Question

A bond that matures in 17 years has a ​$1000 par value. The annual coupon interest rate is 11 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 14 percent. What would be the value of this bond if it paid interest​ annually? What would be the value of this bond if it paid interest​ semiannually?

A) the value of this bond if it paid interest annually would be $ 808.81

B) answer this: the value of this bond if it paid interest semiannually would be$____?

Answer 1

(B)-The value of this bond if it paid interest semiannually

The Value 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 = $55 [$1,000 x 11% x ½]

Semi-annual Yield to Maturity of the Bond = 7.00% [14.00% x ½]

Maturity Period = 34 Years [17 Years x 2]

Therefore, the Value of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $55[PVIFA 7.00%, 34 Years] + $1,000[PVIF 7.00%, 34 Years]

= [$55 x 12.85401] + [$1,000 x 0.10022]

= $706.97 + $100.22

= $807.19

“Hence, the value of this bond if it paid interest semiannually would be $807.19”

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.