Long Term Debt consists of "Junk" Bonds issued at a face value of $7 million. These pay interest semiannually at a rate of 16% p.a. (compounding semi-annually). They have 3 years to maturity. Long Term Debt also includes a secured liability to Huge Company Ltd which currently sits in the books at $3 million. Interest is payable annually on this at a fixed rate of 10% p.a. (which is also the current market rate for this liability). The market yield on the junk bonds is 18%p.a. (compounding semi-annually)

just look at the junk bonds: When calculating the market value of junk bonds, why does the answer use 0.09( 0.18/2) in the formula, rather than r(junk)=18.81%/2? Since the question says '18%p.a. (compounding semi-annually)'. Is this a mistake of the answer?

Cost of debt Junk Bonds The yield on junk bonds is 18% p.a., compounded semi-annually. Converting this to an effective annual rate: 2 R 0.18 1+ 2 -1=18.81% junk Secured Loan All we are told about this secured loan is nat we owe $3m and that 10% intere is payable annually in arrears. This suggests that the 10% interest cost is already an effective annual rate. = 10% Ruoan Market value of debt (D) Junk Bonds There is no indication whether or not the junk bonds are publicly traded. Nonetheless, we know their yield (18% p.a.) and there is sufficient information relating to the coupon payment and remaining term to maturity. In particular, the total coupon payment every 6 months is 8% times the $7m face value. So we can easily estimate the market price for the junk bonds: -6 D 1-(1.09) 560,000 0.09 + 7,000,000 (1.09) = $6,685,986 junk