Exercise Maturity Interest paid Stated rate Effective (market) rate 10 years annually 10% 12%
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1 Exercise Maturity Interest paid Stated rate Effective (market) rate 10 years annually 10% 12% Interest $100,000 x * = $565,022 Principal $1,000,000 x ** = 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 * = $573,496 Principal $1,000,000 x ** = 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 * = $ 747,733 Principal $1,000,000 x ** = 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 * = $1,029,545 Principal $1,000,000 x ** = 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)
2 Exercise 14-2 (concluded) 5. Maturity Interest paid Stated rate Effective (market) rate 20 years semiannually 12% 12% Interest $60,000 x * = $902,778 Principal $1,000,000 x ** = 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)
3 Exercise Price of the bonds at January 1, 2009 Interest $4,000,000 x * = $45,879,680 Principal $80,000,000 x ** = 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, June 30, 2009 Interest expense (6% x $70,823,680)... 4,249,421 Discount on bonds payable (difference) ,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, ,000,000.06(70,823,680) = 4,249, ,421 71,073, ,000,000.06(71,073,101) = 4,264, ,386 71,337, December 31, 2009 Interest expense (6% x [$70,823, ,421])... 4,264,386 Discount on bonds payable (difference) ,386 Cash (5% x $80,000,000)... 4,000,000
4 Exercise January 1, 2009 Interest $4,000,000 x * = $45,879,680 Principal $80,000,000 x ** = 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, June 30, 2009 Cash (5% x $80,000,000)... 4,000,000 Discount on bond investment (difference) ,421 Interest revenue (6% x $70,823,680)... 4,249, December 31, 2009 Cash (5% x $80,000,000)... 4,000,000 Discount on bond investment (difference) ,386 Interest revenue (6% x [$70,823, ,421])... 4,264,386
5 Exercise Price of the bonds at January 1, 2009 Interest $22,500 x * = $145,422 Principal $500,000 x ** = 338,420 Present value (price) of the bonds $483, % 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) ,842 Discount on bonds payable (difference)... 16,158 Bonds payable (face amount) , Amortization schedule Cash Effective Increase in Outstanding Interest Interest Balance Balance 4.5% x Face Amount 5% x Outstanding Balance Discount Reduction 483, , (483,842) = 24,192 1, , , (485,534) = 24,277 1, , , (487,311) = 24,366 1, , , (489,177) = 24,459 1, , , (491,136) = 24,557 2, , , (493,193) = 24,660 2, , , (495,353) = 24,768 2, , , (497,621) = 24,879* 2, ,000 * rounded. 180, ,158 16,158
6 Exercise (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, 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 ,000 Cash ,000
7 Exercise 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) ,889 Cash (5.5% x $800,000,000)... 44,000,000 December 31, 2009 Interest expense (6% x [$739,814, ,889])... 44,412,222 Discount on bonds payable (difference) ,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, ,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.
8 Exercise (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, , ,222]) 44,436,955 Discount on bonds payable (difference) ,955 Cash (5.5% x $800,000,000)... 44,000,000 December 31, 2010 Interest expense (6% x [$739,814, , , ,955]) 44,463,173 Discount on bonds payable (difference) ,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, ,173) 900,128 December 31, 2010, book value (amortized initial amount) $741,516,052
9 Exercise (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
10 Exercise January 1, 2009 Operational assets... 4,000,000 Notes payable... 4,000, Amortization schedule $4,000, = $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 ,261, (4,000,000) = 400, ,881 3,138, ,261, (3,138,119) = 313, ,069 2,190, ,261, (2,190,050) = 219,005 1,042,876 1,147, ,261, (1,147,174) = 114,707* 1,147,174 0 * rounded. 5,047,524 1,047,524 4,000, December 31, 2009 Interest expense (10% x outstanding balance) ,000 Note payable (difference) ,881 Cash (payment determined above)... 1,261, December 31, 2011 Interest expense (10% x outstanding balance) ,005 Note payable (difference)... 1,042,876 Cash (payment determined above)... 1,261,881
11 Exercise November 1, 2009 Component inventory... 24,000,000 Notes payable... 24,000, November 30, 2009 Interest expense (1% x outstanding balance) ,000 Note payable (difference)... 1,892,370 Cash (payment determined below)... 2,132,370 Calculation of installment payment: $24,000, = $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, interest expense $461,076 Journal entry (not required): Interest expense (1% x [$24,000,000 1,892,370]) ,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
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