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Bond value
1. Assume that McDonalds and Burger King have similar $1,000 par value bond issues outstanding. The bonds are equally risky. The Burger King bond has an annual coupon rate of 8 percent and matures 20 years from today. The McDonalds bond has a coupon rate of 8 percent, with interest paid semiannually, and it also matures in 20 years. If the nominal required rate of return, kd, is 12 percent, semiannual basis, for both bonds, what is the difference in current market prices of the two bonds?
Bond value and effective annual rate
2. You are considering investing in a security that matures in 10 years with a par value of $1,000. During the first five years, the security has an 8 percent coupon with quarterly payments (that is, you receive $20 a quarter for the first 20 quarters). During the remaining five years the security has a 10 percent coupon with quarterly payments (that is, you receive $25 a quarter for the second 20 quarters). After 10 years (40 quarters) you receive the par value.
Another 10year bond has an 8 percent semiannual coupon (that is, the coupon payment is $40 every six months). This bond is selling at its par value, $1,000. This bond has the same risk as the security you are thinking of purchasing. Given this information, what should be the price of the security you are considering purchasing?
Bonds with differential payments
3. Semiannual payment bonds with the same risk (Aaa) and maturity (20 years) as your companys bonds have a nominal (not EAR) yield of 9 percent. Your companys treasurer is thinking of issuing at par some $1,000 par value, 20year, quarterly payment bonds. She has asked you to determine what quarterly interest payment, in dollars, the company would have to set in order to provide the same effective annual rate (EAR) as those on the 20year, semiannual payment bonds. What would the quarterly interest payment be, in dollars?
Bond value after reorganization
4. Recently, Ohio Hospitals Inc. filed for bankruptcy. The firm was reorganized as American Hospitals Inc., and the court permitted a new indenture on an outstanding bond issue to be put into effect. The issue has 10 years to maturity and a coupon rate of 10 percent, paid annually. The new agreement allows the firm to pay no interest for 5 years. Then, interest payments will be resumed for the next 5 years. Finally, at maturity (Year 10), the principal plus the interest that was not paid during the first 5 years will be paid. However, no interest will be paid on the deferred interest. If the required annual return is 20 percent, what should the bonds sell for in the market today?
Bond sinking fund payment
5. GP&L sold $1,000,000 of 12 percent, 30year, semiannual payment bonds 15 years ago. The bonds are not callable, but they do have a sinking fund that requires GP&L to redeem 5 percent of the original face value of the issue each year ($50,000), beginning in Year 11. To date, 25 percent of the issue has been retired. The company can either call bonds at par for sinking fund purposes or purchase bonds on the open market, spending sufficient money to redeem 5 percent of the original face value each year. If the nominal yield to maturity (15 years remaining) on the bonds is currently 14 percent, what is the least amount of money GP&L must put up to satisfy the sinking fund provision?
Yield to callsemiannual bond
6. Hood Corporation recently issued 20year bonds. The bonds have a coupon rate of 8 percent and pay interest semiannually. Also, the bonds are callable in 6 years at a call price equal to 115 percent of par value. The par value of the bonds is $1,000. If the yield to maturity is 7 percent, what is the yield to call?
Call pricesemiannual payment
7. A 15year bond with a 10 percent semiannual coupon and a $1,000 face value has a nominal yield to maturity of 7.5 percent. The bond, which may be called after five years, has a nominal yield to call of 5.54 percent. What is the bonds call price?
Annual interest payments remaining
8. You have just been offered a $1,000 par value bond for $847.88. The coupon rate is 8 percent, payable annually, and annual interest rates on new issues of the same degree of risk are 10 percent. You want to know how many more interest payments you will receive, but the party selling the bond cannot remember. Can you determine how many interest payments remain?
Bonds with differential payments
9. Semiannual payment bonds with the same risk (Aaa) and maturity (20 years) as your companys bonds have a nominal (not EAR) yield to maturity of 9 percent. Your companys treasurer is thinking of issuing at par some $1,000 par value, 20year, quarterly payment bonds. She has asked you to determine what quarterly interest payment, in dollars, the company would have to set in order to provide the same effective annual rate (EAR) as those on the 20year, semiannual payment bonds. What would the quarterly, dollar interest payment be?
********************************************************************
Solutions
. Bond value
EMBED Word.Document.8 \s
Financial calculator solution:
Burger King VB
Calculate EAR to apply to Burger King bonds using interest rate conversion feature, and calculate the value, VBK, of Burger King bonds:
Inputs: P/YR = 2; NOM% = 12. Output: EFF% = EAR = 12.36%.
Inputs: N = 20; I = 12.36; PMT = 80; FV = 1,000. Output: PV = $681.54.
McDonalds VB
Inputs: N = 40; I = 6; PMT = 40; FV = 1,000. Output: PV = $699.07. VB = $699.07.
Calculate the difference between the two bonds' PVs
Difference: VB(McD)  VB(BK) = 699.07  681.54 = $17.53.
2. Bond value and effective annual rate
Since the securities are of equal risk, they must have the same effective rate. Since the comparable 10year bond is selling at par, its nominal yield is 8 percent, the same as its coupon rate. Because it is a semiannual coupon bond, its effective rate is 8.16 percent. Using your calculator, enter NOM% = 8; P/YR = 2; and solve for EFF%. (Dont forget to change back to P/YR = 1.) So, since the bond you are considering purchasing has quarterly payments, its nominal rate is calculated as follows: EFF% = 8.16; P/YR = 4; and solve for NOM%. NOM% = 7.9216%. To determine the bonds price you must use the cash flow register because the payment amount changes. CF0 = 0, CF1 = 20; Nj = 20; CF2 = 25; Nj = 19; CF3 = 1,025; I = 7.9216/4 = 1.9804; and then solve for NPV = $1,060.72.
