

   Here, we are finding the YTM of a semiannual coupon bond. The bond price equation is:

   P = $940 = $27(PVIFA_R%,26) + $1,000(PVIF_R%,26)

   Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial and error, we find:

   R = 3.037%

   Since the coupon payments are semiannual, this is the semiannual interest rate. The YTM is the APR of the bond, so:

   YTM = 23.037%

   YTM = 6.07%

   7.

   Enter

   13 ´ 2

   ±940

   $54 / 2

   $1,000

   N

   I/Y

   PV

   PMT

   FV

   Solve for

   3.037%

8. Calculating Coupon Rates with Semiannual Payments

   Volbeat Corporation has bonds on the market with 10.5 years to maturity, a YTM of 6.2 percent, a par value of $1,000, and a current price of $945. The bonds make semiannual payments. What must the coupon rate be on the bonds?

   Here, we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows:

   P = $945 = C(PVIFA_3.1%,21) + $1,000(PVIF_3.1%,21)

   Solving for the coupon payment, we get:

   C = $27.40

   Since this is the semiannual payment, the annual coupon payment is:

   2 × $27.40 = $54.80

   And the coupon rate is the coupon payment divided by par value, so:

   Coupon rate = $54.80 / $1,000

   Coupon rate = 0.0548, or 5.48%