Question

Consider a bond with a coupon of 7.4 percent, six years to maturity, and a current price of $1,029.90. Suppose the yield on the bond suddenly increases by 2 percent.

a. Use duration to estimate the new price of the bond. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Price=?

b. Calculate the new bond price using the usual bond pricing formula. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Price=?

Answer 1

Yield To Maturity(YTM) = (interest per period+ ((Redemption price - Current market price) / life remaining to maturity)) / ((.4*Redemption price)+ (.6*Current market price))

= ((1000*7.4%)+ ((1000-1029.9) / 6)) / ((.4*1000)+ (.6*1029.9))

= (74-4.98333333333) / (400+617.94)

= 0.06780032876

= 6.78%

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

a. Use duration to estimate the new price of the bond.

Time	Cashflow	[email protected]%	Present Value (Cashflow*PVF)	Weight based on present value	Time*Weight
1	74	0.937	69.30	0.0673	0.0673
2	74	0.877	64.90	0.0630	0.1261
3	74	0.821	60.78	0.0590	0.1771
4	74	0.769	56.92	0.0553	0.2211
5	74	0.720	53.31	0.0518	0.2588
6	1074	0.675	724.54	0.7036	4.2217

Duration = Time*Weight

= 5.0720

Modified Duration = Duration/(1+YTM)

= 5.0720/1.0678

= 4.74995317475

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

= 4.74995317475*2

= 9.4999063495

= 9.50

New Price = Old price-change in bond price

= 1029.9-9.5

= 1020.4

b. Calculate the new bond price using the usual bond pricing formula.

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

New yield = 6.78*1.02 = 6.9156%

Year	Cash flow	PVAF/[email protected]%	Present Value (Cashflow*PVAF/PVF)
1-6	74	4.7790	353.64
6	1000	0.6695	669.49

Current Market Price of Bonds = Cashflow*PVAF/PVF

= 3543.64+669.9

= $1023.13