A company has 10% perpetual debt of Rs. 1,00,000. The tax rate is 35%. Which one of the following is the after-tax cost of capital assuming that the debt is issued at 10% premium?
5.91%
Calculating After-Tax Cost of Perpetual Debt
The question asks us to determine the after-tax cost of a perpetual debt instrument issued by a company. The cost of debt represents the return a company pays to its debtholders. Since interest payments are tax-deductible, the company's effective cost of debt is reduced by the tax savings, also known as the tax shield.
For a perpetual debt, which has no maturity date, the interest payment continues indefinitely. The formula for the after-tax cost of perpetual debt considers the annual interest payment, the tax rate, and the net proceeds received by the company when the debt was issued.
Understanding the Components
Here are the key figures given in the problem:
- Face Value of Debt: Rs. 1,00,000
- Coupon Rate (Annual Interest Rate): 10%
- Annual Interest Payment: 10% of Rs. 1,00,000 = Rs. 10,000
- Tax Rate: 35%
- Issue Price: At a 10% premium to face value
Let's calculate the Net Proceeds from the debt issue.
- Premium Amount: 10% of Face Value = 10% of Rs. 1,00,000 = Rs. 10,000
- Net Proceeds: Face Value + Premium Amount = Rs. 1,00,000 + Rs. 10,000 = Rs. 1,10,000
Formula for After-Tax Cost of Perpetual Debt
The after-tax cost of perpetual debt (\(K_d\)) is calculated using the following formula:
\[K_d = \frac{\text{Annual Interest Payment} \times (1 - \text{Tax Rate})}{\text{Net Proceeds}}\]
Step-by-Step Calculation
Now, let's plug in the values we have calculated:
Annual Interest Payment = Rs. 10,000
Tax Rate = 35% or 0.35
Net Proceeds = Rs. 1,10,000
\[K_d = \frac{\text{Rs. 10,000} \times (1 - 0.35)}{\text{Rs. 1,10,000}}\]
\[K_d = \frac{\text{Rs. 10,000} \times 0.65}{\text{Rs. 1,10,000}}\]
\[K_d = \frac{\text{Rs. 6,500}}{\text{Rs. 1,10,000}}\]
\[K_d \approx 0.05909\ldots\]
To express this as a percentage, we multiply by 100:
\[K_d \approx 0.05909 \times 100\%\]
\[K_d \approx 5.91\%\]
Thus, the after-tax cost of capital for this perpetual debt is approximately 5.91%.
Conclusion
Based on the calculations, the after-tax cost of perpetual debt is approximately 5.91%.
Let's look at the given options:
- 10%
- 5.91%
- 6.5%
- 7.22%
The calculated value matches the second option.
Revision Table: Key Concepts
| Concept | Description | Relevance Here |
|---|---|---|
| Perpetual Debt | Debt with no maturity date; interest is paid indefinitely. | Determines the cash flow pattern (constant interest) and the cost calculation formula. |
| After-Tax Cost of Debt | The effective cost of borrowing after accounting for the tax deductibility of interest payments. | The required calculation in the question. Shows the true cost to the company. |
| Tax Shield on Debt | The tax savings resulting from the tax deductibility of interest expense. | \( \text{Interest} \times \text{Tax Rate} \). Reduces the net cost of interest. |
| Net Proceeds | The amount of cash received by the company after issuing debt, less any flotation costs (none in this case, but premium is included). | The base amount against which the annual after-tax interest cost is measured. Issue at premium increases net proceeds. |
Additional Information: Cost of Capital Insights
The cost of debt is a crucial component when calculating a company's Weighted Average Cost of Capital (WACC). WACC is the average rate of return a company expects to earn on its investments in order to satisfy all of its investors (bondholders, preferred stockholders, and common stockholders).
Factors influencing the cost of debt include:
- Interest Rates: General level of interest rates in the economy.
- Credit Risk: The company's creditworthiness. Higher risk means higher interest rates.
- Tax Rate: Higher tax rates lead to a greater tax shield, reducing the after-tax cost of debt.
- Issue Costs/Premium/Discount: How the debt is issued relative to its face value affects the net proceeds and thus the effective cost. Issuing at a premium (as in this case) increases net proceeds, effectively lowering the cost of debt compared to issuing at par or a discount, for the same coupon rate.
For perpetual debt, the calculation is simplified because there is no principal repayment to consider. The annual interest payment and the initial net proceeds are the primary figures needed, adjusted for the tax shield.
Important Questions from Cost of Capital
Company's current price of share is Rs. 60 and dividend per share is Rs. 4 . If its capitalisation rate is 12 percents. What is dividend growth rate?
X Ltd. forfeited 40 shares of Rs. 10 each and on which Rs. 4 per share were paid. If the forfeited shares reissued as Rs. 8 per share paid up, what is the minimum price the company must charge?
Which of the sources of finance has an implicit cost of capital?
Cost of Equity Share Capital is more than cost of Debt because :
- Which one of the following is not a method of calculating cost of equity capital ?
