 # Bond Interest Expense and Balance Sheet Liability

Having a hard time figuring out this one: A firm issues a 4-year semiannual-pay bond with a face value of \$10 million and a coupon of 10%. The market interest rate is 11% when the bond is issued. The interest expense for the first semiannual period and the balance sheet liability at the end of the first semiannual period are closest to: Interest Expense Balance Sheet Liability a)\$532,580 \$9,683,272 b)\$532,580 \$9,715,852 c)\$550,000 \$9,683,272 d)\$550,000 \$9,715,852

The answer is B. Interest expense is 11/2 % of the opening balance sheet liability for each period. Opening balance sheet liability for first period is PV of 10,000,000 discounted at 11/2 % for 8 periods + PV of 500,000 annuity at 11/2% over 8 periods. Ending balance sheet liability is opening liability plus difference between interest expense and coupon payment (500,000).

hi, you can think of this as follows (if this helps…): the liability is the PV of future cashflows, but the PV is calculated using a fixed rate (here 11%): L[t] = sum_{i=1,…,n} CF[t+i] / (1+y)^i here y is the fixed rate (well, use y=11%/2 because of semi-annual compounding). Then we have: L[t+1] = L[t]*(1+y) - CF[t] = L[t] + (L[t]*y-CF[t]) Since the fixed rate (11%) is lower than the coupon (10%), the Liability is below par and has to grow. The PV at the start is L = 9,638,271, and after the first period, it is L = L + (L*11%/2 - 500,000) which means: add 32,579 to L.

Use your calculator: Bond pays semiannually, IE is YTM/2*book value of debt Book value of debt is the bond’s selling price: N=8, I/Y=5.5, PMT=500,000, FV=10,000,000, CTP PV = 9,683,271.7 IE=5.5%*9,683,271.7=532,579.94~532,580 Value of the bond after 1 period: N=7, I/Y=5.5, PMT=500,000, FV=10,000,000, CTP PV = 9,715,851.64 ~ 9,715,852