Both Bond Bill and Bond Ted have 11.8 percent coupons, make semiannual payments,
ID: 2641493 • Letter: B
Question
Both Bond Bill and Bond Ted have 11.8 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 7 years to maturity, whereas Bond Ted has 24 years to maturity. Requirement 1: If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places (e.g., 32.16).) Percentage change in price Bond Bill % Bond Ted % Requirement 2: If rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of these bonds? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) Percentage change in price Bond Bill % Bond Ted %Explanation / Answer
Bond Prices are dependent on many factor, change in interet rate is one of those factors. Now, if the market interest rises the bond price goes below the par value and vice versa happens if it reduces as compared to the coupon rates.
In the given question since the before the change of interest rates the price of bond = par value which means that the interest rate is equal to the coupon rate which is 11.8%.
Part (A)
If the interest rate rises by 2% this will reduce the price of the bond below the par value. If interest rate before change was 11.8% after the increase it will be 13.8%. Now the table below shows the new price by calculating the present value of all cash flows from the bond.
For Bond Bill
Coupon Payment No.
Cash Flow
Present Value of $ 1 at 13.8% (for half year)
Total
1
$ 59
$ 0.93545
$ 55.19
2
$ 59
$ 0.87507
$ 51.63
3
$ 59
$ 0.81859
$ 48.30
4
$ 59
$ 0.76575
$ 45.18
5
$ 59
$ 0.71633
$ 42.26
6
$ 59
$ 0.67009
$ 39.54
7
$ 59
$ 0.62684
$ 36.98
8
$ 59
$ 0.58638
$ 34.60
9
$ 59
$ 0.54853
$ 32.36
10
$ 59
$ 0.51312
$ 30.27
11
$ 59
$ 0.48000
$ 28.32
12
$ 59
$ 0.44902
$ 26.49
13
$ 59
$ 0.42004
$ 24.78
14
$ 59
$ 0.39293
$ 23.18
14
$ 1,000
$ 0.39293
$ 392.93
Grand Total
$ 912.02
Note : Assuming Face Value to be $ 1,000
For Bond Ted
Coupon Payment No.
Cash Flow
Present Value of $ 1 at 13.8% (for half year)
Total
1
$ 59
$ 0.93545
$ 55.19
2
$ 59
$ 0.87507
$ 51.63
3
$ 59
$ 0.81859
$ 48.30
4
$ 59
$ 0.76575
$ 45.18
5
$ 59
$ 0.71633
$ 42.26
6
$ 59
$ 0.67009
$ 39.54
7
$ 59
$ 0.62684
$ 36.98
8
$ 59
$ 0.58638
$ 34.60
9
$ 59
$ 0.54853
$ 32.36
10
$ 59
$ 0.51312
$ 30.27
11
$ 59
$ 0.48000
$ 28.32
12
$ 59
$ 0.44902
$ 26.49
13
$ 59
$ 0.42004
$ 24.78
14
$ 59
$ 0.39293
$ 23.18
14
$ 59
$ 0.36757
$ 21.69
15
$ 59
$ 0.34384
$ 20.29
16
$ 59
$ 0.32165
$ 18.98
17
$ 59
$ 0.30089
$ 17.75
18
$ 59
$ 0.28146
$ 16.61
19
$ 59
$ 0.26330
$ 15.53
20
$ 59
$ 0.24630
$ 14.53
21
$ 59
$ 0.23040
$ 13.59
22
$ 59
$ 0.21553
$ 12.72
23
$ 59
$ 0.20162
$ 11.90
24
$ 59
$ 0.18861
$ 11.13
25
$ 59
$ 0.17643
$ 10.41
26
$ 59
$ 0.16504
$ 9.74
27
$ 59
$ 0.15439
$ 9.11
28
$ 59
$ 0.14443
$ 8.52
29
$ 59
$ 0.13510
$ 7.97
30
$ 59
$ 0.12638
$ 7.46
31
$ 59
$ 0.11823
$ 6.98
32
$ 59
$ 0.11060
$ 6.53
33
$ 59
$ 0.10346
$ 6.10
34
$ 59
$ 0.09678
$ 5.71
35
$ 59
$ 0.09053
$ 5.34
36
$ 59
$ 0.08469
$ 5.00
37
$ 59
$ 0.07922
$ 4.67
38
$ 59
$ 0.07411
$ 4.37
39
$ 59
$ 0.06933
$ 4.09
40
$ 59
$ 0.06485
$ 3.83
41
$ 59
$ 0.06066
$ 3.58
42
$ 59
$ 0.05675
$ 3.35
43
$ 59
$ 0.05309
$ 3.13
44
$ 59
$ 0.04966
$ 2.93
45
$ 59
$ 0.04645
$ 2.74
46
$ 59
$ 0.04346
$ 2.56
47
$ 59
$ 0.04065
$ 2.40
48
$ 59
$ 0.03803
$ 2.24
48
$ 1,000
$ 0.03803
$ 38.03
Grand Total
860.58
Note : Assuming Face Value to be $ 1,000
Percentage Change in Price
Bond Bill
-8.80%
Bond Ted
-13.94%
Part (B)
If the interest rate falls by 2%
For Bond Bill
New Price = Rs. 1,099.62 (using the table except present value at 13.8% now we will use 9.8%)
For Bond Ted
New Price = Rs. 1,184.50 (using the table except present value at 13.8% now we will use 9.8%)
Percentage Change in Price
Bond Bill
9.96%
Bond Ted
18.45%
Coupon Payment No.
Cash Flow
Present Value of $ 1 at 13.8% (for half year)
Total
1
$ 59
$ 0.93545
$ 55.19
2
$ 59
$ 0.87507
$ 51.63
3
$ 59
$ 0.81859
$ 48.30
4
$ 59
$ 0.76575
$ 45.18
5
$ 59
$ 0.71633
$ 42.26
6
$ 59
$ 0.67009
$ 39.54
7
$ 59
$ 0.62684
$ 36.98
8
$ 59
$ 0.58638
$ 34.60
9
$ 59
$ 0.54853
$ 32.36
10
$ 59
$ 0.51312
$ 30.27
11
$ 59
$ 0.48000
$ 28.32
12
$ 59
$ 0.44902
$ 26.49
13
$ 59
$ 0.42004
$ 24.78
14
$ 59
$ 0.39293
$ 23.18
14
$ 1,000
$ 0.39293
$ 392.93
Grand Total
$ 912.02
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