You are planning to retire in 23 years and would like to invest all your current

Question

You are planning to retire in 23 years and would like to invest all your current savings in bonds issued by your state. The bonds have the face value of $5,000, annual coupon rate of 4.2 percent, and maturity of 36 years. The bonds are currently priced to yield 6.7 percent. You expect to be able to reinvest the semiannual coupon payments you will receive over your investment horizon at the annual rate of 5.2 percent. You also expect that the annual yield for comparable bonds at the time you plan to sell your bonds in 23 years (end of your investment horizon) will be 7.2 percent. What is the expected annual realized compound yield of these bonds? (Do not round intermediate calculations and round your final answers to 3 decimal places. (e.g., 32.167))

Explanation / Answer

Answer:

First of all we need current market price of bond, which will present value of all cash flow for 36 years(discounted @ 6.7% yearly/ 3.35% half yearly)

= bond half yearly coupon payments x PVIFA 3.35% for 36 years(72 half yearly payments) + principal amount of bond repayment at the end of 36th year x PVF @ 6.7%

= (105 x 27.067) + (5000 x 0.0968)

= 2842.035 + 484

current market price of bond = $ 3,277.035

so, if we want to invest in this bond, we have to pay $ 3,277.035 at present.

Now we will compute return from this bond investment

Return from bond = (coupon payment x PVIFA @ 5.2% yearly/2.6%) + present value of market price of bond we get at the end of 23rd year discounted @ 5.2% ( market price = PVIFA @ 7.2% xcoupon payment for remaining 13 years period/26 half yearly + (present value of principal repayment x present value factor @ 7.2%, 13 years)

= (105 x 26.6516) + [ 0.3116(105 x 16.7028) + ( $ 5000 x 0.4050)]

= 2798.418 + 1177.47

total return from bond= 3975.888

Annualized yield of bond = (total return from bond/investment cost of bond) x 12 months/(12 months x 23 years)

= (3975.888/3277.035) x 12/276

= 0.05275

= 5.2750% annulized yield

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