Question

Austin Corp. issued a non-callable bond that has 14 years to maturity, an 8% semi-annual coupon, and a $1,000 par value. your required return on the Austin Corp. Bond is 9%, if you buy it, you plan to hold it for 9 years. You (and the market) have expectations that in 9 years, the yield to maturity on a 5-year bond with similar risk will be 9.5%. How much should you be willing to pay for the Austin Corp. Bond Today? No Excel Please.

Answer 1

Bond Coupon = 8 % payable semi-annually, Tenure Remaining at the end of Year 9 = 5 years , Original Tenure = 14 years, Par Value = $ 1000, Interest Rate at the end of Year 9 = 9.5 % or (9.5 / 2) = 4.75 % per half-year,Required Return at Buy = 9 %

Semi-Annual Coupon = 0.08 x 0.5 x 1000 = $ 40

Therefore, Sale Price at the end of Year 9 = Total Present Value of all Remaining Semi-Annual Coupons + Par Value Redeemed at Maturity = 40 x (1/0.0475) x [1-{1/(1.0475)^(10)}] + 1000 / (1.0475)^(10) = $ 941.377 ~ $ 941.38

Current Price = Total Present Value of Semi-Annual Coupons during holding period + Sale Price = 40 x (1/0.045) x [1-{1/(1.045)^(18)}] + 941.38 / (1.045)^(18) = $ 912.657 ~ $ 912.66