Tangshan Mining is considering issuing longdash
term
debt. The debt would have a 30 year maturity and a 6 percent coupon rate and make semiannual coupon payments. In order to sell the​ issue, the bonds must be underpriced at a discount of 1 percent of face value. In​ addition, the firm would have to pay flotation costs of 1 percent of face value. The​ firm's tax rate is 21 percent. Given this​ information, the afterdash
tax
cost of debt for Tangshan Mining would be​ ________.

To determine the after-tax cost of debt for Tangshan Mining, we follow a multi-step calculation. We start by calculating the yield to maturity (YTM) and then apply the tax rate to find the after-tax cost of debt.

### Given Information:
- **Coupon Rate**: 6% (semiannual payments)
- **Maturity**: 30 years
- **Discount**: 1% of face value
- **Flotation Costs**: 1% of face value
- **Tax Rate**: 21%

### Step 1: Calculate the Price of the Bond
The bonds are issued at a discount of 1% and face flotation costs of 1%, which means the effective price at which the bonds are sold is:

\[
\text{Effective Price} = \text{Face Value} \times (1 - 0.01 - 0.01) = \text{Face Value} \times 0.98
\]

### Step 2: Calculate the Yield to Maturity (YTM)

Since the bond pays a 6% coupon rate semiannually:
- **Annual Coupon Payment**: \( \text{Coupon Rate} \times \text{Face Value} = 0.06 \times \text{Face Value} \)
- **Semiannual Coupon Payment**: \( 0.03 \times \text{Face Value} \)

The YTM (\( r \)) is determined using the following bond pricing formula:

\[
\text{Price} = \sum_{t=1}^{60} \frac{\text{Coupon Payment}}{(1 + r)^t} + \frac{\text{Face Value}}{(1 + r)^{60}}
\]

Here:
- \(\text{Price} = 0.98 \times \text{Face Value}\)
- Semiannual coupon payment = \(0.03 \times \text{Face Value}\)
- \(60\) periods (30 years, semiannual)

We solve for \( r \) using numerical methods or a financial calculator to find the semiannual YTM, then multiply by 2 to get the annual YTM.

### Step 3: Calculate the After-Tax Cost of Debt

Once we have the YTM, the after-tax cost of debt (\( k_d \)) is:

\[
k_d = YTM \times (1 - \text{Tax Rate})
\]

Substituting the values:

\[
k_d = YTM \times (1 - 0.21)
\]

### Final Calculation:
- Find the semiannual YTM using the given formula.
- Multiply by 2 to convert to the annual YTM.
- Adjust for taxes using the tax rate of 21%.

Would you like me to calculate the YTM directly or guide you through using a financial calculator?

### Follow-Up Questions:
1. What is the formula for calculating the price of a bond?
2. How does flotation cost affect the effective cost of debt?
3. Why do we use the after-tax cost of debt in capital budgeting?
4. What role does the tax rate play in determining the cost of debt?
5. How would changing the coupon rate affect the YTM and, consequently, the after-tax cost of debt?

**Tip:** Always remember to adjust the YTM by the tax rate when calculating the after-tax cost of debt.

Tangshan Mining is considering issuing long-term debt. The debt would have a 30-year maturity and a 6 percent coupon rate and make semiannual coupon payments. In order to sell the issue, the bonds must be underpriced at a discount of 1 percent of face value. In addition, the firm would have to pay flotation costs of 1 percent of face value. The firm's tax rate is 21 percent. Given this information, the after-tax cost of debt for Tangshan Mining would be ________.

This detailed solution explains how to calculate the after-tax cost of debt for Tangshan Mining's 30-year bond issuance, accounting for a 1% discount and 1% flotation cost. Learn to apply bond pricing formulas, calculate YTM, and adjust for the tax rate of 21%. Suitable for finance students at the undergraduate level.

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