Devine Divots issued a bond a few years ago. The bond has a face value equal to $1,000 and pays investors $30 interest every six months. The bond has eight years remaining until maturity. If an investor requires a 7 percent rate of return to invest in this bond, what is the maximum price the investor should be willing to pay to purchase the bond?

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Quizplus · Accepted Answer

The maximum price an investor should be willing to pay for the bond can be calculated using the present value of an annuity formula for the semi-annual interest payments and the present value formula for the lump sum payment of the bond's face value at maturity. The bond pays $30 every six months for 8 years (16 periods), and the investor requires a 7% annual rate of return, which is 3.5% per period semi-annually. The present value of the annuity (interest payments) is calculated as:$$ PV_{annuity} = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) $$$$ PV_{annuity} = 30 \times \left( \frac{1 - (1 + 0.035)^{-16}}{0.035} \right) $$The present value of the face value ($1,000) is calculated as:$$ PV_{face} = F \times (1 + r)^{-n} $$$$ PV_{face} = 1000 \times (1 + 0.035)^{-16} $$Adding these two present values gives the maximum price the investor should be willing to pay. The correct calculation aligns with option B, $939.53, indicating that this is the present value of the bond's future cash flows discounted at the investor's required rate of return.

Devine Divots Issued a Bond a Few Years Ago