Exercise 14-2 1. Maturity Interest paid Stated rate Effective (market) rate 10 years annually 10% 12% Interest $100,000 x 5.65022 * = $565,022 Principal $1,000,000 x 0.32197 ** = 321,970 Present value (price) of the bonds $886,992 10% x $1,000,000 * present value of an ordinary annuity of $1: n=10, i=12% (Table 4) ** present value of $1: n=10, i=12% (Table 2) 2. Maturity Interest paid Stated rate Effective (market) rate 10 years semiannually 10% 12% Interest $50,000 x 11.46992 * = $573,496 Principal $1,000,000 x 0.31180 ** = 311,800 Present value (price) of the bonds $885,296 5% x $1,000,000 * present value of an ordinary annuity of $1: n=20, i=6% (Table 4) ** present value of $1: n=20, i=6% (Table 2) 3. Maturity Interest paid Stated rate Effective (market) rate 10 years semiannually 12% 10% Interest $60,000 x 12.46221 * = $ 747,733 Principal $1,000,000 x 0.37689 ** = 376,890 Present value (price) of the bonds $1,124,623 6% x $1,000,000 * present value of an ordinary annuity of $1: n=20, i=5% (Table 4) ** present value of $1: n=20, i=5% (Table 2) 4. Maturity Interest paid Stated rate Effective (market) rate 20 years semiannually 12% 10% Interest $60,000 x 17.15909 * = $1,029,545 Principal $1,000,000 x 0.14205 ** = 142,050 Present value (price) of the bonds $1,171,595 6% x $1,000,000 * present value of an ordinary annuity of $1: n=40, i=5% (Table 4) ** present value of $1: n=40, i=5% (Table 2)
Exercise 14-2 (concluded) 5. Maturity Interest paid Stated rate Effective (market) rate 20 years semiannually 12% 12% Interest $60,000 x 15.04630 * = $902,778 Principal $1,000,000 x 0.09722 ** = 97,220 Present value (price) of the bonds $999,998 actually, $1,000,000 if PV table factors were not rounded 6% x $1,000,000 * present value of an ordinary annuity of $1: n=40, i=6% (Table 4) ** present value of $1: n=40, i=6% (Table 2)
Exercise 14-3 1. Price of the bonds at January 1, 2009 Interest $4,000,000 x 11.46992 * = $45,879,680 Principal $80,000,000 x 0.31180 ** = 24,944,000 Present value (price) of the bonds $70,823,680 5% x $80,000,000 * present value of an ordinary annuity of $1: n=20, i=6% (Table 4) ** present value of $1: n=20, i=6% (Table 2) 2. January 1, 2009 Cash (price determined above)... 70,823,680 Discount on bonds (difference)... 9,176,320 Bonds payable (face amount)... 80,000,000 3. June 30, 2009 Interest expense (6% x $70,823,680)... 4,249,421 Discount on bonds payable (difference)... 249,421 Cash (5% x $80,000,000)... 4,000,000 Partial amortization schedule (not required) Cash Effective Increase in Outstanding Interest Interest Balance Balance 5% x Face Amount 6% x Outstanding Balance Discount Reduction 70,823,680 1 4,000,000.06(70,823,680) = 4,249,421 249,421 71,073,101 2 4,000,000.06(71,073,101) = 4,264,386 264,386 71,337,487 4. December 31, 2009 Interest expense (6% x [$70,823,680 + 249,421])... 4,264,386 Discount on bonds payable (difference)... 264,386 Cash (5% x $80,000,000)... 4,000,000
