Let's solve this step by step.

Given Information:

• Face Value (Par Value): $100$ (assuming per $100 bond for simplicity)
• Current Price: $95.82\%$ of par $= 95.82$
• Coupon Rate: $6.1\%$ annually → $3.05\%$ per semi-annual period
• Time to Maturity: $5$ years → $10$ semi-annual periods
• Tax Rate: $28\%$

We will determine the pretax cost of debt by calculating the yield to maturity (YTM).

Step 1: Calculate the Pretax Cost of Debt (YTM)

The bond price is given by the present value of its future cash flows:

$P = \sum \frac{C}{(1+r)^t} + \frac{F}{(1+r)^T}$

where:

• $P = 95.82$ (current bond price)
• $C = \frac{6.1}{2} = 3.05$ (semi-annual coupon payment per $100 bond)
• $F = 100$ (face value)
• $T = 10$ (total periods)
• $r$ is the semi-annual yield (to be solved)

This is a standard bond pricing equation requiring numerical methods (such as trial and error or using a financial calculator). I'll compute $r$ numerically. scipy.optimize import fsolve

Given values

P = 95.82 # Bond price F = 100 # Face value C = 3.05 # Semi-annual coupon payment T = 10 # Total periods

Define bond price equation

def bond_price(r): return sum([C / (1 + r) ** t for t in range(1, T + 1)]) + F / (1 + r) ** T - P

Solve for r (semi-annual yield)

r_semi_annual = fsolve(bond_price, 0.05)[0] # Initial guess: 5% r_annual = r_semi_annual * 2 # Annualize

r_annualThe pretax cost of debt (YTM) is approximately 7.11% per year (rounded to two decimal places).

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Step 2: Calculate the After-Tax Cost of Debt

The after-tax cost of debt is given by:

$r_{\text{after-tax}} = r_{\text{pre-tax}} \times (1 - \text{Tax Rate})$

$r_{\text{after-tax}} = 7.11\% \times (1 - 0.28)$

Let's compute this. Given tax rate tax_rate = 0.28

After-tax cost of debt calculation

r_after_tax = r_annual * (1 - tax_rate) r_after_taxThe after-tax cost of debt is approximately 5.12% per year (rounded to two decimal places).

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Final Answers:

a. Pretax cost of debt: 7.11% per year
b. After-tax cost of debt: 5.12% per year

Would you like a breakdown of the calculations or have any questions?

Here are five related questions to expand your understanding:

1. How does the bond price affect the yield to maturity (YTM)?
2. What happens to the cost of debt if the company’s tax rate changes?
3. How would issuing new bonds at a different coupon rate impact Avicorp’s cost of debt?
4. Why is the after-tax cost of debt important for corporate financial decisions?
5. How does a company's credit rating influence its cost of debt?

Tip: Lower bond prices generally lead to a higher yield to maturity (YTM), increasing the cost of debt.