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26 February, 02:14

Valuing bonds [lo2] union local school district has a bond outstanding with a coupon rate of 3.7 percent paid semiannually and 16 years to maturity. the yield to maturity on this bond is 3.9 percent, and the bond has a par value of $5,000. what is the price of the bond?

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  1. 26 February, 02:17
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    Given:

    coupon rate of 3.7 percent paid semiannually and 16 years to maturity.

    yield to maturity on this bond is 3.9 percent

    the bond has a par value of $5,000

    1. Determine the Number of Coupon Payments:

    16 years * 2 (semiannually) = 32 coupon payments

    2. Determine the Value of Each Coupon Payment:

    Coupon rate: 3.7% / 2 = 1.85%

    Coupon payment: $1,000 x 1.85% = $18.50

    3. Determine the Semi-Annual Yield:

    Required yield: 3.9% / 2 = 1.95%

    4. Plug the Amounts Into the Formula:

    Bond Price = 18.50 [ 1 - [1 / (1+0.0195) ^32]] / 0.0195 + 1000 / (1+0.0195) ^32

    Bond Price = 18.50 [ 1 - (1/1.855) ] / 0.0195 + 1000 / 1.855

    Bond Price = 18.50 [ 1 - 0.5391] / 0.0195 + 539.03

    Bond Price = 18.50 (0.4609 / 0.0195) + 539.03

    Bond Price = 18.50 (23.6359) + 539.03

    Bond Price = 437.26415 + 539.03

    Bond Price = 976.29415 or $976.30
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