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CHAPTER 7
B125
If the YTM declines from 8 percent to 6 percent:
P
J
= $20(PVIFA
3%,18
) + $1,000(PVIF
3%,18
)
= $862.46
P
K
= $60(PVIFA
3%,18
) + $1,000(PVIF
3%,18
)
= $1,412.61
P
J
%
= ($862.46 – 746.81) / $746.81
= + 15.49%
P
K
%
= ($1,412.61 – 1,253.19) / $1,253.19
= + 12.72%
All else the same, the lower the coupon rate on a bond, the greater is its price sensitivity to changes
in interest rates.
18.
The bond price equation for this bond is:
P
0
= $1,068 = $46(PVIFA
R%
,18
) + $1,000(PVIF
R%
,18
)
Using a spreadsheet, financial calculator, or trial and error we find:
R
= 4.06%
This is the semiannual interest rate, so the YTM is:
YTM = 2
4.06% = 8.12%
The current yield is:
Current yield = Annual coupon payment / Price = $92 / $1,068 = .0861 or 8.61%
The effective annual yield is the same as the EAR, so using the EAR equation from the previous
chapter:
Effective annual yield = (1 + 0.0406)
2
– 1 = .0829 or 8.29%
19.
The company should set the coupon rate on its new bonds equal to the required return. The required
return can be observed in the market by finding the YTM on outstanding bonds of the company. So,
the YTM on the bonds currently sold in the market is:
P = $930 = $40(PVIFA
R%
,40
) + $1,000(PVIF
R%
,40
)
Using a spreadsheet, financial calculator, or trial and error we find:
R
= 4.373%
This is the semiannual interest rate, so the YTM is:
YTM = 2
4.373% = 8.75%
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SOLUTIONS
20.
Accrued interest is the coupon payment for the period times the fraction of the period that has passed
since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per
six months is onehalf of the annual coupon payment. There are four months until the next coupon
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 Spring '06
 Tapley
 Finance

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