Part A: Pretax Cost of Debt (Yield to Maturity)

To calculate the pretax cost of debt, we need to determine the yield to maturity (YTM) on the debt. This involves solving for $r$ in the bond price formula:

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

Where:

• $P = 95.39\% \text{ of par } = 0.9539 \times F$
• F = \text{par value (100%)} = 1,000 (assumed per bond for simplicity)
• $C = \text{coupon payment per period} = \frac{\text{coupon rate} \times F}{2} = \frac{0.059 \times 1,000}{2} = 29.50$
• $N = \text{total number of periods} = 5 \text{ years } \times 2 = 10$
• $r = \text{YTM per period (semi-annual yield)}$

The formula becomes:

$0.9539 \times 1,000 = \sum_{t=1}^{10} \frac{29.50}{(1 + r)^t} + \frac{1,000}{(1 + r)^{10}}$

This equation can be solved numerically, as there is no closed-form solution for $r$.

Approximation:

We solve numerically to find $r$ (semi-annual YTM). Doubling this value will give the annualized YTM (annual pretax cost of debt).

Numerical Solution:

$r \approx 3.25\% \text{ (semi-annual yield)} \quad \text{or} \quad 6.50\% \text{ (annualized YTM)}.$

The pretax cost of debt is 6.50%.

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Part B: After-Tax Cost of Debt

The after-tax cost of debt reflects the tax shield from interest payments:

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

Substitute the values: $\text{After-tax cost of debt} = 6.50\% \times (1 - 0.40) = 6.50\% \times 0.60 = 3.90\%.$

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Final Answers:

a. Avicorp's pretax cost of debt is 6.50% (annualized).
b. Avicorp's after-tax cost of debt is 3.90%.

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Would you like further clarification on any part of the calculation? Here are 5 questions that can deepen your understanding:

1. How does the bond price affect the yield to maturity?
2. Why do we annualize the YTM after calculating the semi-annual yield?
3. How does the tax shield influence the cost of debt for a firm?
4. What happens to the cost of debt if the tax rate changes?
5. Can the pretax cost of debt exceed the coupon rate? Why or why not?

Tip: When calculating YTM for a bond, remember that the price reflects all future cash flows discounted at the YTM rate—making it a key indicator of market conditions.