When the market rate of interest was 11%, Valley Corporation issued $100,000, 8%, 10-year bonds that pay interest semiannually. Using the straight-line method, the amount of discount or premium to be amortized each interest period would be
A) $4,000
B) $896
C) $17,926
D) $1,793

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of the bond using the market rate of interest of 11%. 
PV = PMT x [1 - (1 + r/n)^(-nt)] / (r/n)
PV = $4,000 x [1 - (1 + 0.11/2)^(-20)] / (0.11/2)
PV = $65,521.87

Since the bond was issued at $100,000, the amount of premium is the difference between the face value and the present value:
Premium = $100,000 - $65,521.87 = $34,478.13

To amortize the premium using the straight-line method, we divide the premium by the number of interest periods. Since the bond pays interest semiannually for 10 years (20 periods), the amount to be amortized each period is:
Amortization = $34,478.13 / 20 = $1,723.91

Since the bond pays interest semiannually, we multiply this amount by 1/2 for each interest period:
Amortization per interest period = $1,723.91 x (1/2) = $861.96

However, the bond's coupon rate is 8%, which means the company will be paying $4,000 in interest every six months. Since this is higher than the amount of interest expense based on the carrying value ($65,521.87 x 0.11/2 = $3,603.70), we need to reduce the amortization by the amount of excess interest:
Excess interest = $4,000 - $3,603.70 = $396.30
Adjusted amortization per interest period = $861.96 - $396.30 = $465.66

Therefore, the amount of discount or premium to be amortized each interest period using the straight-line method is $465.66, which corresponds to answer choice B).

When the Market Rate of Interest Was 11%, Valley Corporation