The YTM on a bond is the interest rate you earn on your investment if interest r
ID: 2750653 • Letter: T
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).
Suppose that today you buy a bond with an annual coupon of 12 percent for $1,140. The bond has 19 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))
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))
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).
Explanation / Answer
a). Current Price = $1140
Annual Coupon = 12% * 1000 = $120
Maturity = 19 years
As per the bond pricing formula,
1140 = 120/(1 + YTM)1 + 120/(1 + YTM)2 + 120/(1 + YTM)3 + _ _ _ + 120/(1 + YTM)18 + 1120/(1 + YTM)19
where YTM is yield to matruity or expected rate of return. It can be found out using the RATE function of excel. The syntax for the same is: =RATE(19,120,-1140,1000)
The value comes out to be 10.2937%
Thus, expected rate of return = 10.29% (after rounding off)
b1) After 2 years,
YTM = 9.2937%
Maturity = 17 years
Annual Coupon = $120
Price of the bond
= 120/(1 + 9.2937%)1 + 120/(1 + 9.2937%)2 + _ _ _ + 120/(1 + 9.2937%)16 + 1120/(1 + 9.2937%)17
This can be found out using the PV function of excel. The syntax for the same is: =PV(9.2937%,17,120,1000).
The value comes out to be $1226.9212.
Price of the bond = $1226.92 (after rounding off)
b2) The bond is sold for $1226.92 after 2 years.
Purchase price = $1140
We have to calulate the Holding Period Yield.
1140 = 120/(1 + HPY)1 + (120 + 1226.9212)/(1 + HPY)2
where HPY is tthe holding period yield. It can be found out using the RATE function of excel. The syntax for the same is: =RATE(2,120,-1140,1226.9212)
The value comes out to be 14.0877%.
Thus, Holding Period Yield = 14.09% (after rounding off)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.