单选题
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. $ 19484213 31.84%
②B. $ 19484213 33.05%
③C. $ 20000000 33.05%
【正确答案】
B
【答案解析】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%.