1. A 20-year, 8% semiannual coupon bond with a par value of $1,000 may be called
ID: 2741334 • Letter: 1
Question
1. A 20-year, 8% semiannual coupon bond with a par value of $1,000 may be called in 5 years at a call price of $1,040. The bond sells for$1,100. (Assume that the bond has just been issued.)
a. What is the bond’s yield to maturity?
b. What is the bond’s current yield?
c. What is the bond’s capital gain or loss yield?
d. What is the bond’s yield to call?
e. How would the price of the bond be affected by a change in the going market interest rate?
f. Now assume the date is October 25, 2017. Assume further that a 12%, 10-year bond was issued on July 1,2017, pays interest semiannually (on January 1 and July 1), and sells for $1,100. Use your spreadsheet to find the bond’s yield.
PLEASE SHOW WORK!! Thanks!
Explanation / Answer
N = 20*2 (Semi Annual coupon) = 40
Coupon = 0.08/2 = 0.04
Coupon payment = 0.04*1000 = 40
Current market price = 1100
Current market price = c1/(1+y)1 + c2/(1+y)2 + ……+ cn/(1+y)n + 1000/(1+y)n
1100 = 40/(1+y)1 + 40/(1+y)2 + 40/(1+y)3 + ……..+ 40/(1+y)40 + 1000/(1+y)40
Solve for Y using goal seek function in excel
Yield
0.03529574
Year
Cashflow (x)
Discount rate = 1/(1+y)^n
Present Value
1
40
0.96590758
38.6363031
2
40
0.93297745
37.3190979
3
40
0.90116999
36.0467995
4
40
0.87044692
34.8178767
5
40
0.84077127
33.630851
6
40
0.81210734
32.4842938
7
40
0.78442064
31.3768255
8
40
0.75767784
30.3071135
9
40
0.73184676
29.2738706
10
40
0.70689633
28.2758534
11
40
0.68279653
27.311861
12
40
0.65951834
26.3807335
13
40
0.63703376
25.4813504
14
40
0.61531574
24.6126294
15
40
0.59433813
23.7735253
16
40
0.57407571
22.9630282
17
40
0.55450407
22.1801629
18
40
0.53559969
21.4239874
19
40
0.5173398
20.6935918
20
40
0.49970243
19.9880971
21
40
0.48266636
19.3066545
22
40
0.4662111
18.6484438
23
40
0.45031683
18.0126732
24
40
0.43496444
17.3985775
25
40
0.42013545
16.8054179
26
40
0.40581201
16.2324805
27
40
0.3919769
15.6790759
28
40
0.37861346
15.1445382
29
40
0.36570561
14.6282242
30
40
0.35323782
14.1295126
31
40
0.34119508
13.6478033
32
40
0.32956292
13.1825166
33
40
0.31832732
12.7330927
34
40
0.30747477
12.2989907
35
40
0.29699221
11.8796883
36
40
0.28686702
11.474681
37
40
0.27708703
11.0834813
38
40
0.26764046
10.7056186
39
40
0.25851595
10.3406381
40
1040
0.24970252
259.690618
Present value
1100.00058
YTM = 3.5*2% = 7%
b.
Current yield = Annual Interest / Bond price
Current yield = (40+40)/1100 = 80/1100
Current yield = 7.3%
C.
Capital gain/loss = (Par value – cost price)/Cost price
= (1000-1100)/1100
= 9.09%
D.
Yield to call
Similar to the calculation of YTM
Coupon payment = 40
Payment at the end of 5th year = 40+1040 (call price) = 1080
1100 = 40/(1+y)1 + 40/(1+y)2 + 40/(1+y)3 + ……..+ 40/(1+y)10 + 1040/(1+y)10
Yield
0.03164146
Year
Cashflow (x)
Discount rate = 1/(1+y)^n
Present Value
1
40
0.96932901
38.7731605
2
40
0.93959873
37.5839494
3
40
0.91078031
36.4312125
4
40
0.88284578
35.3138313
5
40
0.85576803
34.2307212
6
40
0.82952078
33.1808312
7
40
0.80407856
32.1631423
8
40
0.77941667
31.176667
9
40
0.75551119
30.2204478
10
1080
0.73233892
790.926034
Present value
1100
YTC = 3.16*2 = 6.32%
Yield
0.03529574
Year
Cashflow (x)
Discount rate = 1/(1+y)^n
Present Value
1
40
0.96590758
38.6363031
2
40
0.93297745
37.3190979
3
40
0.90116999
36.0467995
4
40
0.87044692
34.8178767
5
40
0.84077127
33.630851
6
40
0.81210734
32.4842938
7
40
0.78442064
31.3768255
8
40
0.75767784
30.3071135
9
40
0.73184676
29.2738706
10
40
0.70689633
28.2758534
11
40
0.68279653
27.311861
12
40
0.65951834
26.3807335
13
40
0.63703376
25.4813504
14
40
0.61531574
24.6126294
15
40
0.59433813
23.7735253
16
40
0.57407571
22.9630282
17
40
0.55450407
22.1801629
18
40
0.53559969
21.4239874
19
40
0.5173398
20.6935918
20
40
0.49970243
19.9880971
21
40
0.48266636
19.3066545
22
40
0.4662111
18.6484438
23
40
0.45031683
18.0126732
24
40
0.43496444
17.3985775
25
40
0.42013545
16.8054179
26
40
0.40581201
16.2324805
27
40
0.3919769
15.6790759
28
40
0.37861346
15.1445382
29
40
0.36570561
14.6282242
30
40
0.35323782
14.1295126
31
40
0.34119508
13.6478033
32
40
0.32956292
13.1825166
33
40
0.31832732
12.7330927
34
40
0.30747477
12.2989907
35
40
0.29699221
11.8796883
36
40
0.28686702
11.474681
37
40
0.27708703
11.0834813
38
40
0.26764046
10.7056186
39
40
0.25851595
10.3406381
40
1040
0.24970252
259.690618
Present value
1100.00058
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