A 10-year, $1,000 par value zero-coupon rate bond is to be issued to yield 9 percent. a. What...

Question:

A 10-year, $1,000 par value zero-coupon rate bond is to be issued to yield 9 percent.

a. What should be the initial price of the bond?

b. If immediately upon issue, interest rates dropped to 8 percent, what would be the value of the zero-coupon rate bond?

c. If immediately upon issue, interest rates dropped to 10 percent, what would be the value of the zero-coupon rate bond?

Answer and Explanation:

Given -

  • Par Value = $1,000
  • Time (t) = 10 Years
  • Rate (r) = 9% = 0.09

The price of a zero coupon bond is calculated as follows -

  • Price of Bond = Face Value / ( 1 + r ) ^ t

Or,

  • Price of Bond = 1000 / ( 1 + 0.09 ) ^ 10

Or,

  • Price of Bond = $422.41

Scenario 1 - When interest rate drops to 8%

  • Price of Bond = Face Value / ( 1 + r ) ^ t

Or,

  • Price of Bond = 1000 / ( 1 + 0.08 ) ^ 10

Or,

  • Price of Bond = $463.19

Scenario 2 - When interest rate increases to 10%

  • Price of Bond = Face Value / ( 1 + r ) ^ t

Or,

  • Price of Bond = 1000 / ( 1 + 0.10 ) ^ 10

Or,

  • Price of Bond = $385.54

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