Chapter #6
Solutions to Questions and Problems
1.
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.
2.
Price and yield move in opposite directions; if interest rates rise, the price of the bond will
fall. This is because the fixed coupon payments determined by the fixed coupon rate are not
as valuable when interest rates rise–hence, the price of the bond decreases.
3.
P = $1,052.06
4.
P = $910.85
R = YTM = 9.52%
Approximate YTM = .0941 or 9.41%
5.
P = $1,086
C = $77.72
Coupon rate = .0772 or 7.72%
6.
P = $1,040.95
7.
P = $920
R = 4.42%
YTM = 8.85%
8.
P = $1,080
C = $43.60
Coupon rate = .0872 or 8.72%
9.
Approximate r = .06 –.028
Approximate r =.032 or 3.20%
Exact r = .0311 or 3.11%
10. R = .0858 or 8.58%
11. h = .0273 or 2.73%
12. r = .0821 or 8.21%
13. Bid price = $994.375
Previous day’s dollar price = $993.125
14. Current yield = .0517 or 5.17%
Bid-Ask spread = 1/32
15. X:
Y:
P0
P1
P3
P8
P12
P13
P0
P1
P3
P8
P12
P13
= $1,177.05
= $1,167.68
= $1,147.20
= $1,084.25
= $1,018.87
= $1,000
= $841.92
= $849.28
= $865.80
= $920.15
= $981.48
= $1,000
16.
PBill = $948.42
PTed = $815.98
∆PBill%
∆PTed%
= –5.16%
= –18.40%
If the YTM suddenly falls to 5 percent:
PBill = $1,055.08
PTed = $1,251.03
∆PBill% = +5.51%
∆PTed% = +25.10%
17.
PJ = $879.06
PS = $1,241.88
PJ = $775.32
PS = $1,112.34
∆PJ% = – 11.80%
∆PS% = – 10.43%
If the YTM declines from 7 percent to 5 percent:
PJ
PS
= $1,000.000
= $1,391.65
∆PJ% = + 13.76%
∆PS% = + 12.06%
18. Current yield = 7.41%
P0 = $1,080
R = 3.50%
YTM = 7.00%
Effective annual yield = 7.13%
20. Accrued interest = $12
And we calculate the clean price as:
Clean price = Dirty price – Accrued interest
Clean price = $1,108
21. Accrued interest = $72/2 × 3/6
Accrued interest = $18.00
And we calculate the dirty price as:
Dirty price = Clean price + Accrued interest
Dirty price = $883.00
25. Dollar price = $1,195.625
P = $1,195.625
R = 3.29%
YTM = 6.59%
26. P = $671.15
Bid price = $670.52
28. P = $816.584
R = 4.76%
YTM = 9.53%
29. P = $1,130.77
Current yield = .0743 or 7.43%