Questions: BP has a bond outstanding with 15 years to maturity, a 1,000 par value, a coupon rate of 6.6%, with coupons paid semiannually, and a price of 90.31 (percent of par). What is BP's pre-tax cost of debt?

Solution Steps

To find BP's pre-tax cost of debt, we need to calculate the yield to maturity (YTM) of the bond. The YTM is the interest rate that equates the present value of the bond's future cash flows to its current price. Since the bond pays semiannual coupons, we will adjust the coupon rate and the number of periods accordingly. We will use a numerical method, such as the Newton-Raphson method or a root-finding function, to solve for the YTM.

We have a bond with the following characteristics:

• Par value (\(PV\)) = \$1,000
• Coupon rate (\(C\)) = \(6.6\%\)
• Price as a percentage of par = \(90.31\%\)
• Years to maturity = \(15\)
• Coupons paid semiannually

The price of the bond (\(P\)) is calculated as: \[ P = \frac{90.31}{100} \times 1000 = 903.1 \] The semiannual coupon payment (\(C_s\)) is: \[ C_s = \frac{C \times PV}{2} = \frac{0.066 \times 1000}{2} = 33.0 \]

The total number of periods (\(N\)) for the bond is: \[ N = 15 \times 2 = 30 \]

The yield to maturity (\(YTM\)) is found to be: \[ YTM = 0.07700456248832196 \] To express this as an annual yield, we multiply by the number of periods per year: \[ \text{Annual } YTM = YTM \times 2 = 0.15400912497664393 \]

Final Answer