Question

On December 31, year 0, your company issued a 3-year $80,000 bond with 4% coupons payable annually. Proceeds were $78,900. On January 1, year 3, your company repurchased all of the outstanding 4% bonds. Provide the financial statement amounts under each scenario market discount rate applied to the bond at January 1, year 3.

Market discount rate at repurchase	Cash paid to repurchase bonds	Net Book value of bond on Jan. 1, year 3 (just after 2nd coupon payment)	Gain (+) or loss (-) on the repurchase
3.9%
4.5%
5.8%

Answer 1

Solution:

Repurchase price of bond = Present value of remaining interest and maturity on the date of repurchase.

Market discount rate at repurchase 3.9% = ($3,200 * PV factor at 3.9% for 1 period) + ($80,000 * PV factor at 3.9% for 1 period)

= $3,200 *0.962464 + $80,000 * 0.962464

= $80,077

Market discount rate is 4.5% = ($3,200 * PV factor at 4.5% for 1 period) + ($80,000 * PV factor at 4.5% for 1 period)

= $3,200 *0.956938 + $80,000 * 0.956938 = $79,617

Market discount rate is 5.8% = ($3,200 * PV factor at 5.8% for 1 period) + ($80,000 * PV factor at 5.8% for 1 period)

= $3,200 *0.94518 + $80,000 * 0.94518 = $78,639

Net book value of bond at beginning of year 3 = $80,000 - Unamortized discount = $80,000 - ($1,100/3) = $79,633

Market discount rate at repurchase	Cash paid to repurchase bonds	Net Book value of bond on Jan. 1, year 3 (just after 2nd coupon payment)	Gain (+) or loss (-) on the repurchase
3.90%	$80,077.00	$79,633.00	-$444.00
4.50%	$79,617.00	$79,633.00	$16.00
5.80%	$78,639.00	$79,633.00	$994.00