Final answer:
The pre-tax cost of debt cannot be determined without the tax rate information.
Step-by-step explanation:
In this case, the coupon rate is 8% and there is no information provided about the tax rate. Therefore, without the tax rate, it is not possible to determine the pre-tax cost of debt. The value of the bond at $900 and its par value of $1,000 can provide insights into the investor's perception of the bond's risk and expected return.
Annual coupon payment = Coupon rate * Par value
Annual coupon payment = 8% * $1,000 = $80
Since the bond pays semiannual coupons, the semiannual coupon payment will be half of the annual coupon payment:
Semiannual coupon payment = Annual coupon payment / 2
Semiannual coupon payment = $80 / 2 = $40
Next, we can calculate the number of coupon payments remaining until maturity. Since the bond has 18 years to maturity and pays semiannual coupons, there will be 18 * 2 = 36 coupon payments.
Now, let's calculate the YTM using the bond price, coupon payments, and years to maturity. We'll use an approximate method to find the YTM.
Using a financial calculator or spreadsheet software, we can input the following values:
N = 36
PMT = $40
FV = $1,000
PV = -$900
By solving for the interest rate (YTM), we find that the approximate YTM is approximately 4.82%.
Therefore, the pre-tax cost of debt for the XYZ bonds is approximately 4.82%.