Question

An investor wants to find the duration of​ a(n) 30​-year, 6​% semiannual​ pay, noncallable bond​ that's currently priced in the market at ​$690.43​, to yield 9​%. Using a 200 basis point change in​ yield, find the effective duration of this bond.

a) The new price of the bond if the market interest rate decrease by 200 basis points (or 2%) is ___

Answer 1

(a)-The new price of the bond if the market interest rate decreased by 200 basis points (or 2%)

The Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $30 [$1,000 x 6% x ½]

Semi-annual Yield to Maturity = 3.50% [(9% - 2%) x ½]

Maturity Period = 60 Years [30 Years x 2]

The New Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $30[PVIFA 3.50%, 60 Years] + $1,000[PVIF 3.50%, 60 Years]

= [$30 x 24.94473] + [$1,000 x 0.12693]

= $748.35 + $126.93

= $875.28

“Hence, the New Price of the Bond would be $875.28”

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.  

--The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.