Exercise 14-4 1. January 1, 2009 Interest $4,000,000 x 11.46992 * = $45,879,680 Principal $80,000,000 x 0.31180 ** = 24,944,000 Present value (price) of the bonds $70,823,680 5% x $80,000,000 * present value of an ordinary annuity of $1: n=20, i=6% (Table 4) ** present value of $1: n=20, i=6% (Table 2) Bond investment (face amount)... 80,000,000 Discount on bond investment (difference)... 9,176,320 Cash (price determined above)... 70,823,680 2. June 30, 2009 Cash (5% x $80,000,000)... 4,000,000 Discount on bond investment (difference)... 249,421 Interest revenue (6% x $70,823,680)... 4,249,421 3. December 31, 2009 Cash (5% x $80,000,000)... 4,000,000 Discount on bond investment (difference)... 264,386 Interest revenue (6% x [$70,823,680 + 249,421])... 4,264,386
Exercise 14-10 1. Price of the bonds at January 1, 2009 Interest $22,500 x 6.46321 * = $145,422 Principal $500,000 x 0.67684 ** = 338,420 Present value (price) of the bonds $483,842 4.5% x $500,000 * present value of an ordinary annuity of $1: n=8, i=5% (Table 4) ** present value of $1: n=8, i=5% (Table 2) 2. January 1, 2009 Cash (price determined above)... 483,842 Discount on bonds payable (difference)... 16,158 Bonds payable (face amount)... 500,000 3. Amortization schedule Cash Effective Increase in Outstanding Interest Interest Balance Balance 4.5% x Face Amount 5% x Outstanding Balance Discount Reduction 483,842 1 22,500.05 (483,842) = 24,192 1,692 485,534 2 22,500.05 (485,534) = 24,277 1,777 487,311 3 22,500.05 (487,311) = 24,366 1,866 489,177 4 22,500.05 (489,177) = 24,459 1,959 491,136 5 22,500.05 (491,136) = 24,557 2,057 493,193 6 22,500.05 (493,193) = 24,660 2,160 495,353 7 22,500.05 (495,353) = 24,768 2,268 497,621 8 22,500.05 (497,621) = 24,879* 2,379 500,000 * rounded. 180,000 196,158 16,158
Exercise 14-10 (concluded) 4. June 30, 2009 Interest expense (5% x $483,842)... 24,192 Discount on bonds payable (difference)... 1,692 Cash (4.5% x $500,000)... 22,500 5. December 31, 2012 Interest expense (5% x $497,621)... 24,879* Discount on bonds payable (difference)... 2,379 Cash (4.5% x $500,000)... 22,500 * rounded value from amortization schedule Bonds payable... 500,000 Cash... 500,000
Exercise 14-14 Requirement 1 At January 1, 2009, the book value of the bonds was the initial issue price, $739,814,813. The liability, though, was increased when Federal recorded interest during 2009: June 30, 2009 Interest expense (6% x $739,814,813)... 44,388,889 Discount on bonds payable (difference)... 388,889 Cash (5.5% x $800,000,000)... 44,000,000 December 31, 2009 Interest expense (6% x [$739,814,813 + 388,889])... 44,412,222 Discount on bonds payable (difference)... 412,222 Cash (5.5% x $800,000,000)... 44,000,000 Reducing the discount increases the book value of the bonds: Jan.1, 2009, book value $739,814,813 Increase from discount amortization ($388,889 + 412,222) 801,111 December 31, 2009, book value (amortized initial amount) $740,615,924 Comparing the amortized initial amount at December 31, 2009, with the fair value on that date provides the Fair value adjustment balance needed: December 31, 2009, book value (amortized initial amount) $740,615,924 December 31, 2009, fair value 730,000,000 Fair value adjustment balance needed: debit/(credit) $ 10,615,924 Federal would record the $10,615,924 as a gain in the 2009 income statement: December 31, 2009 Fair value adjustment 10,615,924 Unrealized holding gain 10,615,924 Note: A decrease in the value of an asset is a loss; a decrease in the value of a liability is a gain.
Exercise 14-14 (continued) In the balance sheet, the bonds are reported among long-term liabilities at their $730,000,000 fair value: Bonds payable $800,000,000 Less: Discount on bonds payable (59,384,076) December 31, 2009, book value (amortized initial amount) $740,615,924 Less: Fair value adjustment (10,615,924) December 31, 2009, fair value $730,000,000 Requirement 2 If the fair value at December 31, 2010, is $736,000,000 a year later, Federal needs to compare that amount with the amortized initial measurement on that date. That amount was increased when Federal recorded interest during 2010: June 30, 2010 Interest expense (6% x [$739,814,813 + 388,889 + 412,222]) 44,436,955 Discount on bonds payable (difference)... 436,955 Cash (5.5% x $800,000,000)... 44,000,000 December 31, 2010 Interest expense (6% x [$739,814,813 + 388,889 + 412,222 + 436,955]) 44,463,173 Discount on bonds payable (difference)... 463,173 Cash (5.5% x $800,000,000)... 44,000,000 Reducing the discount increases the book value of the bonds: December 31, 2009, book value (amortized initial amount) $740,615,924 Increase from discount amortization ($436,955 + 463,173) 900,128 December 31, 2010, book value (amortized initial amount) $741,516,052
Exercise 14-14 (concluded) Comparing the amortized initial amount at December 31, 2010, with the fair value on that date provides the Fair value adjustment balance needed: December 31, 2010, book value (amortized initial amount) $741,516,052 December 31, 2010, fair value (736,000,000) Fair value adjustment balance needed: debit/(credit) $ 5,516,052 Less: Current fair value adjustment debit/(credit) 10,615,924 Change in fair value adjustment $ (5,099,872) Federal records the $5,099,872 as a loss in the 2010 income statement: December 31, 2010 Unrealized holding loss 5,099,872 Fair value adjustment 5,099,872 Note: An increase in the value of an asset is a gain; an increase in the value of a liability is a loss. In the balance sheet, the bonds are reported among long-term liabilities at their $736,000,000 fair value: Bonds payable $800,000,000 Less: Discount on bonds payable (58,483,948) December 31, 2010, book value (amortized initial amount) $741,516,052 Less: Fair value adjustment (5,516,052) December 31, 2010, fair value $736,000,000
Exercise 14-18 1. January 1, 2009 Operational assets... 4,000,000 Notes payable... 4,000,000 2. Amortization schedule $4,000,000 3.16987 = $1,261,881 amount (from Table 4) installment of loan n=4, i=10% payment Cash Effective Decrease in Outstanding Dec.31 Payment Interest Balance Balance 10% x Outstanding Balance Balance Reduction 2009 1,261,881.10 (4,000,000) = 400,000 861,881 3,138,119 2010 1,261,881.10 (3,138,119) = 313,812 948,069 2,190,050 2011 1,261,881.10 (2,190,050) = 219,005 1,042,876 1,147,174 2012 1,261,881.10 (1,147,174) = 114,707* 1,147,174 0 * rounded. 5,047,524 1,047,524 4,000,000 3. December 31, 2009 Interest expense (10% x outstanding balance)... 400,000 Note payable (difference)... 861,881 Cash (payment determined above)... 1,261,881 4. December 31, 2011 Interest expense (10% x outstanding balance)... 219,005 Note payable (difference)... 1,042,876 Cash (payment determined above)... 1,261,881
Exercise 14-19 1. November 1, 2009 Component inventory... 24,000,000 Notes payable... 24,000,000 2. November 30, 2009 Interest expense (1% x outstanding balance)... 240,000 Note payable (difference)... 1,892,370 Cash (payment determined below)... 2,132,370 Calculation of installment payment: $24,000,000 11.25508 = $2,132,370 amount (from Table 4) installment of loan n=12, i=1% payment 3. December 31, 2009 November (1% x $24,000,000) $240,000 December (1% x [$24,000,000 1,892,370]) 221,076 2009 interest expense $461,076 Journal entry (not required): Interest expense (1% x [$24,000,000 1,892,370])... 221,076 Note payable (difference)... 1,911,294 Cash (payment determined above)... 2,132,370 The McGraw-Hill Companies, Inc., 2009 Solutions Manual, Vol.2, Chapter 14 14-39