A 10-year U.S. Treasury bond with a par value of $1000 is currently for $1015 from various security dealers. The bond carries a 7.5-percent coupon rate with payments made annually. If purchased today and held to maturity, what is its expected yield to maturity?

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Accepted Answer

(Hint - the following relationships can help in solving for the yield:

If price < par value, then yield > coupon rate;

If price = par value, then yield = coupon rate;

If price > par value, then yield < coupon rate.)

Since the bond is selling at a premium, that is, price > par value, the yield will be less than the coupon rate, or a yield < 7.5%.

The relevant formula is:

[latex]\$ 1015=\frac{\$ 75}{(1+ YTM )^{1}}+\frac{\$ 75}{(1+ YTM )^{2}}+\ldots+\frac{\$ 75}{(1+ YTM )^{10}}+\frac{\$ 1000}{(1+ YTM )^{10}}[/latex]

YTM = 7.29% (using a financial calculator)

Question 10.P.1: A 10-year U.S. Treasury bond with a par value of $1000 is cu...

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