Cost of debt

Introduction: Why Cost of Debt Matters

Welcome to the world of financing! In this chapter, we are looking at Cost of Debt (\(K_d\)). Think of this as the "rental price" a company pays to use someone else's money. When a company wants to start a new capital project (like building a factory), it needs cash. If it borrows that cash, it needs to know exactly how much that debt is costing them.

Don't worry if this seems a bit math-heavy at first. We are going to break it down into simple steps. In the F2 exam, understanding the cost of debt is vital because it is a key ingredient in calculating the Weighted Average Cost of Capital (WACC).

Did you know? Debt is usually the cheapest form of finance for a company. Why? Because it is less risky for the lender (they get paid before shareholders), and the government gives companies a "tax break" on interest payments!

1. The Golden Rule: The Impact of Taxation

Before we look at formulas, you must remember one thing: Interest is tax-deductible. When a company pays interest, it reduces its taxable profit, which means it pays less tax to the government. This makes the debt even cheaper for the company.

Analogy: Imagine you buy a coffee for \$10, but your boss says, "Because you bought that coffee for work, I’ll give you \$2 back in your paycheck." The coffee didn't really cost you \$10; it cost you \$8. That is exactly how the Tax Shield works for debt.

The formula to find the post-tax cost of a simple interest payment is:
Interest \(\times (1 - t)\)
Where \(t\) is the corporation tax rate (e.g., if tax is 20%, you multiply by 0.80).

Key Takeaway: Always check if the question asks for the pre-tax or post-tax cost of debt. In WACC calculations, we almost always use the post-tax cost.

2. Irredeemable Debt

Irredeemable debt is debt where the company pays interest forever and never actually pays back the original lump sum (the principal). While rare in the real world, it’s a common starting point for exam questions.

To find the cost of irredeemable debt (\(K_d\)), we use this simple formula:
\(K_{d(post-tax)} = \frac{I(1-t)}{P_0}\)

Where:
I = Annual Interest (Coupon) payment
t = Tax rate
\(P_0\) = Current Market Price of the debt (ex-div)

Example: A company has 8% irredeemable bonds with a market price of \$90. Tax is 20%.
\nStep 1: Annual interest = 8% of \$100 (par value) = \$8.
\nStep 2: Post-tax interest = \$8 \(\times (1 - 0.20) = \$6.40\).
\nStep 3: \(K_d = \$6.40 / \$90 = 0.071\) or 7.1%.

3. Redeemable Debt: The "Big" Calculation

Most debt is redeemable, meaning the company pays interest for a few years and then pays back the original loan amount at the end. Because there is a final repayment, we can't use the simple formula above. Instead, we use Internal Rate of Return (IRR).

Step-by-Step Process:
\n1. Identify the Cash Outflows (The market price you pay today - \(P_0\)).
\n2. Identify the Cash Inflows (The annual post-tax interest payments and the final redemption value).
\n3. Pick two discount rates (usually 5% and 10%) and calculate the Net Present Value (NPV) for each.
\n4. Use Interpolation to find the exact rate where NPV is zero.

The Interpolation Formula:
\n\(K_d = L + \frac{NPV_L}{NPV_L - NPV_H} \times (H - L)\)

Where:
\nL = Lower discount rate used
\nH = Higher discount rate used
\n\(NPV_L\) = NPV at the lower rate
\n\(NPV_H\) = NPV at the higher rate

Memory Aid: Think of interpolation as "finding the sweet spot" between two guesses. If your first guess (5%) gives a positive result and your second guess (10%) gives a negative result, the true answer is somewhere in the middle!

4. Convertible Debt

Convertible debt is a bit of a "hybrid." The lender has the choice: at the end of the term, they can either take the Cash (redemption value) or Shares in the company.

To calculate the cost of convertible debt, follow the same IRR steps as redeemable debt, but with one twist: The final cash flow is the higher of the two choices.

Why? Because investors are rational! If the shares are worth \$120 and the cash redemption is \$100, the investor will choose the shares. As a student, you must calculate the value of the shares at the redemption date (Current Share Price \(\times (1+g)^n \times\) Conversion Ratio) and compare it to the cash redemption price.

Quick Review Box:
\n• For Redeemable Debt: Final flow = Cash payback.
\n• For Convertible Debt: Final flow = Higher of Cash or Share Value.

5. Bank Loans and Non-Tradable Debt

Not all debt is traded on the stock exchange. If a company has a bank loan, finding the cost is much easier! Since there is no "market price" that changes every day, the cost of the debt is simply the interest rate the bank charges, adjusted for tax.

Formula: \(K_d = Interest Rate \times (1 - t)\)

Common Mistake to Avoid: Students often try to do complex IRR calculations for bank loans. Stop! If there is no market price, just use the interest rate and apply the tax shield.

6. Summary of Key Terms

Par Value (Face Value): Usually \$100. Interest is always calculated as a % of this, regardless of what the market price is.
Coupon Rate: The interest rate printed on the bond certificate.
Market Price (\(P_0\)): What the bond is selling for today. Use this in your formulas!
Ex-div vs. Cum-div: In F2, we always want the Ex-div price. If the question gives you a Cum-div price, subtract the interest payment to get the Ex-div price.

Key Takeaway Summary:
• Debt is cheaper than equity because of lower risk and tax relief.
• For irredeemable debt, use the simple formula.
• For redeemable or convertible debt, use IRR.
• Always use post-tax cash flows for interest, but do not apply tax to the final redemption repayment (the principal).

Don't worry if the IRR calculation takes a few tries to master. It's a mechanical process—once you practice it three or four times, it will become second nature!