Question

The YTM on a bond is the interest rate you 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).

a.	Suppose that today you buy a bond with an annual coupon of 7 percent for $1,020. The bond has 16 years to maturity. What rate of return do you expect to earn on your investment? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

b-1.	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 answer to 2 decimal places, e.g., 32.16.)

b-2.	What is the HPY on your investment? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

	a. Expected rate of return % b-1. Bond price b-2. HPY

Answer 1

a) YTM = (Coupon + ((F - P)/n)) / ((F + P)/2)

Here,

F (Face value) = $1,000 (assumed)

P (Price) = $1,020

Coupon = Face value * Rate

Coupon = $1,000 * 7% = $70

n (years) = 16 years

Now,

YTM = ($70 + (($1000 - $1020)/16)) / (($1,000 + $1,020)/2)

YTM = ($70 - $1.25) / $1,010

YTM = $68.75 / $1,010

YTM (rate of return) = 0.0681 or 6.81%

b) 1)After 2 years, YTM declines by 1%

So, new YTM @ 5.81% (6.81% - 1%)

n (years remaining) = 14 years (16 - 2 years)

i = 0.0581 or 5.81%

Coupon = $70

Price = Coupon * ((1 - (1/(1+i)^n)) / i) + Face value * (1/(1+i)^n)

Price = $70 * ((1 - (1/(1+0.0581)^14)) / 0.0581) + $1,000 * (1 / (1+0.0581)^14)

Price = $70 * ((1 - 0.4536)/0.0581) + ($1,000 * 0.4536)

Price = ($70 * 9.4045) + $453.60

Price (sale) = $1,111.92

b) 2)HPY = (Income + End value - Start value) / Start value

Here,

Income (Dividend for 2 year) = $70 *2 years = $140

End value = $1,111.92

Start value = $1,020

Now,

HPY = ($140 + $1,111.92 - $1,020) / $1,020

HPY = $231.92 / $1,020

HPY = 0.2274 or 22.74%