Question

Kaiser Industries has bonds on the market making annual payments, with 14 years to maturity, a par value of $1,000, and a current price of $1,108.60. At this price, the bonds yield 7.5 percent. What is the coupon rate?

Answer 1

Answer:

The coupon rate=8.781%

Explanation:

The current price can be expressed as;

Current price=C×{1-(1/(1+r)^n)}/r+{F.V/(1+r)^n}

where;

C=current price

r=annual yield to maturity rate

n=number of years to maturity

F.V=face value

In our case;

C=$1,108.60

r=7.5%=7.5/100=0.075

n=14 years

F.V=$1,000

replacing;

1,108.60=C×{1-(1/(1+0.075)^14)}/0.075+{1,000/(1+0.075)^14}

1,108.60=C×{1-1/(1.075^14)}/0.075+{1,000/1.075^14}

1,108.60=(C×0.637/0.075)+363.313

1,108.60-363.313=8.48915 C

C=$87.81

But;

Annual coupon payments=coupon rate×face value

where;

annual coupon payments=$87.81

coupon rate=R%=(1/100)R=0.01 R

face value=$1,000

replacing;

87.81=0.01 R×1,000

R=87.81/(0.01×1,000)=8.781%

The coupon rate=8.781%