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 rate of 8 percent for $1,170. The bond has 16 years to maturity. What rate of return do you expect to earn on your investment? Assume a par value of $1,000. (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.)

Answer 1

Assuming a par value of $ 1,000.

The price a which the bond is purchased is $1,170. Clearly it sells at a premium to the bond(price>par value). This suggests that the coupon rate is much higher thanthe YTM.

The coupon is paid annually and the bond horizon is 16 years.

The YTM calculation resembles the following equation,

The coupon rate is 8% so 8% of 1000 = $ 80 is the annual coupon

The LHS of equation is 1170$, the denominators are unknown, i.e YTM and the numerators are 80,80,....1080 .

This can be calculated using a financial calculator or Excel.

BA 2 Plus financial calcuator,

N=16

PMT=80

FV=1080

PV =-1170

CPT I/Y = 6.28% is the YTM

b-1) Two years from now, the YTM has declined by 1%, 100 bps so the new YTM is 5.28%

I decide to sell after two years, I should sell at a price equal to the present value of all the future cash flows till maturity discounted at the new YTM of 5.28%. The price of the bond is expected to rise due to the inverse relationship between the YTM and price of the bond.

So, Price to sell =  

N=14

FV=1080

PMT=80

I/Y = 5.28

CPT PV =$ 1264.48

b-2)If you actually sell the bond before it matures, your realized return is known as the holding period yield

So I buy the bond at $ 1170 and sell it at $1264.48 after two years. My holding period yield(HPY) of the investment is

P0 =1170

P1=1264.48

D1 = Year 1 and Year 2 interest = 80+80 = 160

So HPY =