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 12 percent for $1,070. The bond has 12 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.)

a.Expected rate of return%?

b-1.Bond price?

b-2.HPY%?

Answer 1

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Ans to a

$

Ans to b

$

Face value (par value)

1,000.00

A

Here it is given Ytm is down by 1% so we first calculate current YTM

Holding period of return

Purchase price

1,070.00

B

YTM=

(C+((F-P)/n))/((F+P)/2)

HPY=

Income + (End of Period Value – Initial Value) / Initial Value

Coupon rate

12%

C

C=

Coupon amount

120.00

C

120.00

Income=

Coupon amount for 2 years

240

M

120*2

Coupon amount

120.00

D= A*C

F=

Face value (par value)

1,000.00

A

(5.83)

114.17

Initial value=

Purchase price

1,070.00

N

Expected return %

11.21%

E=D/B

P=

Purchase price

1,070.00

B

1,035.00

0.110306

End of Period Value=

Sale price

1,035.81

O

n=

Years of maturity

12

F

HPY=

19.23%

P=(M+O-N)/N

F-P=

(70.00)

G=A-B

(F-P)/n=

(5.83)

H=G/F

F+P=

2,070.00

I=A+B

(F+P)/2=

1,035.00

J=I/2

YTM=

11.03%

K=(H+C)/J

YTM after 2 years will be 1 % less that is 10.03%

If we will use same formula as above we can calculate the sale price of bond after 2 years

YTM=

(C+((F-P)/n))/((F+P)/2)

C=

Coupon amount

120

C

F=

Face value (par value)

1000

A

P=

Purchase price

To find

L

n=

Years bond held

2

M

As bond was held for 2 years

F-P=

1000-L

(F-P)/n=

(1000-L)/2

F+P=

1000+L

(F+P)/2=

(1000+L)/2

YTM

(120+(1000-L)/2)/((1000+L)/2)

10.03%=

(120+(1000-L)/2)/((1000+L)/2)

Solving the above equation we will get L= $ 1035.81