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Solution Chapter: Problem: 5 24 A 20-year, 8% semiannual coupon bond with a par value of $1,000 may be called in 5 years at a call price of $1,040. The bond sells for $1,100. (Assume that the bond has just been issued.) Basic Input Data: Years to maturity: Periods per year: Periods to maturity: Coupon rate: Par value: Periodic payment: Current price Call price: Years till callable: Periods till callable: 20 2 40 8% $1,000 $40 $1,100 $1,040 5 10 a. What is the bond's yield to maturity? Peridodic YTM = Annualized Nominal YTM = 3.53% 7.06% Hint: This is a nominal rate, not the effective rate. Nominal rates are gen b. What is the bond's current yield? Current yield = Ann. Coupon Current yield = $80 Current yield = 7.27% / Price $1,100 / Hint: Write formula in words. Hint: Cell formulas should refer to Input Section (Answer) c. What is the bond's capital gain or loss yield? Cap. Gain/loss yield = Cap. Gain/loss yield = Cap. Gain/loss yield = YTM 7.06% -0.21% - Current yield Hint: Write formula in words. 7.27% Hint: Cell formulas should refer to Input Section (Answer) Note that this is an economic loss, not a loss for tax purposes. d. What is the bond's yield to call? Here we can again use the Rate function, but with data related to the call. Peridodic YTC = Annualized Nominal YTC = 3.16% 6.33% This is a nominal rate, not the effective rate. Nominal rates are generally q The YTC is lower than the YTM because if the bond is called, the buyer will lose the difference between the call price and the current price in just 4 years, and that loss will offset much of the interest imcome. Note too that the bond is likely to be called and replaced, hence that the YTC will probably be earned. The YTC is lower than the YTM because if the bond is called, the buyer will lose the difference between the call price and the current price in just 4 years, and that loss will offset much of the interest imcome. Note too that the bond is likely to be called and replaced, hence that the YTC will probably be earned. NOW ANSWER THE FOLLOWING NEW QUESTIONS: e. How would the price of the bond be affected by changing the going market interest rate? (Hint: Conduct a sensitivity analysis of price to changes in the going market interest rate for the bond. Assume that the bond will be called if and only if the going rate of interest falls below the coupon rate. That is an oversimplification, but assume it anyway for purposes of this problem.) Nominal market rate, r: Value of bond if it's not called: Value of bond if it's called: 8% $1,000.00 $1,027.02 The bond would not be called unless r