A 101/2% bond matures in 11 years. Assuming the coupon is paid semiannually and the par value is $1,000, what is the value of this bond to an investor requiring a 10% rate of return?

Question

Quizplus · Accepted Answer

The value of the bond can be calculated using the formula for the present value of an annuity (for the semiannual coupon payments) plus the present value of a lump sum (for the maturity value of the bond). The coupon rate is 10.5% of $1,000, which equals $105 per year or $52.50 per semiannual period. The required rate of return is 10% annually, or 5% per semiannual period. The bond matures in 11 years, which equals 22 semiannual periods. The present value of the annuity (coupon payments) is calculated using the formula PV = P * [(1 - (1 + r)^-n) / r], where P is the payment per period, r is the rate per period, and n is the number of periods. The present value of the lump sum (the par value of the bond) is calculated using the formula PV = F / (1 + r)^n, where F is the future value or par value of the bond. Adding these two present values gives the total value of the bond to the investor.

A 101/2% Bond Matures in 11 Years