Question

You find a bond with 21 years until maturity that has a coupon rate of 6.0 percent and a yield to maturity of 5.2 percent. Suppose the yield to maturity on the bond increases by 0.25 percent.

a. What is the new price of the bond using duration and using the bond pricing formula? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

estimated price

actual price

b. Now suppose the original yield to maturity is increased by 1 percent. What is the new price of the bond? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

   

estimated price

actual price

Answer 1

Step 1: Calculation of bond price & duration

Time	Cashflow	[email protected]%	Present Value (Cashflow*PVF)	Weight based on present value	Time*Weight
1	60	0.951	57.03	0.0518	0.0518
2	60	0.904	54.22	0.0493	0.0985
3	60	0.859	51.54	0.0468	0.1405
4	60	0.816	48.99	0.0445	0.1780
5	60	0.776	46.57	0.0423	0.2115
6	60	0.738	44.26	0.0402	0.2413
7	60	0.701	42.08	0.0382	0.2676
8	60	0.667	40.00	0.0363	0.2907
9	60	0.634	38.02	0.0345	0.3108
10	60	0.602	36.14	0.0328	0.3283
11	60	0.573	34.35	0.0312	0.3433
12	60	0.544	32.66	0.0297	0.3560
13	60	0.517	31.04	0.0282	0.3666
14	60	0.492	29.51	0.0268	0.3753
15	60	0.467	28.05	0.0255	0.3822
16	60	0.444	26.66	0.0242	0.3875
17	60	0.422	25.34	0.0230	0.3914
18	60	0.402	24.09	0.0219	0.3939
19	60	0.382	22.90	0.0208	0.3953
20	60	0.363	21.77	0.0198	0.3955
21	1060	0.345	365.57	0.3321	6.9741

Duration = Time*Weight

= 12.8802

Modified Duration = Duration/(1+YTM)

= 12.8802/1.052

= 12.2435

Current Market Price of Bonds = Cashflow*/PVF

= 1100.79

a. What is the new price of the bond using duration and using the bond pricing formula?

estimated price

Modified Duration measures the change in bond price with respect to change in YTM. But the direction of change is opposite. That is when YTM increases, bond price decreases. Similarly when YTM decreases, bond price increases.

% change in bond price = Modified Duration * % change in YTM

= 12.2435*.25%

= 3.060875%

estimated price = 1100.79-(1100.79*3.060875%)

= $1067.10

actual price

Bond Valuation: The value of bond is the present value of the expected cashflows from the bond,discounted at Yield to Maturity(YTM).

Year	Cash flow	PVAF/[email protected]%	Present Value (Cashflow*PVAF/PVF)
1-21	60	12.3282	739.69
21	1000	0.3281	328.11

Current Market Price of Bonds = Cashflow*PVAF/PVF

= 739.69+328.11

= $1067.80

b. Now suppose the original yield to maturity is increased by 1 percent. What is the new price of the bond? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

   estimated price

% change in bond price = Modified Duration * % change in YTM

= 12.2435*1%

= 12.2435%

estimated price = 1100.79-(1100.79*12.2435%)

= $966.01

actual price

Year	Cash flow	PVAF/[email protected]%	Present Value (Cashflow*PVAF/PVF)
1-21	60	11.5687	694.12
21	1000	0.2827	282.74

Current Market Price of Bonds = Cashflow*PVAF/PVF

= 694.12+282.74

= $976.86

Formula to calculate PV in excel is as follows "=PV(interest rate,Year,0,cashflow)"

You can use the equation 1/(1+i)^n to find PVF using calculator

You can use the equation (1-(1+r)^-n)/r to find PVAF using calculator

note: It is general practice to take $1,000 as face value when no details are given.