CHAPTER 14: BOND PRICES AND YIELDS
Solutions to Suggested Problems
5.
Annual coupon rate: 4.8%  $48 Coupon payments
Current yield:
 $48 

  4.95%
 $970 
6.
a.
Effective annual rate for 3-month T-bill:
4
 100, 000  97, 645 
1 
  1  0.10  10%
97, 645


b.
Effective annual interest rate for coupon bond selling at par and paying 10%
semiannually:
(1.05)2—1 = 0.1025 or 10.25%
Note that since Price = Par value, 𝑦𝑡𝑚 = coupon rate. 10% coupon semiannually
implies a semiannual coupon payment of $50 or 5% coupon rate per six months.
Therefore, the coupon bond has the higher effective annual interest rate.
8.
The bond price will be lower. As time passes, the bond price, which is now above par
value, will approach par.
13. For zero coupon bonds with annual coupon payments,
𝑷=
𝑭𝑽
(𝟏 + 𝒓)𝑻
Where 𝑃 = Price, 𝐹𝑉 = Face value, 𝑟 = YTM and 𝑇 = maturity
From the above equation, we can solve for 𝑟 and 𝑇.
Solving for 𝑟:
𝟏
𝑭𝑽 𝑻
𝒓=( ) −𝟏
𝑷
Solving for 𝑇:
𝑃=
𝐹𝑉
(1 + 𝑟)𝑇
𝐹𝑉
𝐹𝑉
→ 𝑇ln(1 + 𝑟) = ln ( )
𝑃
𝑃
𝑭𝑽
𝐥𝐧 ( 𝑷 )
→𝑻=
𝐥𝐧(𝟏 + 𝒓)
→ (1 + 𝑟)𝑇 =
Use the above formulae to fill in the blanks.
Maturity
Bond Equivalent
Price
(years)
YTM
$400
20
4.69%
$500
20
3.53%
$500
10
7.18%
$385.54
10
10.00%
$463.19
10
8.00%
$400
11.91
8.00%
14. a) Price of the bond can be solved as:
𝑃0 =
𝑃0 =
𝐶
1
𝐹𝑉
[1 −
]+
𝑇
(1 + 𝑟)
(1 + 𝑟)𝑇
𝑟
50
1
1000
[1 −
]+
= $1,052.42
6
(1 + 0.04)
(1 + 0.04)6
0.04
After 6 months, the price of the bond will be:
𝑃1 =
50
1
1000
[1 −
]+
= $1,044.52
5
(1 + 0.04)
(1 + 0.04)5
0.04
b) 6-month rate of return on the bond:
=
$50 + $1,044.52 − $1,052.42
$1,052.42
= 4%
15.
The reported bond price is: $1,001.25 (The Wall Street Journal reports bond prices as
percentage of par value. Therefore, a price quotation of 100.125 means
$1000 × 100.125% = $1000 × 1.00125 = $1,001.25
However, 15 days have passed since the last semiannual coupon was paid, so:
Accrued interest = $35 * (15/182) = $2.885
The invoice price is the reported price plus accrued interest: $1,004.135