Question

A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has duration of 11.54 years and convexity of 192.4. The bond currently sells at a yield to maturity of 8%.

4.34points

Time Remaining 2 hours 42 minutes 16 seconds

02:42:16

eBook

Print

References

Check my workCheck My Work button is now enabled

Item22

Item 22 4.34 points

Time Remaining 2 hours 42 minutes 16 seconds

02:42:16

A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has duration of 11.54 years and convexity of 192.4. 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

Item22

4.34points

Time Remaining 2 hours 41 minutes 51 seconds

02:41:51

eBook

Print

References

Check my workCheck My Work button is now enabled

Item22

Item 22 4.34 points

Time Remaining 2 hours 41 minutes 51 seconds

02:41:51

A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has duration of 11.54 years and convexity of 192.4. 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.)

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

4.34points

Time Remaining 2 hours 41 minutes 22 seconds

02:41:22

eBook

Print

References

Check my workCheck My Work button is now enabled

Item22

Item 22 4.34 points

Time Remaining 2 hours 41 minutes 22 seconds

02:41:22

A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has duration of 11.54 years and convexity of 192.4. 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.)

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

c. What price would be predicted by the duration-with-convexity rule?


d-1. What is the percent error for each rule? (Enter your answers as positive values. Do not round intermediate calculations. Roun

Answer 1

A	B	C	D	E	F	G	H
2
3		Face value	$1,000
4		Coupon rate	12.00%
5		Market interest rate (i)	8.00%
6		Maturity	30	years
7		Annual Coupon (C)	$120	=D3*D4
8		Duration	11.54	Years
9		Convexity	192.4
10		Current Price of Bond	=C*(P/A,i,n)+F*(P/F,i,n)
11			=$120*(P/A,8%,30)+$1000*(P/F,8%,30)
12			$1,450.31	=D7*PV(D5,D6,-1,0)+D3*(1/((1+D5)^D6))
13
14		Calculation of Bond Price at YTM of 7%:
15		Bond Price will be the present value of bond cash flows at market rate.
16
17		Coupon rate	12%
18		Maturity (n)	30	years
19		YTM (i)	7%
20		Face value (F)	$1,000
21		Annual Coupon (C)	$120
22		Price of the bond at YTM of 7%	=C*(P/A,i,n)+F*(P/F,i,n)
23			=$120*(P/A,7%,30)+$1000*(P/F,7%,30)
24			$1,620.45	=D21*PV(D19,D18,-1,0)+D20*(1/((1+D19)^D18))
25
26		Hence Price of the bond before change in Yield	$1,620.45
27		b)
28		Calculation of price of bond on the basis of duration rule:
29		Using duration rule, change in bond price can be calculated as:
30		Change in Bond price/Price of the bond = - (Duration / (1+ Yield)) * Change in yield
31
32		Present Yield	8.00%
33		New Yield	7.00%
34		Change in Yield	-1.00%
35		Current Price of Bond	$1,450.31
36		Duration	11.54	Years
37
38		Change in Bond price/Price of the bond	= - (Duration / (1+ Yield)) * Change in Yield
39			0.106851852	=-(D36/(1+D32))*D34
40
41		Change in Bond Price	$154.97	=D39*D35
42
43		New Bond Price	=Current Price of Bond + Change in Bond Price
44			$1,605.28	=D38+D44
45
46		Hence as per duration rule,
47		New Bond Price	$1,605.28
48