A bond with annual coupon rate of 5.10% and price of $1,090 just yesterday paid a coupon. A total of 23 coupons remain to be paid. Suppose you buy the bond at today’s price, hold it and receive 8 coupons, and then sell the bond. If at the time you sell the bond its YTM has decreased a total of 50 basis points, find the selling price of the bond. (FYI; 0.01=1%=100 basis points; use semiannual compounding)

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Asked Jul 3, 2019
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A bond with annual coupon rate of 5.10% and price of $1,090 just yesterday paid a coupon. A total of 23 coupons remain to be paid. Suppose you buy the bond at today’s price, hold it and receive 8 coupons, and then sell the bond. If at the time you sell the bond its YTM has decreased a total of 50 basis points, find the selling price of the bond. (FYI; 0.01=1%=100 basis points; use semiannual compounding)

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Expert Answer

Step 1

Calculation of Yield to Maturity of the Bond:

B5
-RATE(B4,B3,-B2,В1)*2
C
A
В
1Face Value
2 Bond Price
3 Coupon Payment
4 No. of Periods
5 Yield to Maturity
S1,000
$1,090
$25.50
23
4.11%
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B5 -RATE(B4,B3,-B2,В1)*2 C A В 1Face Value 2 Bond Price 3 Coupon Payment 4 No. of Periods 5 Yield to Maturity S1,000 $1,090 $25.50 23 4.11%

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Step 2

Excel Spreadsheet:

fiRATE(B4,B3,-B2,B1)*2
B5
A
B
T1000
1090
1 Face Value
2 Bond Price
3 Coupon Payment =1000*(5.1%/2)
4 No. of Periods 23
5Yield to Maturity =RATE(B4,B3,-B2,B1)*2
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fiRATE(B4,B3,-B2,B1)*2 B5 A B T1000 1090 1 Face Value 2 Bond Price 3 Coupon Payment =1000*(5.1%/2) 4 No. of Periods 23 5Yield to Maturity =RATE(B4,B3,-B2,B1)*2

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Step 3

Calculation of Selling Price of Bond:

...
в7
f=PV(B6,B3,-B2,-B1)
с
A
В
1 Face Vahue
$1,000
2 Coupon Payment
3 No. of Periods
4 Actual Yield to Maturity
5 Decrease in Basis Points
6 Net YTM
Bond Price
$25.50
15
4.11%
0.50%
1.81%
$1,097.13
7
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в7 f=PV(B6,B3,-B2,-B1) с A В 1 Face Vahue $1,000 2 Coupon Payment 3 No. of Periods 4 Actual Yield to Maturity 5 Decrease in Basis Points 6 Net YTM Bond Price $25.50 15 4.11% 0.50% 1.81% $1,097.13 7

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