Answer :
The first bond yield is 9.87%, and second bond yield is 9.19%, the third bond YTM is 7.69% and fourth-bond yield is 5.97%
Yield to Maturity: What is it?
The yield to maturity is one of the important factors taken into account when valuing bonds, along with the par value, coupon rate, and term to maturity. The return an investor will receive if they hold a bond until it matures is indicated by its yield to maturity. It is comparable to a bond's internal rate of return.
n = 10 years =10*2 = 20
Face value = $1,000
Coupon payment = (0.09/2)* 1,000 = 45
First bond
Current market value =$945.50
Period(n) Cash flows
0 (945.50)
1 45.00
2 45.00
3 45.00
4 45.00
5 45.00
6 45.00
7 45.00
8 45.00
9 45.00
10 45.00
11 45.00
12 45.00
13 45.00
14 45.00
15 45.00
16 45.00
17 45.00
18 45.00
19 45.00
20 1,045.00
IRR 4.9349%
Convert to the annual YTM = 4.9349*2 =9.8698%
YTM = 9.87%
Second bond
Current market value =$987.50
Period(n) Cash flows
0 (987.50)
1 45.00
2 45.00
3 45.00
4 45.00
5 45.00
6 45.00
7 45.00
8 45.00
9 45.00
10 45.00
11 45.00
12 45.00
13 45.00
14 45.00
15 45.00
16 45.00
17 45.00
18 45.00
19 45.00
20 1,045.00
IRR 4.5969%
Convert to the annual YTM = 4.5969*2 =9.1938%
YTM = 9.19%
Third bond
Current market value= $1,090.00
Period(n) Cash flows
0 (1,090.00)
1 45.00
2 45.00
3 45.00
4 45.00
5 45.00
6 45.00
7 45.00
8 45.00
9 45.00
10 45.00
11 45.00
12 45.00
13 45.00
14 45.00
15 45.00
16 45.00
17 45.00
18 45.00
19 45.00
20 1,045.00
IRR 3.8467%
Convert to the annual YTM = 3.8467*2 =7.6934%
YTM = 7.69%
Fourth bond
Current market value$1,225.87.
Period(n) Cash flows
0 (1,225.87)
1 45.00
2 45.00
3 45.00
4 45.00
5 45.00
6 45.00
7 45.00
8 45.00
9 45.00
10 45.00
11 45.00
12 45.00
13 45.00
14 45.00
15 45.00
16 45.00
17 45.00
18 45.00
19 45.00
20 1,045.00
IRR 2.9840%
Convert to the annual YTM = 2.9840*2 =5.968%
YTM = 5.97%
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