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Assume that you are considering the purchase of a 15-year bond with an annual coupon rate of 9.5%. The bond has face value of $1,000 and makes semiannual interest payments. If you require an 11.0% nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?

Respuesta :

TomShelby

Answer:

We are going to pay  $892.137 or less for the bonds.

Explanation:

We need to calculate the present value of the bond at 11% interet rate

Cashflow from the bond:

Principal x interest = interest service

1,000 x 9.5% = 95

Present value of annuity of 95 during 15 year at 11%

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

[tex]95 * \frac{1-(1+.11)^{-15} }{.11} = PV\\[/tex]

Present value of the interest service 683,1326097

Second we have to calculate the present value of the 1,000 principal in 15 years

[tex]\frac{Amount}{(1+rate)^{time}} ) = PV[/tex]

[tex]\frac{1,000}{(1+0.11)^{15}} ) = PV[/tex]

209.0043467

Finally we add both together for the present value fothe bond at our rate

209.0043467+ 683,1326097 = 892.1369564 = 892.137

Zviko

The maximum price you should be willing to pay for the bond is $489.71

Bond Price Theory

  • The price of any Bond is eqial to the Present Value of the expected Cashflows. That is the Present Value of Coupons and the Principle.
  • The Principle Amount is the Norminal Amount or the amount that the bond holder will receive at maturity.

Bond Price Calculation

N = 15 x 2 = 30

Pmt = ($1,000 x 9.5%)/ 2 = - $47.50

FV =  $1,000

i =  11.0%

PV =  $489.71

In conclusion, If you require an 11.0% nominal yield to maturity on this investment, the maximum price you should be willing to pay for the bond is $489.71

Learn more about Bond Prices here : https://brainly.com/question/1697523

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