Chapter 04
Valuing Bonds
Multiple Choice Questions:
1. A government bond issued in Germany has a coupon rate of 5%, face value of euros
100 and maturing in five years. The interest payments are made annually. Calculate
the price of the bond (in euros)if the yield to maturity is 3.5%.
a. 100
B. 106.77
c. 106.33
d. None of the above
The annual interest payment = (100) x (0.05) = 5 euros Price = PV; Using a financial
Calculator: PMT = 5; I = 3.5; FV = 100; & N = 5; Compute: PV = 106.77 euros
2.
A government bond issued in Germany has a coupon rate of 5%, face value of euros
100 and maturing in five years. The interest payments are made annually. Calculate
the yield to maturity of the bond (in euros) if the price of the bond is 106 euros.
a. 5.00%
B. 3.80%
c. 3.66%
d. None of the above
The annual interest payment = (100) x (0.05) = 5 euros Using a financial Calculator: PMT =
5; FV = 100; & N = 5; & PV = -106 Compute: I = 3.66%
3. A 3-year bond with 10% coupon rate and $1000 face value yields 8% APR.
Assuming annual coupon payment, calculate the price of the bond.
a. $857.96
b. $951.96
c. $1000.00
D. $1051.54
PV = (100/1.08) + (100/(1.08^2)) + (1100/(1.08^3)) = $1051.54
4. A 5-year treasury bond with a coupon rate of 8% has a face value of $1000. What is
the semi-annual interest payment?
a. $80
B. $40
c. $100
d. None of the above
Annual interest payment = 1000(0.08) = $80; Semi-annual payment = 80/2 = $40
5. A three-year bond has 8.0% coupon rate and face value of $1000. If the yield to
maturity on the bond is 10%, calculate the price of the bond assuming that the bond
makes semi-annual coupon interest payments.
a. $857.96
B. $949.24
c. $1057.54
d. $1000.00
PV = (40/1.05) + (40/(1.05^2)) +. . . + (1040/(1.05^6)) = $949.24
6. A four-year bond has an 8% coupon rate and a face value of $1000. If the current
price of the bond is $878.31, calculate the yield to maturity of the bond (assuming
annual interest payments).
a. 8%
b. 10%
C. 12%
d. 6%
Use trial and error method. (80/1.12) + (80/(1.12^2)) + (80/(1.12^3)) + (1080/(1.12^4)) =
$870.51. Therefore, yield to maturity is 12%. Or use a financial calculator: PV = -878.31; N =
4; PMT = 80; FV = 1000; COMPUTE: I = 12%
7. A 5-year bond with 10% coupon rate and $1000 face value is selling for $1123.
Calculate the yield to maturity on the bond assuming annual interest payments.
a. 10.0%
b. 8.9%
C. 7.0%
d. None of the above
Use a financial calculator: PV = -1123; FV = 1000; PMT = 100 and N = 5 and compute I =
7.0%
8. Moerdyk Corporation's bonds have a 10-year maturity, a 6.25% semiannual coupon, and a par
value of $1,000. The going interest rate (rd) is 4.75%, based on semiannual compounding. What
is the bond’s price?
A. 1,063.09
B. 1,090.35
C. 1,118.31
D. 1,146.27
E. 1,174.93
Bond valuation:
semiannual coupons
Par value
$1,000
Coupon rate
6.25%
Periods/year
2
Yrs to maturity
10
N = periods
20
Annual rate
4.75%
Periodic rate
2.38%
PMT/period
$31.25
FV
$1,000
PV
$1,118.31
Answer: c
MEDIUM
9. Consider some bonds with one annual coupon payment of 7.25%. The bonds have a par value
of $1,000, a current price of $1,125, and they will mature in 13 years. What is the yield to
maturity on these bonds?
a.
5.56%
b.
5.85%
c.
6.14%
d.
6.45%
e.
6.77%
Yield to maturity:
Coupon rate
N
Answer: b
7.25%
13
PV = Price
$1,125
PMT
$72.50
FV = Par
$1,000
I/YR
5.85% = YTM
10.
McCue Inc.'s bonds currently sell for $1,250. They pay a $120 annual coupon, have a
15-year maturity, and a $1,000 par value, but they can be called in 5 years at $1,050. Assume
that no costs other than the call premium would be incurred to call and refund the bonds, and
also assume that the yield curve is horizontal, with rates expected to remain at current levels
on into the future. What is the difference between this bond's YTM and its YTC? (Subtract the
YTC from the YTM.)
a.
2.11%
b.
2.32%
c.
2.55%
d.
2.80%
e.
3.09%
Yields to maturity and call
Answer: a
If held to maturity:
N = Maturity
If called in 5 years:
15
PV
$1,250
PMT
$120
N = Call
PV
PMT
5
$1,250
$120
FV = Par
$1,000
FV=Call Price
$1,050
I/YR = YTM
8.91%
I/YR = YTC
6.81%
Difference:
2.11%
11.
Wachowicz Corporation issued 15-year, noncallable, 7.5% annual coupon bonds at their
par value of $1,000 one year ago. Today, the market interest rate on these bonds is 5.5%.
What is the current price of the bonds, given that they now have 14 years to maturity?
a.
$1,077.01
b.
$1,104.62
c.
$1,132.95
d.
$1,162.00
e.
$1,191.79
Bond valuation: annual coupons
Par value
Coupon rate
Answer: e
$1,000
7.5%
N
14
I/YR
5.5%
PMT
$75
FV
$1,000
PV
$1,191.79
12.
Taussig Corp.'s bonds currently sell for $1,150. They have a 6.75% annual coupon rate
and a 15-year maturity, but they can be called in 6 years at $1,067.50. Assume that no costs
other than the call premium would be incurred to call and refund the bonds, and also assume
that the yield curve is horizontal, with rates expected to remain at current levels on into the
future. Under these conditions, what rate of return should an investor expect to earn if he or
she purchases these bonds, the YTC or the YTM?
A. 3.92%
B. 4.12%
C. 4.34%
D. 4.57%
E. 4.81%
Yields to maturity and call
If the coupon rate exceeds the YTM, then it is likely that the bonds will be called and
replaced with new, lower coupon bonds. In that case, the YTC will be earned.
Otherwise, one should expect to earn the YTM.
Answer: e
If held to maturity
If called
Par value
$1,000
Par value
$1,000
Coupon
6.75%
Coupon
6.75%
N
PV
15
$1,150.00
PMT
FV
N
PV
$67.50
PMT
$1,000.00
I/YR
Expected rate of return:
5.28%
YTC
FV
YTM
4.81% YTC
I/YR
6
$1,150.00
$67.50
$1,067.50
4.81%