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Chapter 6 - ~ftS TO PRACTICE QUESTIONS is bond is 30...

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~ftS TO PRACTICE QUESTIONS - is bond is 30 payments of $3 plus a maturity value of $100 thirty 6-month periods from now. e of the cash flow when discounted at one-half the yields of 7.2%, 7.6%, and 7.8%. The ~ in Chapter 5 was used so the information is provided for the present value of the coupon .•••••,•• ::r.saltyalue of the maturity value. Annual rate (BEY) 7.2% 7.6% 7.8% Semiannual rate 3.6% 3.8% 3.9% Present value of: Coupon payments 54.49 53.16 52.51 Maturity value 34.61 32.66 31.74 Total present value 89.10 85.82 84.25 -' __ IICt: ~-- ount rate of 3.9% equates the present value of the cash flows to the price of $84.25, 3.9% - maturity. Doubling this yield gives a yield to maturity of 7.8% on a bond equivalent basis . •• __ •. ~oeuars from an investment of $89.32 ifthe yield is 7% is:
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Total future dollars Return of principal Total dollar return $353.64 $ 89.32 $264.32 214 Yield Measures, Spot Rates, and Forward Rates $89.32 X (1.035)40 = $353.64 Decomposing the total future dollars we see that: Without reinvestment income, the dollar return is: Coupon interest Capital gain Dollar return $120.00 $ 10.68 $130.68 The dollar return shortfall is therefore $133.64 ($264.32 - $130.68). This shortfall is made up if the coupon pay- ments can be reinvested at a yield of7% (the yield on the bond at the time of purchase). For this bond, the reinve - ment income is 51% of the total dollar return needed to produce a yield of 7% ($133.64/$264.32).
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