# Principal payment at maturity 10000000 x 3 300000

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Principal payment at maturity . \$10,000,000 x 3% = \$300,000 \$10,000,000 \$ 6,000,U 10,000,00:: \$16,000, 10 years x 2 = 20 1 Specifically, the bond agreement dictates that the borrower must make 20 semiannual paymen of \$300,000 each, computed as \$10,000,000 X (6%/2). At maturity, the borrower must repay \$10,000,000 face amount. To price bonds, investors identify the number of interest payments use that number when computing the present value of both the interest payments and the princi (face) payment at maturity. The bond price is the present value of the periodic interest payments (the annuity) plus the pres- ent value of the principal payment (the lump sum). In our example, assuming that investors desire 3% semiannual market rate (yield), the bond sells for \$10,000,000, which is computed as follow Present value of a single payment in 20 periods discounted at 3% per period. d Rounded. Because the bond contract pays investors a 3% semiannual rate when investors demand a .3 semiannual market rate, given the borrower's credit rating and the time to maturity, the inve purchase those bonds at the par (face) value of \$10 million. DiscountBonds As a second illustration, assume investors demand a 4% semiannual return for the 3% semiza- nual coupon bond, while all other details remain the same. The bond now sells for \$8,640, computed as follows: Payment Present Value Factor Present Value Interest. . . . . . . . . . . . . . . . . \$ 300,000 Principal. . . . . . .. . . . . . . .. \$10,000,000 13.59033" 0.45639 b \$4,077,099 4,563,900 \$8,640,999 a Present value of an ordinary annuity for 20 periods discounted at 4% per period. b Present value of a single payment in 20 periods discounted at 4% per period. Because the bond carries a coupon rate lower than what investors demand, the bond is less dI able and sells at a discount. More generally, bonds sell at a discount whenever the coupon is less than the market rate.

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Module 7 I Liability Recognition and Nonowner Financing 7-14 ium Bonds third illustration, assume that investors demand a 2% semiannual return for the 3% sernian- coupon bonds, while all other details remain the same. The bond now sells for \$11,635,129, ed as follows: . Payment Present Value Factor Present Value I erest . . . . . . . . . . . . . . . . . \$ 300,000 :JOncipal . . . . . . . . . . . . . . .. \$10,000,000 16.35143 a 0.67297 b \$ 4,905,429 6,729,700 \$11,635,129 •.:>resentvalueof an ordinaryannuityfor 20 periods discounted at 2% per period. '" :>resentvalueofa singlepayment in 20 periods discounted at 2% per period. e the bond carries a coupon rate higher than what investors demand, the bond is more Ie and sells at a premium. More generally, bonds sell at a premium whenever the coupon -- greater than the market rate.' Exhibit 7.1 summarizes this relation for bond pricing. ! EXHIBIT 7.1 Coupon Rate, Market Rate, and Bond Pricing Coupon rate > market rate Coupon rate = market rate Coupon rate < market rate -7 Bond sells at a premium (above face amount) -7 Bond sells at par (at face amount) -7 Bond sells at a discount (below face amount) Exhibit 7.2 shows an announcement (called a tombstone) of a Union Pacific Corp \$500 debt issuance. It has a 4% coupon rate paying 2% semiannual interest, maturing in 2021, an issue price of 99.525 (sold at a discount). Union Pacific Corp's underwriters took 0.65% (\$3.25 million) for underwriting and selling this debt issue." tive Cost of Debt a bond sells for par, the cost to the issuing company is the cash interest paid. In our first
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