To calculate the cost of debt for Titan Mining Corporation, we need to find the yield to maturity (YTM) of the bonds. The cost of debt is the effective rate that the company pays on its current debt, and since the bonds are selling at a price different from the par value, we will compute the YTM. Here are the steps:

Given Data:

• Par value of bonds (FV) = $1,000
• Semiannual coupon payment (PMT) = $30
• Number of bonds outstanding = 175,000
• Price of each bond (PV) = $1,060
• Years to maturity = 5 years
• Number of periods = 5 years × 2 (semiannual) = 10 periods
• Tax rate = 21%

The cost of debt before tax is the YTM of the bond. The formula for YTM can be approximated, or we can solve it iteratively. However, in this context, I will use an approximation formula for YTM:

$YTM \approx \frac{Coupon \, Payment}{Bond \, Price} + \frac{(Face \, Value - Bond \, Price)}{Number \, of \, Periods \times Bond \, Price}$

Let's break this down:

$YTM = \left( \frac{30}{1,060} \right) + \left( \frac{1,000 - 1,060}{10 \times 1,060} \right)$

$YTM = 0.0283 - 0.00566 = 0.02264 \, \text{(semiannual)}$

Since YTM is semiannual, we multiply by 2 to annualize it:

$YTM = 0.02264 \times 2 = 0.04528 \, \text{or} \, 4.528\%$

After-Tax Cost of Debt:

The cost of debt for a company is typically calculated after taxes because interest payments on debt are tax-deductible.

$\text{After-tax cost of debt} = YTM \times (1 - \text{Tax rate})$

$\text{After-tax cost of debt} = 0.04528 \times (1 - 0.21)$

$\text{After-tax cost of debt} = 0.04528 \times 0.79 = 0.03577 \, \text{or} \, 3.577\%$

Conclusion:

The after-tax cost of debt for Titan Mining Corporation is approximately 3.58%.

Would you like more details or explanations?

Related Questions:

1. How does the beta of the company's stock affect the overall cost of capital?
2. What is the importance of the tax shield on debt for the company?
3. How would the cost of debt change if the bond price decreased?
4. Why do we use the after-tax cost of debt in the Weighted Average Cost of Capital (WACC)?
5. How does the semiannual nature of bonds affect their yield calculation?

Tip:

Remember that the cost of debt is usually lower than the cost of equity because of the tax shield, making debt a potentially cheaper financing option.