Rivendale Enterprises issued a 3-year, $ 20 million face, 8% semiannual coupon bond when market interest rates were at 9%. What was the initial balance sheet liability and what percent-age of the cumulative interest expense occurred through year 1 Initial liability Year 1 interest expense（）①A. $ 1948421331.84% ②B. $ 1948421333.05% ③C. $ 2000000033.05%
A. ①
B. ②
C. ③
参考答案：B
解析：
The initial liability booked is the present value of the cash flows, or FV=20000000; PMT= 800000 (20000000×0.08/2); N=6(3×2); L/Y=4.5(9/2); PV=$19484213. The interest expenses in year 1=(effective interest rate×beginning book valuePeriod 1)+(effective interest rate×beginning book valuePeriod 2). The amount added to the book value each period is the difference between the coupon payment of 800000 and the interest expense for that period. IntEx l=19484213×0.045=$ 876790. IntEx 2=( 19484213+876790-800000)×0.045=19561003×0.045=$ 880245. Cumulative interest expense year 1=IntExl+IntEx2=$1757035. Total interest expense on the bond=amount received from the bondholder less the amount paid by the issuer. Amount received from the bondholder=initial liability=19484213. The amount paid by the issuer=(sum of the coupon payments+face value)=800000×6+20000000=24800000. The difference=5315787. Thus, cumulative interest expense through year 1 to total interest expense=1757035/5315787=33.05%.