Consider a bond with a coupon rate of 8 percent that pays semiannual interest and matures in eight years.The market rate of return on bonds of this risk is currently 11 percent.What is the current value of a $1,000 face value bond?

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Quizplus · Accepted Answer

The current value of the bond can be calculated using the formula for the present value of an annuity (for the semiannual interest payments) plus the present value of a lump sum (for the face value of the bond at maturity). Given a semiannual coupon rate of 4% (8% annual rate divided by 2), a market rate of 5.5% per semiannual period (11% annual rate divided by 2), and a total of 16 semiannual periods (8 years times 2), the calculation is as follows:Present value of the annuity (interest payments) = C * [(1 - (1 + r)^-n) / r]= $40 * [(1 - (1 + 0.055)^-16) / 0.055]= $40 * 10.5753= $423.41Present value of the lump sum (face value) = F / (1 + r)^n= $1,000 / (1 + 0.055)^16= $419.66Current value of the bond = $423.41 + $419.66 = $843.07

Consider a Bond with a Coupon Rate of 8 Percent