Question

Problem 10-30 Using Duration (LO4, CFA3) You find a bond with 26 years until maturity that has a coupon rate of 6.0 percent and a yield to maturity of 5.4 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.) b. Now suppose the original yield to maturity is increased by 1 percent. What is the new price of the bond? \

Answer 1

a). Current bond price:

FV (par value) =1,000; PMT (annual coupon) = coupon rate*par value = 6%*1,000 = 60; N (number of coupons) = 26; rate = 5.40%, solve for PV.

Bond price = 1,082.80

Using DURATION formula in excel, we have:

Note: Any settlement date and maturity date can be taken as long as the time period between the two equals 26 years (time to maturity of the bond).

Modified duration = duration/(1+yield) = 14.25/(1+0.054) = 13.52 years

If yield changes by +0.0025 then

change in price = -price*modified duration*change in yield

= -1,082.80*13.52*0.0025 = -36.59

New price = current price + change in price

= 1,082.80 -36.59 = 1,046.21 (estimated price)

Actual new price: FV = 1,000; PMT = 60; N = 26; rate = 5.40%+0.25% = 5.65%, solve for PV.

Bond price = 1,047.11 (Actual price)

b). If change in yield = + 0.01 then

change in price = -1,082.80*13.52*0.01 = -146.36

New price = 1,082.80 - 146.36 = 936.45 (Actual price)

Actual new price: FV = 1,000; PMT = 60; N = 26; rate = 5.40%+1% = 6.40%, solve for PV.

Bond price = 949.46 (Actual price)