Question

An investor wants to find the duration of​ a(n) 25​-year, 7​%semiannual​ pay, noncallable bond​ that's currently priced in the market at $481.01​, to yield 15​%. Using a 250 basis point change in​ yield, find the effective duration of this bond (Hint​: use Equation​ 11.11).

The new price of the bond if the market interest rate decreases by 250 basis points​ (or 2.5​%) is ​$_____. (Round to the nearest​ cent.)

Answer 1

The new price of the bond if the market interest rate decreased by 250 basis points (or 2.50%)

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 = $35 [$1,000 x 7% x ½]

Semi-annual Yield to Maturity = 6.25% [(15% - 2.50%) x ½]

Maturity Period = 50 Years [25 Years x 2]

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

= $35[PVIFA 6.25%, 50 Years] + $1,000[PVIF 6.25%, 50 Years]

= [$35 x 15.22790] + [$1,000 x 0.04826]

= $532.97 + $48.26

= $581.23

“Hence, the new price of the bond if the market interest rate decreases by 250 basis points (or 2.5%) is $581.23”

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.