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Freiburg Faucets Incorporated issued 20.00-year bonds 4.00 years ago with a coupon rate of 9.25% APR. The bonds pay semi-annual coupons, have a face value of $1,000 each and were issued at par value. What is the price of the Freiburg bond’s today if investors want a 7.16% APR return for bonds of similar risk and maturity?

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To determine the price of Freiburg Faucets Incorporated's bond today, we can use the present value of the bond's cash flows approach. The cash flows consist of the semi-annual coupon payments and the face value received at maturity.

Here are the steps to calculate the price:

  1. Gather the bond information:

    • Face value (FV) = $1,000
    • Coupon rate = 9.25% per annum
    • Coupons per year = 2 (since they are paid semi-annually)
    • Coupon payment = (Coupon rate / Coupons per year) * Face value
    • Years remaining = 20.00 - 4.00 = 16.00 years

  2. Calculate the annual coupon payment: \[ \text{Coupon payment} = \frac{9.25%}{2} \times 1000 = 0.04625 \times 1000 = 46.25 \]

  3. Calculate the total number of coupon payments remaining: \[ \text{Total payments} = 16.00 \text{ years} \times 2 = 32 \text{ payments} \]

  4. Calculate the required return per period:

    • The required return (APR) is 7.16%, so the semi-annual required return is: \[ \text{Semi-annual return} = \frac{7.16%}{2} = 0.0358 \]

  5. Determine the present value of the coupon payments: The present value of an annuity formula is used here: \[ PV = C \times \left(1 - (1 + r)^{-n}\right) / r \]

    • Where \( C \) is the coupon payment, \( r \) is the semi-annual required return, and \( n \) is the total number of payments. \[ PV_{\text{coupons}} = 46.25 \times \left(1 - (1 + 0.0358)^{-32}\right) / 0.0358 \]

    Let's calculate it step-by-step: \[ PV_{\text{coupons}} = 46.25 \times \left(1 - (1 + 0.0358)^{-32}\right) / 0.0358 \]

    First calculate \( (1 + 0.0358)^{-32} \): \[ (1 + 0.0358)^{-32} \approx 0.3688 \] Therefore: \[ PV_{\text{coupons}} = 46.25 \times \left(1 - 0.3688\right) / 0.0358 = 46.25 \times 0.6312 / 0.0358 \approx 46.25 \times 17.6357 \approx 816.52 \]

  6. Determine the present value of the face value: We also need the present value of the face value: \[ PV_{\text{face value}} = \frac{FV}{(1+r)^n} = \frac{1000}{(1+0.0358)^{32}} \] Now calculate \( (1 + 0.0358)^{32} \): \[ (1 + 0.0358)^{32} \approx 3.4112 \] Thus: \[ PV_{\text{face value}} = \frac{1000}{3.4112} \approx 292.68 \]

  7. Calculate the total price of the bond: Finally, combine the present values of the coupons and the face value: \[ \text{Bond Price} = PV_{\text{coupons}} + PV_{\text{face value}} = 816.52 + 292.68 \approx 1109.20 \]

The price of the Freiburg bond today, given the required return of 7.16%, is approximately $1,109.20.