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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?

Respuesta :

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
Tundexi

The price of the annual coupon bond is  $992.64.

EAR = (1 + YTM/m)^m - 1

EAR = (1+0.08/2)^2 - 1

EAR = 8.16%

Given Information

C/Y = 1

P/Y = 1

N = 6

I/Y = 8.16%

PMT = -$80 (8%*1000)

FV = -1000

Now, we will employ the use of PV function of Financial calculator to allow us derive the

Price of bond = CPT PV (C/Y, P/Y, N, I/Y, -PMT, -FV)

Price of bond = CPT PV (1, 1, 6, 8.16%, -80, 1000)

Price of bond = $992.64.

Therefore, the price of the annual coupon bond is  $992.64.

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