3. Bonds with differential payments
EMBED Word.Document.8 \s
Numerical solution:
Step 1: Solve for the EAR of 9% nominal compounded semiannually.
EARS = (1 + 0.09/2)2  1 = 0.09203.
Step 2: Solve for kNom of 9.203% EAR but with quarterly compounding.
1 + EAR = (1 + kNOM/4)4 = 1.09203.
kNom/4 = periodic rate = 0.02225. kNom = 0.02225 4 = 0.08901.
Step 3: Calculate the quarterly payment using the periodic rate.
Multiply 0.02225 $1,000 = $22.25 = quarterly payment.
Financial calculator solution:
Step 1: Calculate the EAR of 9% nominal yield bond compounded semiannually. Use interest rate conversion feature.
Inputs: P/YR = 2; NOM% = 9. Output: EFF% = 9.2025%.
Step 2: Calculate the nominal rate, kNom, of a 9.2025% EAR but with quarterly compounding.
Inputs: P/YR = 4; EFF% = 9.2025. Output: NOM% = 8.90%.
Step 3: Calculate the quarterly periodic rate from kNom of 8.9% and calculate the quarterly payment.
kPER = kNom/4 = 8.90%/4 = 2.225%.
Inputs: N = 80; I = 2.225; PV = 1,000; FV = 1,000. Output: PMT = $22.25.
Bond value after reorganization
EMBED Word.Document.8 \s
Tabular solution:
PVbond = EMBED Equation.2 + EMBED Equation.2
ADVANCE \l1VB = $100(PVIFA20%,10 PVIFA20%,5) + $1,500(PVIF20%,10)
= $100(4.1925  2.9906) + $1,500(0.1615)
= $120.19 + $242.25 = $362.44.
Financial calculator solution:
Method 1. Cash flows:
Inputs: CF0 = 0; CF1 = 0; Nj = 5; CF2 = 100; Nj = 4; CF5 = 1,600; I = 20.
Output: NPV = $362.44. VB = $362.44.
Method 2. Time value discounting: (Calculate VB as of Year 5, V5)
Inputs: N = 5; I = 20; PMT = 100; FV = 1,500.
Output: PV5 = $901.878.
Calculate VB or PV of V5
Inputs: N = 5; I = 20; PMT = 0; FV = 901.878. Output: PV = $362.44. VB = $362.44.
5. Bond sinking fund payment
The company must call 5 percent or $50,000 face value each year. It could call at par and spend $50,000 or buy on the open market. Since the interest rate is higher than the coupon rate (14% vs. 12%), the bonds will sell at a discount, so open market purchases should be used.
EMBED Word.Document.8 \s
Tabular solution:
VB = $60(PVIFA7%,30) + $1,000(PVIF7%,30)
ADVANCE \r2= $60(12.4090) + $1,000(0.1314) = $744.54 + $131.40 = $875.94.
The company would have to buy $50,000/$1,000 = 50 bonds at $875.94 each = $43,797.
Financial calculator solution:
Inputs: N = 30; I = 7; PMT = 60; FV = 1,000.
Output: PV = $875.91.
The company would have to buy 50 bonds at $875.91 each = $43,795.50 $43,796.
6. Yield to callsemiannual bond
First, calculate the bond price as follows: N = 20 2 = 40; I = 7/2 = 3.5; PMT = 0.08/2 1,000 = 40; FV = 1,000; and then solve for PV = $1,106.78. VB = $1,106.78.
Now, we can calculate the YTC as follows, recognizing that the bond can be called in 6 years at a call price of 115% 1,000 = 1,150: N = 6 2 = 12; PV = 1,106.78; PMT = 40; FV = 1,150; and then solve for I = 3.8758% 2 = 7.75%.
7. Call pricesemiannual payment
Step 1: Find the bond price using the YTM:
Enter the following input data in the calculator:
N = 30; I = 7.5/2 = 3.75; PMT = 50 (0.10/2 ( 1,000); FV = 1,000; and then solve for PV = $1,222.87. VB = $1,222.87.
Step 2: Solve for the call price:
Enter the following input data in the calculator:
N = 10; I = 5.54/2 = 2.77; PV = 1,222.87; PMT = 50; and then solve for FV = $1,039.938 ( $1,040.
8. Annual interest payments remaining
EMBED Word.Document.8 \s
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EMBED Word.Document.8 \s
Step 1: Calculate the EAR of 9% nominal yield bond compounded semiannually. Use interest rate conversion feature.
Inputs: P/YR = 2; NOM% = 9. Output: EFF% = 9.2025%. (Remember to change back to P/YR = 1.)
Step 2: Calculate the nominal rate, kNom, of a 9.2025% EAR but with quarterly compounding.
Inputs: P/YR = 4; EFF% = 9.2025. Output: NOM% = 8.90%. (Remember to change back to P/YR = 1.)
Step 3: Calculate the quarterly periodic rate from kNom of 8.9% and calculate the quarterly payment.
kPER = kNom/4 = 8.90%/4 = 2.225%.
Inputs: N = 80; I = 2.225; PV = 1,000; FV = 1,000. Output: PMT = $22.25.
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