Question

A. Bond Prices A $1,000 par bond that pays interest semiannually has a quoted coupon rate of 7%, a promised yield to maturity of 7.6% and exactly 4 years to maturity. What is the bond's current value? B. Bond Prices A $1,000 par bond that pays interest semiannually has a quoted coupon rate of 6%, a promised yield to maturity of 4.8% and exactly 12 years to maturity. The present value of the coupon stream represents ______ of the total bond's value.

C. Bond Yields Find the promised yield to maturity for a 8% coupon, $1,000 par 30 year bond selling at $981.45. The bond makes semiannual coupon payments.

Answer 1

Solution:-

A) Current value of bond

          = Semiannual interest*PVIFA(i,N)+Maturity value*PVIF(i,N)

Where ,

Semiannual interest = $1,000*7%*1/2 =$35

Number of periods= 4*2 =8

Semiannual YTM(i)=7.6%/2 =3.8%

Maturity value = $1000

Substituting the value we get,

Current value of bond = 35*PVIFA(3.8%,8)+1000*PVIF(3.8%,8)

                                        =35*6.7887+1000*0.7420

                                        =$979.63

Hence the current value of bond =$979.63

B) Total value of bond

          = Semiannual interest*PVIFA(i,N)+Maturity value*PVIF(i,N)

Where ,

Semiannual interest = $1,000*6%*1/2 =$30

Number of periods= 12*2 =24

Semiannual YTM(i)=4.8%/2 =2.4%

Maturity value = $1000

Substituting the value we get,

Total value of bond = 30*PVIFA(2.4%,24)+1000*PVIF(2.4%,24)

                                        =30*18.08417+1000*0.56598

                                        =$1,108.5

Present value of value of the coupon stream= Semiannual interest*PVIFA(i,N

= 30*PVIFA(2.4%,24)

=30*18.08417

=$542.53

Percentage of PV of coupons stream to total bond value

     = $542.53/$1,108.5= 0.48942 i.e 48.94%

The present value of the coupon stream represents 48.94% of the total bond's value.

C) Calculation of YTM bond

Current price of bond = $981.45

Par value= $1000

Coupon rate= 8%

Semiannual interest= $1000*8%*1/2 = $40

Number of periods (n) = 30*2 = 60 periods

Calculation of YTM if it is selling at $981.45

            We will use hit and trail method to calculate the YTM .

First we take discount rate 5% as discount rate ,

            Price of bond = 40*PVIFA(5%,60)+1000*PVIF(5%,60)

                                    = 40*18.92929+1000*0.053536

                                    =$810.7071

Now we will assume discount rate to be 4%.

Price of bond = $1000

Since when the YTM of bond is equal to bond coupon rate bond trade at par.

Now YTM of bond can be calculated as follows

Hal yearly YTM=Lower DR+Difference b/w DRs{[PV of lower DR-PV]/Absolute difference B/w DRs}

Where, DR stands for discount rate

            PV stands for present value

            B/W stands for between.

Now substituting the value

Half yearly YTM = 4%+1%*(1000-981.45)/(1000-810.7071)

            =4%+0.097996%

            =4.097996%

Hence the YTM = 2*4.097996%=8.20%

Hence the promised YTM is 8.20% (Approx).

Please feel free to ask if you have any query in the comment section.