Prince Rupert Corporation issued a 15-year, $200,000 bond with a semi-annual coupon rate of 6% when market rates were 4%.What were the proceeds of the bond at the time of issue?

Question

Quizplus · Accepted Answer

First, calculate the semi-annual coupon payment: 
Coupon payment = Bond face value x Semi-annual coupon rate 
Coupon payment = $200,000 x 6%/2 
Coupon payment = $6,000

Next, calculate the present value of the bond: 
PV = Coupon payment x [1 - (1 + r)^-n] / r + Face value / (1 + r)^n 
Where: 
r = Market rate / 2 = 4%/2 = 2% 
n = Number of semi-annual periods = 15 years x 2 = 30

PV = $6,000 x [1 - (1 + 2%)^-30] / 2% + $200,000 / (1 + 2%)^30 
PV = $6,000 x 22.1465 + $53,151.70 
PV = $177,762.70

Therefore, the proceeds of the bond at the time of issue were $244,791.78 rounded to the nearest dollar, not one of the given answer choices.

Prince Rupert Corporation Issued a 15-Year, $200,000 Bond with a Semi-Annual