Question

 

Jack and Jill Jones are considering the purchase of a one-thousand-dollar par value bond that pays a six percent coupon. The bond that they are considering has no default (credit) risk. Coupon interest payments are made semi-annually. There are exactly eight-years remaining until maturity. This bond’s market price is equal to $1,019.00. What is the yield-to-maturity for this bond?

1. 3.70 percent
2. 4.70 percent
3. 5.70 percent
4. 6.70 percent

Jack and Jill Jones are considering the purchase of a one-thousand-dollar par value bond that pays a four percent coupon. The bond that they are considering has no default (credit) risk. Coupon interest payments are made semi-annually. There are exactly thirty-years remaining until maturity. This bond’s yield-to-maturity is equal to three percent. What is the market price for this bond?

1. $1,096.50
2. $1,196.50
3. $1,296.50
4. $   996.50

Answer 1

1. There will be sixteen semi annual payment each=1000*(6/2)%=$30

Payment at end of sixteenth paeriod =Face value (Principal)returned=$1000

Hence Last payment =$1030

If r=Semi annual yield

Sum of Present Value of all futre payments=market Price=$1019.00

Present Value of first period=30/(1+r)

Present value of Second Period =30/(1+r)^2

Present Value of Last Period =1030/(1+r)^16

Assume : 1+r=x

The Equation we need to solve is:

1019.00=30/x+(30/(x^2)+(30/(x^3))+........................+(30/(x^15))+(1030/(x^16))

Once we solve for x, we get semi annual yield=r

Annual yield =2*r

Since, it is not possible to solve sixteen degree polymonial manually,

It can be solved by using excel as given in uploaded image

Yield To Maturity =3%

Semi annual yield to maturity=3/2=1.5%

Number of semi annual period=30*2=60

Semi annual Coupon =(4%*1000)/2=$20

Payment at maturity =$1000

Current Market Price =Present Value of Future Cash Flow

A. Present value of annuity of $20 paid semi annually for 60 periods:

Uniform Series Present Worth Factor(USPWF)=(P/A,i,N)=(((1+i)^N)-1)/(i*((1+i)^N))

i=Interest rate=1.5%=0.015

N=Number of periods=60

USPWF=(P/A,1.5%,60)=(((1+0.015)^60)-1)/(0.015*((1+0.015)^60))=39.380269

Present value of annuity of $20 paid semi annually for 60 period=20*USPWF=20*39.380269=$787.61

B. Present Value of $1000 received as maturity payment at end of 30 years=1000/((1+0.015)^60)=$409.30

Current Market Value of Bond =A+B=787.61+409.30=$1196.90

The Answer Should be $1196.50 ( there may be little difference due to approximination

ANSWER: B $1196.50

Excel Calculation is uploaded below: