- Which of the following events would make it more likely that a company would choose to call its outstanding callable bonds?
- A reduction in market interest rates.
- The company’s bonds are downgraded.
- An increase in the call premium.
- Answers a and b are correct.
- Answers a, b, and c are correct.
- Which of the following statements is most correct?
- All else equal, if a bond’s yield to maturity increases, its price will fall.
- b. All else equal, if a bond’s yield to maturity increases, its current yield will fall.
- c. If a bond’s yield to maturity exceeds the coupon rate, the bond will sell at a premium over par.
- All of the answers above are correct.
- None of the answers above is correct.
- Assume that you wish to purchase a 20-year bond that has a maturity value of $1,000 and makes semiannual interest payments of $40. If you require a 10 percent nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?
- $619
- $674
- $761
- $828
- $902
- Consider a $1,000 par value bond with a 7 percent annual coupon. The bond pays interest annually. There are 9 years remaining until maturity. What is the current yield on the bond assuming that the required return on the bond is 10 percent?
- 10.00%
- 8.46%
- 7.00%
- 8.52%
- 8.37%
- A corporate bond with a $1,000 face value pays a $50 coupon every six months. The bond will mature in ten years, and has a nominal yield to maturity of 9 percent. What is the price of the bond?
- $634.86
- $1,064.18
- $1,065.04
- $1,078.23
- $1,094.56
- The current market price of Smith Corporation’s 10 percent, 10 year bonds is $1,297.58. A 10 percent coupon interest rate is paid semiannually, and the par value is equal to $1,000. What is the YTM (stated on a nominal, or annual, basis) if the bonds mature 10 years from today?
- 8%
- 6%
- 4%
- 2%
- 1%
- Which of the following has the greatest price risk?
- A 10-year, $1,000 face value, 10percent coupon bond with semiannual interest payments.
- A 10-year, $1,000 face value, 10percent coupon bond with annual interest payments.
- A 10-year, $1,000 face value, zero coupon bond.
- A 10-year $100 annuity.
- All of the above have the same price risk since they all mature in 10 years.
- You just purchased a 10-year corporate bond that has an annual coupon of 10 percent. The bond sells at a premium above par. Which of the following statements is most correct?
- The bond’s yield to maturity is less than 10 percent.
- The bond’s current yield is greater than 10 percent.
- If the bond’s yield to maturity stays constant, the bond’s price will be the same one year from now.
- Statements a and c are correct.
- None of the answers above is correct.
- JRJ Corporation recently issued 10-year bonds at a price of $1,000. These bonds pay $60 in interest each six months. Their price has remained stable since they were issued, i.e., they still sell for $1,000. Due to additional financing needs, the firm wishes to issue new bonds that would have maturity of 10 years, a par value of $1,000, and pay $40 in interest every six months. If both bonds have the same yield, how many new bonds must JRJ issue to raise $2,000,000 cash?
a.2,400
b.2,596
c.3,000
d.5,000
e.4,275
10.Assume that a 15-year, $1,000 face value bond pays interest of$37.50 every 3 months. If you require a nominal annual rate of return of 12 percent, with quarterly compounding, how much should you be willing to pay for this bond? (Hint: The PVIFA and PVIF for 3 percent, 60 periods are 27.6748 and 0.1697, respectively.)
a.$821.92
b.$1,207.57
c.$986.43
d.$1,120.71
e.$1,358.24
- Your client has been offered a 5-year, $1,000par value bond with a 10 percent coupon. Interest on this bond is paid quarterly. If your client is to earn a nominal rate of return of 12 percent, compounded quarterly, how much should she pay for the bond?
a.$800
b.$926
c.$1,025
d.$1,216
e.$981
- A $1,000 par value bond sells for $1,216. It matures in 20 years, has a 14 percent coupon, pays interest semiannually, and can be called in 5 years at a price of $1,100.What is the bond’s YTM and YTC?
YTMYTC
a.6.05%9.00%
b.10.00%10.26%
c.10.06%10.00%
d.11.26%14.00%
e.11.26%10.00%
- a. A reduction in market interest rates.
