Answer:
A) $61,654,600
B) June 30, 2016, first coupon payment
Dr Interest expense 4,840,000
Dr Premium on bonds payable 60,000
Cr Cash 4,900,000
C) If you use the effective interest rate, the bond premium is higher, so the actual interest expense would be lower:
June 30, 2016, first coupon payment
Dr Interest expense 4,756,406
Dr Premium on bonds payable 143,594
Cr Cash 4,900,000
D) The actual difference between the coupon rate and the effective interest rate (with a $72,400,000 issue price) = 14% (coupon rate) - 13.93% = 0.07%.
The bond's issue price is generally determined by the market rate, but sometimes a company might believe that the interest rate applicable to them is actually different. A company might under estimate the riskiness of their operations, but the market doesn't. Generally the market rate is correct. So any variation in the coupon rate is due to a mistake by the firm. Usually companies do not make huge mistakes, if they miss on the coupon rate it generally is not significant.
Explanation:
issued $70 million face amount of 20-year, 14% stated rate bonds when market interest rates were 16%. The bonds pay interest semi-annually each June 30 and December 31, each coupon = $4,900,000
bonds market price = PV of maturity value + PV of coupons
- PV of maturity value = $70,000,000 x 0.04603 = $3,222,100
- PV of coupons = $4,900,000 x (8% annuity, 40 periods) = $4,900,000 x 11.925 = $58,432,500
- total issue price = $61,654,600
if instead the issue price was $72,400,000 (resulting in a $2,400,000 premium), then the premium would be amortized by $2,400,000 / 40 = $60,000 during each coupon payment
if the effective interest method, (not the compound interest method), was used to amortize bond premium, then we first need to calculate the effective interest rate:
$72,400,000 - $70,000,000 = $2,400,000 / 40 = $60,000
$4,900,000 + $60,000 = $4,960,000 / {($72,400,000 + $70,000,000) / 2} = 0.0696629
bond premium discount using effective interest rate = ($72,400,000 x 0.0696629) - $4,900,000 = $5,043,594 - $4,900,000 = $143,594
