A General Power bond carries a coupon rate of 9.6%, has 9 years until maturity, and sells at a yield to maturity of 8.6%.

A General Power bond carries a coupon rate of 9.6%, has 9 years until maturity, and sells at a yield to maturity of 8.6%. (Assume annual interest payments.)



a. What interest payments do bondholders receive each year?

 

b. At what price does the bond sell? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

 



c. What will happen to the bond price if the yield to maturity falls to 7.6%? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

 

d. If the yield to maturity falls to 7.6%, will the current yield be less, or more, than the yield to maturity?

 

Explanation

Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

a.

Interest payment	=	Coupon rate × Face value
	=	$1,000 × 0.096
	=	$96

b.

Bond price	=	PV of coupon payments + PV of face value
	=	C × ((1 / r) – {1 / [r(1 + r)t]}) + FV / (1 + r)t
	=	$96 × {(1 / 0.086) – [1 / (0.086 × 1.0869)]} + $1,000 / 1.0869
	=	$1,060.94

c.

Bond price	=	PV of coupon payments + PV of face value
	=	C × ((1 / r) – {1 / [r(1 + r)t]}) + FV / (1 + r)t
	=	$96 × {(1 / 0.076) – [1 / (0.076 × 1.0769)]} + $1,000 / 1.0769
	=	$1,127.04

Price increase	=	$1,127.04 – 1,060.94
	=	$66.10

d.
More. The current yield exceeds the yield to maturity on the bond because the bond is selling at a premium. At maturity the holder of the bond will receive only the $1,000 face value, reducing the total return on investment as measured by yield to maturity.

There is an inverse relationship between the YTM and the bond price. As the YTM decreases, the price increases and vice versa.

Calculator computations:

When you have a PV, a PMT, and a FV, you must carefully assign positive and negative values. The key is to have the same sign (+ or –) on all cash flows that move in the same direction. With a bond, the PMT and FV flow in the same direction.

For example, if you purchase a bond, the PV is a cash outflow and the PMT and FV are cash inflows. It does not matter if you assign positive or negative signs to the PMT and FV as long as the signs are consistent with each other.

a.

Enter

9

8.6

–96

–1,000

N

I/Y

PV

PMT

FV

Solve for

1,060.94

b.

Enter

9

7.6

–96

–1,000

N

I/Y

PV

PMT

FV

Solve for

1,127.04

Thank you!