Question

A 6-year bond, 8% semiannual coupon bond sells at par ($1,000). Another bond of equal risk, maturity, and par value pays an 8% annual coupon. What is the price of the annual coupon bond?

Answer 1

Answer:

Explanation:

• The bond has 8% coupon paid semiannually, and those bonds sell at their par value.
• Since the bond sales at par value, Market rate (Yield) = Coupon rate =8%

Second bond:

• Coupon rate = 8%

• Par value = $1,000

• Semiannual coupon amount = 1000 x 8%/2 = $40

• Time to maturity = 6 years = 12 semiannual periods

• Semiannual Yield = 8%/2 = 4%

To get price of this bond we will use PV function of excel:

= PV (rate, nper, pmt, fv, type)

= PV (4%, 12, -40, -1000, 0)

= $1053.32

• Price of this bond = $1,053.3

Answer 2

Answer:

$936.65

Explanation:

we firstly need to calculate the yield to maturity in order to calculate the Price of the bond  Since the semiannual bond has the same risk as the annaul bond we will calculate the YTM of the semiannual bond

YTM=C+(F-P)/F+P/2

       =80+(1000-1000)/1000+1000/6*2

        =0.0738/7.38%

 Then we calculate the value of the bond

P= C/(1+YTM)+F/(1+YTM)

  =80/(1+0.0738)^6+1000/(1+1.0738)^6

  =69.38+867.27

   =$936.65