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

1-
Period = Year	cash flow	present value of cash flow = cash flow/(1+r)^n r = 5.2%	present value*period
1	60	57.03422053	57.03422053
2	60	54.21503853	108.4300771
3	60	51.53520773	154.6056232
4	60	48.98784004	195.9513602
5	60	46.56638788	232.8319394
6	60	44.26462726	265.5877635
7	60	42.07664188	294.5364932
8	60	39.99680787	319.974463
9	60	38.01977934	342.1780141
10	60	36.14047466	361.4047466
11	60	34.35406337	377.894697
12	60	32.65595377	391.8714453
13	60	31.04178115	403.543155
14	60	29.50739653	413.1035514
15	60	28.04885602	420.7328403
16	60	26.66241066	426.5985706
17	60	25.34449683	430.8564461
18	60	24.09172702	433.6510864
19	60	22.9008812	435.1167428
20	60	21.76889848	435.3779696
21	1060	365.5740239	7677.054502
value of bond = sum of present value of cash inflow		1100.787515
sum of (present value of cash flow*period)			14178.33571
Maculay's duaration = sum of (present value of cash flow*period) / value of bond	14178.33/1100.78		12.88017489
Modified duation = maculay's duration/(1+YTM)	12.88/(1.052)		12.24351225
Estimated Price of bond using duration	current price-(duration*change in rate*current price)	1100.78-(0.25%*12.24*1100.78)	1067.20621
Actual Price of Bond Using Present value function in MS excel =pv(rate,nper,pmt,fv,type)	rate= 5.45% nper = 21 pmt =-60 fv =-1000 type =0	$1,067.81	$1,067.81
If YTM increased by 1%	5.2+1	6.20%
Estimated Price of bond using duration	current price-duration*change in rate*	1100.78-(1%*12.2435*1100.78)	966.0060007
Actual Price of Bond Using Present value function in MS excel =pv(rate,nper,pmt,fv,type)	rate= 6.2% nper = 21 pmt =-60 fv =-1000 type =0	PV(6.2%,21,-60,-1000,0)	$976.86