UOP, a petroleum processing technology firm, issued a 10% coupon, 20 year to maturity first mortgage bond five years ago. If the current market rate of debt for UOP is 8%, at what price should this bond sell, to the nearest dollar? Assume a par value of $1,000 and that it pays interest semiannually.

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The bond should sell at a premium because its coupon rate (10%) is higher than the current market rate (8%). To find the price, we use the formula for the present value of a bond, which includes the present value of the annuity (interest payments) and the present value of the lump sum (par value at maturity). Given that interest is paid semiannually, the coupon payment per period is $50 (10% of $1,000 divided by 2), the number of periods remaining is 30 (15 years * 2), and the market rate per period is 4% (8% divided by 2). Using the present value formula for an annuity and a lump sum, the calculation is as follows:$$ \text{Price} = \left( \frac{\$50}{0.04} \right) \left(1 - \frac{1}{(1+0.04)^{30}}\right) + \frac{\$1,000}{(1+0.04)^{30}} $$$$ \text{Price} \approx \$1,173 $$Therefore, the bond should sell for approximately $1,173, to the nearest dollar.

UOP, a Petroleum Processing Technology Firm, Issued a 10% Coupon