On January 1 2014 TCU Utilities issued 1006000 in bonds that

On January 1, 2014, TCU Utilities issued $1,006,000 in bonds that mature in 4 years. The bonds have a stated interest rate of 9 percent and pay interest on June 30 and December 31 each year. When the bonds were sold, the market rate of interest was 12 percent. The company uses the effective-interest amortization method.

What is the book value of the bonds on (a) June 30, 2014? and (b) December 31, 2014?

What amount of interest expense should be recorded on (a) June 30, 2014? and (b) December 31, 2014?

Solution

PV = FV / (1+i)^n

Face Value

PV = $1,006,000 / 1.12⁴
PV = $639,331

Interest Portion

PV = $45,270 * (1 –(1/ (1+i)ⁿ)) / i
PV = $45,270* (1 - 1.045⁸) / 0.045

PV=$45,270 x 6.595886
PV = $298,596

Issue Price: $639,331+298,596=$937,927

2. Interest Expense $937,927 * 0.12 *1/2 = $56,276for June 30; $948,933 * 0.12 * 1/2 = $56,936 for Dec. 31

3. Cash Interest $1,006,000 * 0.09 * 1/2 = $45,270

4. Book Value $56,276- $45,270 = $11,006 + $937,927 = $948,933 for June 30; $56,936 - $45,270 = $11,666+ $948,933 = $960,599