Due to a number of lawsuits related to toxic wastes,a major chemical manufacturer has recently experienced a market reevaluation.The firm has a bond issue outstanding with 15 years to maturity and a coupon rate of 8 percent,with interest being paid semiannually.The required simple rate on this debt has now risen to 16 percent.What is the current value of this bond?
A) $1,273
B) $1,000
C) $7,783
D) $550
E) $450

Question

Quizplus · Accepted Answer

The current value of the bond can be calculated using the formula for the present value of a bond, which includes the present value of the annuity (coupon payments) and the present value of the face value (the amount paid at maturity). Given the coupon rate of 8% on a face value of $1,000, the semiannual coupon payment is $40 ($1,000 * 8% / 2). With 30 periods remaining (15 years * 2) and a new semiannual required rate of 8% (16% annual rate / 2), the present value of the bond is calculated as follows:Present value of the annuity (coupon payments) = $40 * [1 - (1 + 0.08)^-30] / 0.08 = $40 * 12.2066 = $488.26Present value of the face value (paid at maturity) = $1,000 / (1 + 0.08)^30 = $1,000 / 10.0627 = $99.37Adding these two components gives the current value of the bond: $488.26 + $99.37 = $587.63. However, since this exact value is not an option and the closest provided option is $550, the correct choice is D.

Due to a Number of Lawsuits Related to Toxic Wastes,a