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

Question

The YTM on a bond is the interest rate you earn on your investment if interest rates don't change tf you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY). Suppose that today you buy a bond with an annual coupon of 8 percent for $1,100 The bond has 15 years to maturity What rate of return do you expect to earn on your investment? (Do not round intermediate calculations and round your final answer to 2 decimal places, (e.g., 32.16))Expected rate of return 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? (Do not round intermediate calculations and round your final answer to 2 decimal places, (e.g., 32.16)) Bond price $ What is the HPY on your investment? (Do not round intermediate calculations and round your final answer to 2 decimal places, (e.g., 32.16))

Explanation / Answer

Yield-to-Maturity Approximation Formula for Bonds

Approximate Yield-to-Maturity Percentage

=

Annual Interest Payment + (Par Value - Bond Price)/Number of Years until Maturity

(Par Value + Bond Price)/2

Annual Interest= 80

Bond price =1100

Years to maturity =15

Par value=1000

YTM= [80+(1000-1100)/15 ]/(1100+1000)/2

= 73.34/1050

=6.98%

So expected return on bond is 6.98%

B1. After 2 years , YTM= 5.98%

Years to maturity = 13

Let bond price is b,

So , 0.0598= [80+(1000-b)/13]/(1000+b)/2

Or, 0.0598=2[(1040+1000-b)/13]/(1000+b)

Or, 59.8+0.0598b= (2080+2000-2b)/13

Or, 777.40+0.7774b=2080+2000-2b

Or, 2.7774b=3302.60

Or, b=1189.10

So bond price will be $1189.10

B2. Holding period yield =( Interest +capital gain)/Investment

= (80*2 + 1189.10-1100)/1100

=(160+89.10)/1100

=22.64%

HPY in two years is 22.64%

Yield-to-Maturity Approximation Formula for Bonds

Approximate Yield-to-Maturity Percentage

=

Annual Interest Payment + (Par Value - Bond Price)/Number of Years until Maturity

(Par Value + Bond Price)/2

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