Question

A 30-year maturity bond making annual coupon payments with a coupon rate of 16.5% has duration of 11.19 years and convexity of 180.9. The bond currently sells at a yield to maturity of 8%.

a. Find the price of the bond if its yield to maturity falls to 7%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Price of the bond            $

b. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Predicted price            $

c. What price would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Predicted price            $

d-1. What is the percent error for each rule? (Enter your answer as a positive value. Do not round intermediate calculations. Round "Duration Rule" to 2 decimal places and "Duration-with-Convexity Rule" to 3 decimal places.)

	Percent Error
YTM	Duration Rule	Duration-with- Convexity Rule
7%	%	%

d-2. What do you conclude about the accuracy of the two rules?

	The duration-with-convexity rule provides more accurate approximations to the actual change in price.
	The duration rule provides more accurate approximations to the actual change in price.

e-1. Find the price of the bond if it's yield to maturity rises to 9%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Price of the bond            $

e-2. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Predicted price            $

e-3. What price would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Predicted price            $

e-4. What is the percent error for each rule? (Do not round intermediate calculations. Round "Duration Rule" to 2 decimal places and "Duration-with-Convexity Rule" to 3 decimal places.)

	Percent Error
YTM	Duration Rule	Duration-with- Convexity Rule
9%	%	%

e-5. Are your conclusions about the accuracy of the two rules consistent with parts (a) – (d)?

	Yes
	No

Answer 1

A1	B	C	D	E	F	G	H	I	J
2
3
4		Face Value of Bond	$1,000.00
5		Maturity Period	30.00	years
6		Coupon rate	16.50%
7		YTM	8.0%
8
9		Annual Coupon	$165.00	=D4*D6
10		Price of the Bond will be the present value of future cash flows of the bond.
11		Cash Flow of the Bond will be as follows:
12		Year	0	1	2	3	…	30
13		Cash Flow		$165.00	$165.00	$165.00	$165.00	$1,165.00
14
15		Calculation of Price of Bond:
16		Year (t)	0	1	2	3	…	30
17		Cash FLow (Ct)		$165.00	$165.00	$165.00	$165.00	$1,165.00
18		YTM (i)	8.00%
19		Price of the bond	=$165*(P/A,8%,30)+$1,000*(P/F,8%,30)
20			$1,956.91	=E17*PV(D18,D5,-1,0)+D4*(1/((1+D7)^D5))
21
22		Hence current price of the bond is	$1,956.91
23
24		a)
25
26		New Yield to maturity	7%
27
28		New Price of the bond	=$165*(P/A,7%,30)+$1,000*(P/F,7%,30)
29			$2,178.86	=D9*PV(D26,D5,-1,0)+D4*(1/((1+D26)^D5))
30
31		Hence new price of the bond is	$2,178.86
32
33		b)
34		Calculation of price of bond on the basis of duration rule:
35		Using duration rule, change in bond price can be calculated as:
36		% Change in Bond price	= - Modified Duration * Change in Yield
37
38		Using the Following Data
39		Duration	11.19	Years
40		Yield	8.0%
41		Modified duration	=Duration / (1+ Yield)
42			10.36	=D39/(1+D40)
43
44		New Yield	7.00%
45		Change in Yield	-1.00%
46
47		Using duration rule, change in bond price can be calculated as:
48		% Change in Bond price	= - Modified Duration * Change in Yield
49			10.36%	=-D110*D113
50
51		Hence % Change in Bond price	10.36%
52
53		Price of bond Before change	$1,957
54
55		Price of predicted using Duration method	=Price before the change*(1+%change)
56			$2,159.67	=D53*(1+D51)
57
58		Hence price predicted using duration method	$2,159.67
59