The problem provides information about Qatar Airways issuing a bond and its financial details. We need to calculate the firm's before-tax and after-tax cost of debt.

1. Problem Description

The problem provides information about Qatar Airways issuing a bond and its financial details. We need to calculate the firm's before-tax and after-tax cost of debt.

2. Solution Steps

First, we need to determine the before-tax cost of debt. The bond has a face value of $1000$ and a coupon rate of $7\%$, which means the annual coupon payment is $1000 * 0.07 =$70$. The bond was sold at$945$with a flotation cost of$6$per bond. Thus, the net amount received from the bond sale is$945 - 6 = $939$.

We can approximate the before-tax cost of debt using the following formula:

$BeforeTaxCostOfDebt = \frac{AnnualCouponPayment}{NetAmountReceived}$

$BeforeTaxCostOfDebt = \frac{70}{939}$

$BeforeTaxCostOfDebt = 0.07454739084131 \approx 0.0745$ or $7.45\%$

The tax rate is $40\%$, which is $0.4$. The after-tax cost of debt can be calculated using the following formula:

$AfterTaxCostOfDebt = BeforeTaxCostOfDebt * (1 - TaxRate)$

$AfterTaxCostOfDebt = 0.0745 * (1 - 0.4)$

$AfterTaxCostOfDebt = 0.0745 * 0.6$

$AfterTaxCostOfDebt = 0.0447$ or $4.47\%$

3. Final Answer

The firm's before-tax cost of debt is approximately $7.45\%$.

The firm's after-tax cost of debt is approximately $4.47\%$.