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# bond - INTEREST RATE PROBLEM SET YIELD FORMULAS There are a...

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INTEREST RATE PROBLEM SET YIELD FORMULAS : There are a number of different ways of calculating different yields. A few of these formulas are shown below. 1. Current yield of a bond : annual coupon interest in dollars = C Current yield = Current Price P 2. Yield to maturity of a bond (r) : a. Approximation formula: Par Value - Current Price coupon interest + n___________ Current Price + Par Value 2 where n is the number of years to maturity and PV = par value b. Exact formula: C 1 + C 2 + . . . . + C n + PV Price= (l + r) (l + r) 2 (l + r) n Solve for r by trial and error. 3. Treasury bill yields : a. Discount yield (d): d= 360 100 - Price n 100 where n is number of days to maturity; price is expressed in dollars per \$100 of par value or face amount. b. Equivalent bond or coupon yield (i): I = 365 100 - Price n Price 4. Yield compounding : a. Realized yield = (l + r/m) m - 1 where r = stated interest rate per year, m = number of times interest is compounded per year. b. For continuous compounding: Realized yield = e r - 1

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5. Stock : a. Constant Growth Model P o = D 1 K e - g b. General Dividend Model P o = Σ D t t=1 (1 + K) t m c. 2 Period Growth Model D o (1 + g 1 ) t + I 1 D m+1 I t = 1 (1 + K e ) t (1 + K e ) m K e - g 2
ASSIGNMENT: INTEREST RATES This assignment explores several aspects of interest rates including (1) yield calculations, (2) yield differentials, and (3) the term structure of yields. Show all calculations. 1. Find, in the (Date to be Announced), Wall Street Journal , the close price for the American Telephone and Telegraph (ATT) bond listed as the "ATT 7 3/4 07." The prices can be found in the "US Bonds" section of the paper. Assume that the bond matures in exactly 5 years. a. What is the dollar amount of interest paid on this bond each year? b. What is the bond's current yield? c. What is the yield to maturity of the bond using the short cut formula? d. What is the yield to maturity using the exact formula, assuming interest is paid once a year?

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