The YTM on a bond is the interest rate you can earn on your investment if intere

Question

The YTM on a bond is the interest rate you can earn on your investment if interest rates don't change. if you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY ). Suppose that today you buy an 8 percent annual coupon bond for $1,1 50. The bond has 10 years to maturity. What rate of return do you expect to earn on your investment? Two years from now. the YTM on your bond has declined by 1 percent, and you decide to sell. What price will your bond sell for? What is the HPY on your investment? Compare this yield to the YTM when you first bought the bond. Why are they different?

Explanation / Answer

10 years

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Annual Coupon Rate 8% Current Price of the Bond $1,150 Number of Years to Maturity

10 years

Par Value of the Bond $1,000 Yield to Maturity (YTM)

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Calculating YTM: (Using Ms-Excel "RATE"Function): Number of Periods(Nper) 10 Coupon Payment (PMT) [$1,000 * 7.375%] -$80.00 Present Value of the Bond (PV) $1,150 Future Value (or) Par Value of the Bond(FV) -$1,000 Yield to Matuiry (YTM) 5.97% Calculating Bond Value, if theYTM on the bond id decreased by 1% : Bond Value = C *[1-1/(1+r)t]/r    +    F /(1+r)t BondValue = $80 *   [1-1/(1+0.0497)10] / 0.0497   + $1,000 / (1+0.0497)10 BondValue = $80 *   [1-1/(1.0497)10] / 0.0497   + $1,000 /(1.0497)10 BondValue = $80 *   7.732997  + $615.67 BondValue = $618.64 + $615.67 Bond Value =$1,234.31 Note: To calculate theHPY, we need to find the interest rate that equates the pricewe          paid for the bondwith the cash flows we received. The cash flows we received          were $80 each yearfor two years, and the price of the bond when we sold it. Calculating Holding Period Yield(HPY) (Using Ms-Excel "RATE"Function): Number of Periods (Nper) 2 Coupon Payment (PMT) -$80 Present Value of the Bond (PV) $1,150 Future Value of the Bond (FV) -$1,234.31 Holding Period Yield (HPY) 10.44% Note: The realized HPYis greater than the expected YTM when the bond was boughtbecause          Interest ratesdropped by 1 percent' bond prices rise when yield fall.

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