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31 December, 21:47

What must be the price of a $10000 bond with a 6.8% coupon rate, semiannual coupons, and eight years to maturity if it has a yield to maturity of 8% APR?

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  1. 31 December, 22:13
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    Coupon (R) = 6.8% x 10,000 = $680

    Face value (FV) = $10,000

    Number of times coupon is paid in a year (m) = 2

    No of years to maturity = 8 years

    Yield to maturity (Kd) = 8% = 0.08

    Po = R/2 (1 - (1 + r/m) - nm) + FV / (1+r/m) n m

    r/m

    Po = 680/2 (1 - (1+0.08/2) - 8x2) + 10,000 / (1 + 0.08/2) 8x2

    0.08/2

    Po = 340 (1 - (1 + 0.04) - 16) + 10,000 / (1 + 0.04) 16

    0.04

    Po = 340 (1-0.5339) + 10,000/1.8730

    0.04

    Po = 3,961.85 + 5,339.03

    Po = $9,300.88

    Explanation:

    The current market price of a bond is a function of the present value of semi-annual coupon and present value of the face value. The present value of semi-annual coupon is obtained by multiplying the coupon by the present value of annuity factor at 8% for 8 years. The present value of face value is obtained by discounting the face value at the discount factor for 8 years. The addition of the two gives the present value of the bond. All these explanations have been captured by the formula.
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