Yamaska Mining issued a. 5-year, $ 50 million face,6% semiannual bond when market interest rates were at 7%. What is the initial balance sheet liability and what is the cumulative interest expense (in dollars) that the company should report following the first half of the second year of the bond’s life (the third semiannual period) Initial liabilityCumulative interest expense to end of first half of year 2 ①A. $ 47920849$4500000 ②B. $ 47920849$ 5051494 ③C. $ 50000000$ 9000000
A.
A. ① |
B.
B. ② |
C.
C. ③ |
参考答案:B
解析:This is a discount bond since the market interest rate exceeds the coupon rate. The initial liability is equal to the proceeds received when the bond was issued. We can find this amount from the following calculation : FV = 50000000 ; N = 10 ; I = 3.5 ; PMT = 1500000 ; CPT→PV = $ 47920848.67. Round to $ 47920849. The interest expense in the first 6-month period is the initial proceeds multiplied by the semiannual market interest rate of 3.5%. We get: $ 47920849×3.5% = $1677230. Since the total coupon payment is $ 50000000×3.0% = $ 1500000 the closing liability for the first period is change in liability= $1677230 - $1500000 = 177230 plus the initial proceeds, or: $ 47920849 + $177230 = $48098079. The interest expense" in the second 6-month period is the opening liability for the period (the closing liability for the first period) multiplied by the semiannual market interest rate of 3.5 %. We get: $ 48098079×3.5% = $1683433. Proceeding in the same way as in the first two periods we should find that the interest expense for the third 6-month period is $1689853. Adding up these three interest expenses gives the cumulative interest expense to the end of the third 6-month period. We get- $ 1677230 + $1683433 + $1690853 = $5050516.