ABC corp. issued a 3 year, $20 Million face, 8% semi-annual coupon bond when market interest rates were at 9%. What was the initial balance sheet liability and what % of the cumulative interest expense occurred through year 1? A) initial liability = 19,484,213; Year 1 Interest expense - 31.84% B) initial liability = 19,484,213; Year 1 Interest expense - 33.05% C) initial liability = 20,000,000; Year 1 Interest expense - 33.05% D) initial liability = 20,000,000; Year 1 Interest expense - 31.84%

B?? FV=20mil N=6 I/Y=4.5 PMT=800000 CPT->PV=19484213 Since the bond is priced to yield 9% a year… 19484213* (1.09)^3=25232620.08 25232620-20mil=5232620 = total interest expense 19484213*(.045)= 876789.58 = first 6 months interest expense 876789.58-800k=76789.58= increase in carrying value for next period 19561002.57*(0.45)= 880245.12= second 6 months interest expense (876789.58+880245.12)/ 5232620= 33.5% I probably took the long way to calculate this…hope someone can show me an easier way

N = 6 FV = 20m I/Y = 4.5 PMT = 0.8m CPT -> PV = 19.48421275 ----> this is the initial liability recorded in the Books IE = BV*0.09 Year-1 BV = 19.48421275 IE = 1.753579 CP = 1.6 BV = 19.48421275 + 0.153579 Year-2 BV = 19.63779175 IE = 1.7674012 CP =1.6 BV = 19.63779175 + 0.16740 = 19.80519175 Year-3 BV = 19.80519175 IE = 1.7824672575 CP =1.6 BV = 19.80519175 + 0.1824672575 = 19.9876590075 Total IE = 1.753579 + 1.7674012 + 1.7824672575 = 5.3034474575 IE% = 1.753579/5.3034474575 = 0.33064888 = 33.06% Is it B??? - Dinesh S

initial liability is 19,484,213 since the interest rate is higher than coupon —> bond trades at discount. no calculation needed. if you want to do so: FV=20M I/Y=4.5 N=6 PMT=0.8M CMT - PV … year…Initial Liability… Interest…Coupon…Amortization…Liab.end 0…19,484,213 1…19,484,213…876,789…800,000…76,789…19,561,002 2…19,561,002…880,245…800,000…80,245…19,641,247 Interest occurred 880,245+876,789= 1,757,034 Total expense is: 20,000,000 (FV) + 6*800,000 (in PMT’s) = 24,800,000 So that the difference 24,800,000 - 19,484,213= 5,315,787 is the total amount paid. 1,757,034/5,315,787 is 33.05%. B is the answer

i give up. I’m never the first to answer… lol. congrats long and dinesh.

thanks barthezz, Your calculations look straight forward and easy. My calculations had some errors in it (calculation of total expense is wrong), but got me close enough to get the right answer.

Total Interest expense can be calculated in a simpler manner. Bond Discount = 20000000 - 19484213 = 515787 Coupon Amount = 800000* 6 = 4.8 Mill Total Interest expense = 4.8M + .515787 = 5.315787 M Rest of it has been solved above… Just thought to share the simpler method to arrive at Interest expense for a Discount Bond. For a Premium Bond == Total Coupon Payment - Bond Premium = Interest Expense. HTH, CP

B is correct, good job everyone.

thanks barthezz and cpk… LongOnCFA, Mine is not a good method either, I used approximations and that got me close enough to answer the question but most of all, It took me 5 mins to get to the answer, probably would have left this (for later) in the exam. - Dinesh S

excellent problem. I got the answer but it took me 2 min. i like cpk’s shortcut.