Marshall Manufacturing has a bond outstanding that was issued 20 years ago at a coupon rate of 9%. The $1,000 par value bond pays interest semiannually and was originally issued with a term of 30 years. If today's interest rate is 14%, what is the value of the bond today?

Question

Quizplus · Accepted Answer

The value of a bond is calculated using the present value of its future cash flows, which include the semiannual interest payments and the principal amount to be received at maturity. The formula for the present value of an annuity (for the interest payments) and the present value of a lump sum (for the principal repayment) are used. Given a 9% annual coupon rate on a $1,000 bond, the semiannual interest payment is $45 ($1,000 * 9% / 2). There are 20 years left until maturity, which means 40 semiannual periods. The current market interest rate is 14% annually, or 7% per semiannual period. Using the present value formulas:- Present value of the semiannual interest payments (Annuity): PV = Pmt * [(1 - (1 + r)^-n) / r] = $45 * [(1 - (1 + 0.07)^-40) / 0.07] ≈ $435.15- Present value of the principal amount (Lump Sum): PV = F / (1 + r)^n = $1,000 / (1 + 0.07)^40 ≈ $300Adding these two components gives the total current value of the bond: ≈ $435.15 + $300 ≈ $735.15.

Marshall Manufacturing Has a Bond Outstanding That Was Issued 20