Callable bond
Statement a is correct; the other statements are false. A bond downgrade generally raises the cost of issuing new debt. Therefore, the callable bonds would not be called. If the call premium (the cost paid in excess of par) increases, the cost of calling debt increases; therefore, callable bonds would not be called.
- a. All else equal, if a bond’s yield to maturity increases, its price will fall.
Bond concepts
Statement a is correct; the other statements are false. A bond’s price and YTM are negatively related. If a bond’s YTM is greater than its coupon rate, it will sell at a discount.
- d. $828
Bond value – semiannual payment
Tabular solution:
VB= $40(PVIFA”%,“™) + $1,000(PVIF”%,“™)
= $40(17.1591) +$1,000(0.1420) = $828.36 ÷ $828.
Financial calculator solution:
Inputs: N = 40; I = 5; PMT = 40; FV = 1,000.
Output: PV = -$828.41; VB÷ $828.
- b.8.46%
Current yield
Find the price of the bond as N = 9, I = 10, PMT = 70, FV = 1,000, and solve for PV = ? = -$827.23. The current yield is $70/$827.23 =8.46%.
- c. $1,065.04
Bond value – semiannual payment
N= 10 x 2 = 20
I= 9/2 = 4.5
PMT= 50
FV= 1,000
Solve for PV = -$1,065.04.
- b. 6%
Yield to maturity
Financial calculator solution:
Inputs: N = 20; PV = -1,297.58; PMT = 50; FV = 1,000.
Output: I = 3.0% per period. kd= YTM = 3.0% x 2 periods = 6%.
- c. A 10-year, $1,000 face value, zero coupon bond.
Price risk
The correct answer is c; the other statements are false. Zero coupon bonds have greater price risk than either of the coupon bonds or the annuity.
- a. The bond’s yield to maturity is less than10 percent.
Current yield and yield to maturity
Statement a is correct; the other statements are false. If the bond sells for a premium, this implies that the YTM must be less than the coupon rate. As a bond approaches maturity, its price will move toward the par value.
- b. 2,596
Bond value – semiannual payment
Tabular solution:
Since the old bond issue sold at its maturity (or par) value, and still sells at par, its yield (and the yield on the new issue) must be 6 percent semiannually. The new bonds will be offered at a discount:
VB = $40(PVIFA•%,?™) + $1,000(PVIF•%,?™)
= $40(11.4699) + $1,000(0.3118) = $770.60.
Number of bonds = $2,000,000/$770.60 = 2,595.38 ÷ 2,596.
Financial calculator solution:
Inputs: N = 20; I = 6; PMT = 40; FV = 1,000.
Output: PV = -$770.60; VB = $770.60.
Number of bonds: $2,000,000/$770.60 ÷ 2.596 bonds.*
*Rounded up to next whole bond.
- b. $1,207.57
Bond value – quarterly payment
Tabular solution: (PVIFA and PVIF are given in the problem.)
VB = $37.50(PVIFA%,•™) + $1,000(PVIF%,•™)
= $37.50(27.6748) + $1,000(0.1697) = $1,207.51
Financial calculator solution:
Inputs: N = 60; I = 3; PMT = 37.50; FV = 1,000.
Output: PV = -$1,207.57; VB = $1,207.57.
Note: Tabular solution differs from calculator solution due to interest factor rounding.
- b. $ 926
Bond value – quarterly payment
Tabular solution:
VB = $25(PVIFA%,Ž™) + $1,000(PVIF%,Ž™)
= $25(14.8775) + $1,000(0.5537) = $925.64 ÷ $926.
Financial calculator solution:
Inputs: N = 20; I = 3; PMT = 25; FV = 1,000.
Output: PV = -$925.61; VB ÷ $926.
- e. 11.26%; 10.00%
Yield to call
Financial calculator solution:
YTM Inputs: N = 40; PV = -1,216; PMT = 70; FV = 1,000.
Output: I = 5.6307% ÷ 5.63% = kd/2. YTM = 5.63% x 2 = 11.26%.
YTC Inputs: N = 10; PV = -1,216; PMT = 70; FV = 1,100.
Output: I = 4.9981% ÷ 5.0% = kd/2. YTC = 5.0% x 2 = 10.0%.
