# Con ie computations are avoided by using annuity

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nt value (with 1cent rounding error) is derived by summing the three separate multipliers from Table 1.Con- Ie computations are avoided by using annuity tables. d Valuation that a bond agreement specifies a pattern of future cash flows-usually a series of interest payments and a _ e payment of the face amount at maturity, and bonds are priced using the prevailing market rate on the day the i sold. This is the case for the original bond issuance and for subsequent open-market sales. The market rate e date of the sale is the rate we use to determine the bond's market value (its price). That rate is the bond's o The selling price of a bond is determined as follows: Use Table) to compute the present value of the future principal payment at the prevailing market rate. Use Table 2 to compute the present value of the future series of interest payments (the annuity) at the prevailing market rate. Add the present values from steps 1 and 2. ~ ~ -~- ~ ~ EXHIBIT 7A.1 Calculation of Bond Price Using Present Value Tables Multiplier (Table 1) Multiplier (Table 2) Future Cash Flows Present Values at 4% Semiannually (1) \$100,000 of 8%, 4-year bonds with interest payable semiannually priced to yield 8%. Principal payment, \$100,000 (a single amount received after 8 semiannual periods). . . . . . . . . . . . . . . . .. 0.73069 Interest payments, \$4,000 at end of each of 8 semiannual periods. . . . . . . . . . 6.73274 Present value (issue price) of bonds . \$ 73,069 26,931 \$100,000 Calculator N=8 l/Yr = 4 PMT = 4,000 FV = 100,000 = 100,000 Future Cash Flows Multiplie (Table 1) (2) \$100,000 of 8%, 4-year bonds with interest payable semiannually priced to yield 10%. Principal payment, \$100,000 (a single amount received after 8 semiannual periods). . . . . . . . . . . . . . . . .. 0.67684 Interest payments, \$4,000 at end of each of 8 semiannual periods 0 6.46321 Present value (issue price) of bonds . \$ 67,684 25,853 \$ 93,537 Calculator N=8 IlYr = 5 PMT = 4,000 FV = 100,000 I PV = 93,536.79 Multiplier (Table 1) Multiplier (Table 2) Future Cash Flows Present Values at 3% Semiannually (3) \$100,000 of 8%, 4-year bonds with interest payable semiannually priced to yield 6%. Principal repayment, \$100,000 (a single amount received after 8 semiannual periods). . . . . . . . . . . . . . . . .. 0.78941 Interest payments, \$4,000 at end of each of 8 semiannual periods 0 7.01969 Present value (issue price) of bonds . \$ 78,941 28,079 \$107,020 Calculator N=8 IlYr = 3 PMT = 4,000 FV = 100,000 PV = 107,019.69

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We illustrate in Exhibit 7A.l the price of \$100,000,8%, four-year bonds paying interest semiannually and so. when the prevailing market rate was (1) 8%, (2) 10% or (3) 6%. Note that the price of 8% bonds sold to yield 8%- the face (or par) value of the bonds. A bond issue price of \$93,537 (discount bond) yields 10%. A bond issue pri of \$107,020 (premium bond) yields 6%. 7-31 Module 7 I Liability Recognition and Nonowner Financing Calculator N=5 l/Yr = 6 PMT = 0 PV = 6,000 I FV = 8, 029 1 Calculator N = 10 l/Yr = 3 PMT= 0 PV = 6,000 I FV = 8, 064 1 Time Value of Money Computations Using a Calculator We can use a financial calculator for time value of money computations. There are five important function keys these calculations. If we know values for four of those five, the calculator will compute the fifth. Those functi keys are: N Number of compounding (or discounting) periods IlYr Interest (yield) rate per period-entered in % terms, for example, 12% is entered as 12 and not as 0.12.
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