Question

Rocky believes that a bond he is purchasing today has an effective annual discount rate of 15%. The bond has 8 remaining coupons of $700 each. The first coupon will be paid in 1 month, and each subsequent payment will be one year after. On the date of the last coupon payment the bond will pay out a face value of $10,000. What is the bond’s present value if Rocky’s assumption of the discount rate is correct?

Answer 1

Value of Each Remaining Coupon = $ 700, Effective Annual Discount Rate = 15 %, Face Value = $ 10000, Number of Remaining Coupons = 8 with first coming in one-month from now and the following ones at intervals of 1 year each

Total Present Value of Remaining Coupons + Redeemed Par Value at Maturity one-month from now = P1 = 700 + 700 x (1/0.15) x [1-{1/(1.15)^(7)}] + 10000 / (1.15)^(7) = $ 7371.66

Monthly Effective Discount Rate = [1+(15/100)]^(1/12) - 1 = 0.011715 or 1.1715 %

Therefore, Total Present Value now = P0 = P1 / (1.011715) = 7371.66 / 1.011715 = $ 7286.302 ~ $ 7286.3