Niendorf Corporation's 25-year maturity bonds have an 8.75% coupon rate with interest paid semiannually, and a par value of $1,000. if your required rate of return is 13% what is the intrinsic value of the bond

$687.10

Explanation:

The value of a bond is the present value of the bond's coupon payments plus the present value of the bond's par value at maturity.

First convert terms to semi-annual periods as the coupon rate is semi annual:

Coupon payment = (1,000 * 8.75%) / 2 = $43.75

Required return = 13% / 2 = 6.5%

Number of periods = 25 * 2 = 50 semi annual periods

The coupon payment is an annuity so the value of the bond is:

= Present value of annuity + Present value of par

= (43.75 * ( 1 - (1 + 6.5%) ⁻⁵⁰) / 6.5%) + 1,000 / ( 1 + 6.5%)⁵⁰

= $687.10

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