# 1000 x 1200611 future value 12006 pen dix 7 b

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\$1,000 x 12.00611 Future Value \$12,006 PEN DIX 7 B: Economics of Gains and Losses on Bond Repurchases reported gain or loss on bond repurchases before maturity of economic substance? The short answer is no. To e, assume that on January 1, a company issues \$50 million face value bonds with an 8% annual coupon The interest is to be paid semiannually (4% each semiannual period) for a term of five years (10 semiannual ), at which time the principal will be repaid. If investors demand a 10% annual return (5% semiannually) on - investment, the bond price is computed as follows: Present value of semiannual interest (\$2,000,000 x 7.72173) Present value of principal (\$50,000,000 x 0.61391) Present value of bond \$15,443,460 30,695,500 \$46,138,960 bond's amortization table follows: ----- - EXHIBIT 7B.1 Bond Discount Amortization Table [A] [B] [C] [0] [E] ([EJ x market%) (Face x coupon%) ({AJ - [BJ) (Prior bat - (CJ) (Face - [OJ) Interest Cash Discount. Discount Bond'T Period Expense Interest Paid Amortization Balance Payable, Net 0 \$3,861,040 \$46,138,960 1 \$2,306,948 \$2,000,000 \$306,948 3,554,092 46,445,908 2 2,322,295 2,000,000 322,295 3,231,797 46,768,203 3 2,338,410 2,000,000 338,410 2,893,387 47,106,613 4 2,355,331 2,000,000 355,331 2,538,056 47,461,944 5 2,373,097 2,000,000 373,097 2,164,959 47,835,041 6 2,391,752 2,000,000 391,752 1,773,207 48,226,793 7 2,411,340 2,000,000 411,340 1,361,867 48,638,133 8 2,431,907 2,000,000 431,907 929,960 49,070,040 9 2,453,502 2,000,000 453,502 476,458 49,523,542 10 2,476,458 2,000,000 476,458 0 50,000,000 ext, assume we are at period 6 (three years after issuance) and the market rate of interest for this bond has from 10% to 12%. The firm decides to retire (redeem) the outstanding bond issue and finances the retirement _ issuing new bonds. That is, it issues bonds with a face amount equal to the market value of the old bonds and the proceeds to retire the existing (old) bonds. The new bond issue will have a term of two years (four semian- periods), the remaining life of the existing bond issue. Calculator N=5 IIYr = 8 PMT = 2,000 PV= ° I FV = 11,733 I Calculator N = 10 IIYr = 4 PMT = 1,000 PV = 0 Calculator N = 10 IIYr = 5 PMT = 2,000,000 FV = 50,000,000 [Pv~46,138,132-1 'rounding difference

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7-33 Module 7 I Liability Recognition and Nonowner Financing Calculator N=4 IIYr = 6 PMT = 2,000,000 FV = 50,000,000 l~Yo=~,~~~,~~~*] *rounding difference At the end of the third year, there are four \$2,000,000 semiannual interest payments remaining on the bonds, plus the repayment of the face amount of the bond due at the end of the fourth semiannual period. The pres-- ent value of this cash flow stream, discounted at the current 12% annual rate (6% semiannual rate) is: Present value of semiannual interest (\$2,000,000 x 3.46511) Present value of principal (\$50,000,000 x 0.79209) Present value of bond \$ 6,930,220 39,604,500 \$46,534,720 This means the company pays \$46,534,720 to redeem a bond that is on its books at a carrying amount of \$48 ,226 ,793 The difference of \$1 ,692,073 is reported as a gain on repurchase (also called redemption). GAAP requires this gaia be reported in income from continuing operations unless it meets the tests for treatment as an extraordinary ite (the item is both unusual and infrequent). Although the company reports a gain in its income statement, has it actually realized an economic gain? C~ sider that this company issues new bonds that carry a coupon rate of 12% (6% semiannually) for \$46,534,720. If we assume that those bonds are sold with a coupon rate equal to the market rate, they will sell at par (no disco or premium). The interest expense per six-month period, therefore, equals the interest paid in cash, or \$2,792,0~ (\$46,534,720 X 6%). Total expense for the four-period life of the bond is \$11,168,333 (\$2,792,083 X 4). Tb2: amount, plus the \$46,534,720
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