As with most bonds, consider a bond with a face value of $1,000. The bond's maturity...

As with most bonds, consider a bond with a face value of $1,000. The bond's maturity is 22 years, the coupon rate is 10% paid semiannually, and the discount rate is 14%.

What is the estimated value of this bond today?

Solutions

Expert Solution

The Value of the Bond today

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 = $50 [$1,000 x 10% x ½]

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

Maturity Period = 44 Years [22 Years x 2]

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

= $50[PVIFA 7.00%, 44 Years] + $1,000[PVIF 7.00%, 44 Years]

= [$50 x 13.55791] + [$1,000 x 0.05095]

= $677.89 + $50.95

= $728.84

“Hence, the Value of the Bond will be $728.84”

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.

jeff jeffy answered 6 months ago

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