Understanding the Cost of Debenture Capital

The cost of debenture capital represents the cost incurred by a company for using debt financing. For redeemable debentures, which have a fixed maturity date, the cost is calculated considering the interest payments, any premium or discount on issue or redemption, and the tax benefit on interest payments.

Interest paid on debentures is a tax-deductible expense for the company. Therefore, the effective cost of debentures is the after-tax cost.

Key Information from the Question

Let's break down the given information about the debenture issue:

• Face Value per debenture: Rs. 100
• Number of debentures: 1000
• Total Face Value: $1000 \times Rs. 100 = Rs. 1,00,000$
• Annual Interest Rate: 10%
• Annual Interest per debenture: 10% of Rs. 100 = Rs. 10
• Total Annual Interest: 10% of Rs. 1,00,000 = Rs. 10,000
• Issued at Discount: 2%
• Discount amount per debenture: 2% of Rs. 100 = Rs. 2
• Issue Price (Net Proceeds) per debenture: Rs. 100 - Rs. 2 = Rs. 98
• Total Net Proceeds from issue: $1000 \times Rs. 98 = Rs. 98,000$
• Redeemable after: 10 years
• Redemption Value: Assuming redemption at par, Redemption Value per debenture = Rs. 100
• Total Redemption Value: $1000 \times Rs. 100 = Rs. 1,00,000$
• Corporate Tax Rate: 40% or 0.40

Note: The statement "A company raises Rs. 1,00,000 by issue of..." likely refers to the total face value of the issue, as the actual amount raised after a 2% discount on a total face value of Rs. 1,00,000 would be Rs. 98,000.

Formula for Cost of Redeemable Debentures After Tax

The approximate formula for calculating the after-tax cost of redeemable debentures (Kd) is:

$$ Kd = \frac{I(1-t) + \frac{(RV - NP)}{n}}{\frac{(RV + NP)}{2}} $$

Where:

• $I$ = Annual Interest per debenture
• $t$ = Corporate Tax Rate
• $RV$ = Redemption Value per debenture
• $NP$ = Net Proceeds per debenture
• $n$ = Number of years to maturity

Step-by-Step Calculation of Debenture Cost

Using the values we identified:

• $I = Rs. 10$
• $t = 0.40$
• $RV = Rs. 100$
• $NP = Rs. 98$
• $n = 10$ years

1. Calculate Annual Interest after Tax:

After-tax Interest = $I \times (1 - t) = Rs. 10 \times (1 - 0.40) = Rs. 10 \times 0.60 = Rs. 6$

2. Calculate Amortization of Discount/Premium per year:

This term accounts for the gain (if redeemed at premium or issued at discount) or loss (if redeemed at discount or issued at premium) spread over the life of the debenture.

Amortization = $\frac{(RV - NP)}{n} = \frac{(Rs. 100 - Rs. 98)}{10} = \frac{Rs. 2}{10} = Rs. 0.20$

Since the debenture was issued at a discount and redeemed at par, there is a gain of Rs. 2 per debenture over its life, which effectively reduces the cost.

3. Calculate the Average Value of RV and NP:

Average Value = $\frac{(RV + NP)}{2} = \frac{(Rs. 100 + Rs. 98)}{2} = \frac{Rs. 198}{2} = Rs. 99$

4. Apply the formula for Kd:

$$ Kd = \frac{After-tax Interest + Amortization}{Average Value} $$

$$ Kd = \frac{Rs. 6 + Rs. 0.20}{Rs. 99} $$

$$ Kd = \frac{Rs. 6.20}{Rs. 99} $$

Now, calculate the decimal value:

$$ Kd \approx 0.062626... $$

Convert to percentage:

$$ Kd \approx 0.062626 \times 100\% \approx 6.26\% $$

Comparing with Options

The calculated cost of debenture capital is approximately 6.26%. Let's compare this with the given options:

Our calculated value of 6.26% is closest to Option 3, which is 6.18%. Small differences can sometimes occur due to rounding in calculations or slight variations in the formula used (though the one used is standard approximation).

Revision Table: Key Concepts

Additional Information: Cost of Finance

Understanding the cost of different sources of finance is crucial for financial management and capital budgeting decisions. Besides debentures (debt), companies also use equity (share capital) and sometimes preference shares.

• Cost of Equity: This is the return required by equity shareholders. It is typically calculated using models like the Dividend Discount Model (DDM) or the Capital Asset Pricing Model (CAPM). It is generally higher than the cost of debt because equity holders bear more risk.
• Cost of Preference Shares: This is the fixed dividend rate paid to preference shareholders. It is typically higher than the cost of debt but lower than the cost of equity, and preference dividends are usually not tax-deductible.
• Weighted Average Cost of Capital (WACC): This is the average cost of all the different sources of finance used by a company, weighted by their proportion in the company's capital structure. It represents the overall required rate of return for the company's investments.

Accurately calculating the cost of each component, like the cost of redeemable debentures, is the first step towards determining the overall cost of capital for the firm.