To calculate the weighted average cost of capital (WACC), we need to find the cost of debt and the cost of equity, and then weight them by the proportions of debt and equity in the company's capital structure.
First, let's calculate the cost of debt. We can use the yield to maturity (YTM) formula to find the cost of debt:
YTM = (annual interest payment + (face value - bond price) / years to maturity) / ((face value + bond price) / 2)
The annual interest payment is 0.065 x $1,000 = $65. The bond price is 0.99 x $1,000 = $990. The face value is $1,000. The years to maturity is 10, so we can plug these values into the YTM formula:
YTM = ($65 + ($1,000 - $990) / 10) / (($1,000 + $990) / 2) = 0.0676 or 6.76%
So, the cost of debt is 6.76%.
Next, we need to calculate the market value of debt. This is simply the number of bonds outstanding multiplied by the bond price:
Market value of debt = 45,000 x $990 = $44,550,000
Now, we can calculate the cost of equity using the capital asset pricing model (CAPM):
Cost of equity = risk-free rate + beta x market risk premium
Cost of equity = 0.03 + 1.60 x 0.07
Cost of equity = 0.03 + 0.112
Cost of equity = 0.142 or 14.2%
Now, we can calculate the WACC using the formula:
WACC = (cost of debt x (1 - tax rate) x (market value of debt / total value of firm)) + (cost of equity x (market value of equity / total value of firm))
Total value of firm is the sum of the market value of debt and the market value of equity:
Total value of firm = $44,550,000 + (470,000 x $55) = $72,985,000
Market value of equity is the number of shares outstanding multiplied by the stock price:
Market value of equity = 470,000 x $55 = $25,850,000
Now, we can plug in the numbers and calculate the WACC:
WACC = (0.0676 x (1 - 0.25) x ($44,550,000 / $72,985,000)) + (0.142 x ($25,850,000 / $72,985,000))
WACC = 0.0318 + 0.0504
WACC = 0.0822 or 8.22%
Therefore, the WACC for Vector Company is 8.22%. Option D, 8.36%, is the closest choice to this answer but it is not the correct one.