Cost of Debt

Meaning and Importance

Every finance manager faces a fundamental question: what does it cost the firm to borrow money? The cost of debt is the required rate of return that lenders expect when investing in a company's bonds, debentures, or long-term loans. It's a cornerstone of capital structure decisions and directly shapes the firm's weighted average cost of capital (WACC).

Why does this matter? Because financing through debt isn't free. It impacts profit, risk, and ultimately shareholder value. The cost of debt helps management decide whether to borrow, how much to borrow, and from which sources.

Before-Tax vs. After-Tax Cost

a. Before-Tax Cost of Debt

The before-tax cost of debt represents the explicit rate paid to creditors—simply, the interest rate on borrowed funds. If a company issues a debenture at 10% interest, then the before-tax cost is 10%. Straightforward, isn't it?

Formula:
Before-tax cost of debt (K_d) = Interest Paid / Net Proceeds

b. After-Tax Cost of Debt

Interest on debt is tax-deductible—a crucial benefit for companies. The after-tax cost of debt reflects this advantage, showing the true cost borne by the firm after accounting for tax savings.

For example, if you borrow at 10% and the corporate tax rate is 30%, the after-tax cost is:
K_d = 10% × (1 – 0.3) = 7%

The after-tax cost is always lower than the before-tax cost, owing to the tax shield provided by interest expenses.

Cost of Redeemable and Irredeemable Debt

a. Redeemable Debt

Redeemable debt carries a maturity date. The cost of such debt must reflect not only interest payments but also the premium/discount at redemption. The calculation requires the present value concept, which is why time value of money is interlinked with cost of capital.

Formula (Approximation):
K_d = [Interest × (1 – Tax Rate) + (Redemption Value – Net Proceeds) / N] / [(Redemption Value + Net Proceeds)/2]
Where:
Interest = Annual interest paid
Redemption Value = Amount repaid at maturity
Net Proceeds = Cash received from issue
N = Number of years to maturity

Let's see this in action.

Example

A company issues ₹1,00,000 of 8% debentures at ₹96,000 (net proceeds). These are redeemable at par after 5 years. Tax rate is 30%.

1. Interest paid = ₹8,000
2. Tax shield = ₹8,000 × 30% = ₹2,400
3. After-tax interest = ₹8,000 – ₹2,400 = ₹5,600
4. Redemption premium = ₹1,00,000 – ₹96,000 = ₹4,000
5. Annual premium = ₹4,000 / 5 = ₹800
6. Numerator = ₹5,600 + ₹800 = ₹6,400
7. Denominator = (₹1,00,000 + ₹96,000) / 2 = ₹98,000
8. K_d = ₹6,400 / ₹98,000 = 6.53%

b. Irredeemable Debt

Irredeemable debt (or perpetual debt) has no maturity date. The computation is simpler since there is no redemption premium or discount.

Formula:
K_d = Interest × (1 – Tax Rate) / Net Proceeds

For instance, if a firm issues perpetual bonds at 12% interest, net proceeds ₹1,00,000, and the tax rate is 25%:
K_d = 12,000 × 0.75 / 1,00,000 = 9%

Cost of Convertible Debentures

Convertible Debentures

These hybrid instruments convert into equity after a specified period. Their cost calculation is nuanced, as investors expect a lower return due to conversion privileges.

The cost of convertible debentures is computed in two stages:
1. Calculate cost of debt up to the conversion period using the regular formula.
2. Estimate the value of the conversion option and adjust the cost accordingly.

In practice, the computation may require present value techniques (discounting future cash flows until conversion, then considering the market value of equity received).

Conceptual Trap: Many students mistakenly calculate cost of convertible debentures as if they were regular redeemable debentures, ignoring the benefit embedded in the conversion feature. Always factor in the equity conversion value.

Yield to Maturity (YTM) Concept and Calculation

a. Meaning of YTM

Yield to Maturity is the internal rate of return (IRR) earned by an investor if the bond is held until maturity, accounting for all coupon payments and any difference between purchase price and redemption value. For companies, YTM is a practical measure of the actual cost of debt, especially for market-traded instruments.

b. Calculating YTM

The formula for YTM is derived from the present value equation:

\[ P = \frac{C}{(1 + YTM)^1} + \frac{C}{(1 + YTM)^2} + ... + \frac{C + RV}{(1 + YTM)^N} \] Where:
P = Current price of the bond
C = Annual coupon (interest payment)
RV = Redemption value
N = Number of years to maturity
YTM = Yield to maturity (cost of debt)

Because this equation requires iteration, for most exam purposes, use the approximation method:

YTM (Approximate) =
[Annual Interest + (Redemption Value – Current Price) / N] / [(Redemption Value + Current Price) / 2]

Example

A 5-year bond is priced at ₹950, pays ₹100 annual interest, and will be redeemed at ₹1,000.

1. Annual interest = ₹100
2. Redemption gain = ₹1,000 – ₹950 = ₹50
3. Annualized gain = ₹50 / 5 = ₹10
4. Numerator = ₹100 + ₹10 = ₹110
5. Denominator = (₹1,000 + ₹950) / 2 = ₹975
6. YTM = ₹110 / ₹975 = 11.28%

On the actual exam, you may be asked to compute YTM using either the approximation or present value method. Don't rush—read carefully!

MCQ-Type Conceptual Traps

• If a company's bond is trading above par, will its YTM be higher or lower than the coupon rate?
  The YTM will be lower than the coupon rate because the investor pays more upfront than the face value, reducing effective yield.
• Is the after-tax cost of debt ever higher than the before-tax cost of debt?
  No. The tax shield always reduces the effective cost.
• If a debenture is issued at a discount, does the cost of debt increase or decrease?
  It increases, since the net proceeds are lower, raising the effective rate paid to investors.
• Can redeemable debt have a lower cost than irredeemable debt?
  Yes, if the redemption premium is negative (i.e., redeemable at a discount).
• Does the cost of convertible debentures equal the coupon rate?
  No. The conversion privilege typically allows the company to pay a lower coupon, so the true cost is less than the coupon rate.