Calculate the premium or discount on the sale of a 25-year, $1,000 Enron Corporation bond that was issued 6 years ago with a coupon rate of 8.2% and is trading today at a yield rate of 15.8% (compounded semiannually).

Question

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The bond is trading at a discount because the current yield rate (15.8%) is higher than the coupon rate (8.2%). To calculate the present value of the bond (which will show us the discount), we use the formula for the present value of an annuity (for the semiannual coupon payments) and the present value of a lump sum (for the bond's face value at maturity). The bond has 19 years left until maturity (25 - 6), which equals 38 six-month periods. The semiannual coupon payment is $41 (0.082 * $1,000 / 2). The semiannual yield rate is 7.9% (15.8% / 2).Present value of the annuity (coupon payments) = C * [1 - (1 + r)^-n] / r= $41 * [1 - (1 + 0.079)^-38] / 0.079= $41 * [1 - (1 + 0.079)^-38] / 0.079= $41 * 15.046= $616.886Present value of the lump sum (face value) = F / (1 + r)^n= $1,000 / (1 + 0.079)^38= $1,000 / 10.192= $98.14Total present value = $616.886 + $98.14 = $715.026The bond's face value is $1,000, so the discount is $1,000 - $715.026 = $284.974, which is closest to option C, $454.26 Discount. However, it seems there was a calculation error in my explanation. The correct calculation should lead to the answer closest to the options provided, which indicates a discount. The correct approach involves using the given yield rate and coupon rate to find the present value of all future cash flows (coupon payments and the face value at maturity), but the exact calculation provided here has a mistake in the final numbers. The principle of why it's a discount is correct, but the specific numbers provided do not accurately lead to one of the given choices due to a computational error. The correct choice based on the principle should be a discount, and among the options given, C is a discount option, but please note the calculation discrepancy.

Calculate the Premium or Discount on the Sale of a 25-Year