2. You just bought a newly issued bond which has a face value of $1,000 and pays
ID: 2808769 • Letter: 2
Question
2. You just bought a newly issued bond which has a face value of $1,000 and pays its coupon once annually. Its coupon rate is 6%, maturity is 20 years and the yield to maturity for the bond is currently 8%. a. Do you expect the bond price to change in the future when the yield stays at 890? Why or why not? Explain. (No calculation is necessary.) (2 marks) b. Calculate what the bond price would be in one year if its yield to maturity stays at 8%. (2 marks) c. Find the before-tax holding-period return for a one- year investment period if the bond sells at a yield to maturity of 7% by the end of the year (year 1 ) a marks) d. When the ordinary income tax rate is higher than the capital gains tax rate, tax authorities typically tax anticipated price appreciations from bonds at the ordinary income rate in order to prevent tax aversion with discount bonds. Suppose that from t total dollar return in part c), the coupon payment and the difference between the hypothetical prices in part b) and the purchase price are taxed at the ordinary income tax rate, 40%. The rest of the dollar return is considered capital gains (due to unanticipated change in yield-to-maturity from 8% to 790) taxed at 30%. In other words, coupon payments and the anticipated price apprecia taxed at the ordinary income tax rate and the rest at the lower capital gains rate. Using your answers in part b) and c), calculate the after-tax holding period return over one year if the yield to maturity is 7% at the end of the year he tion are (5 marks)Explanation / Answer
(a) Yes I expected the future bond prices to change becuase the number of year to maturity changes and as the bond nears its maturity it moves towards its face value
(b) Bond price in 1 year at 8% = PV(rate,nper,pmt,fv) =PV(0.08,19,60,1000) = 807.93
(c) When the yield decrease to 7%, bond Price = PV(rate,nper,pmt,fv) = PV(0.07,19,60,1000) = $896.64
Purchase price =PV(0.08,20,60,1000) = 803.64
before tax holding period return = 896.64-803.64 + 60 = 153.01
Holding period return (%) = 153.01/803.64 = 0.1904 = 19.04%
(d) Taxed at 40% = 60 + 807.93-803.64 = 64.29.
After tax return = 64.29*(1-0.4) = 38.57
Capital gain taxed at 30% = 153.01 -64.29 = 88.72
After tax return = 88.72*(1-0.3) = 62.10
Total after tax return = 100.68
After tax holding periodreturn = 100.68/803.64 = 12.53%
(e) Price after two year = PV(0.07,18,60,1000) = 899.41
Total return = 899.41-803.64 +60*1.03 +60 = 217.57
Holding period return = 217.57/803.64 =0.270734
Annualized return = (1+0.270734)^(1/2)-1 = 0.1273 = 12.73%
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