Risk-Free Interest Rate in ESOP Valuation:

Introduction: : Why Does the Risk-Free Interest Rate Matter in ESOP Valuation?

Did you know that a change in interest rates can affect the fair value of employee stock options—even when the company’s share price remains unchanged?

The risk-free interest rate is one of the key inputs in the Black-Scholes Model. It influences the present value of the exercise price and helps determine the theoretical fair value of an ESOP option.

Understanding this component is important for companies valuing employee stock options and calculating compensation expense under Ind AS 102.

What is the Risk-Free Interest Rate?

The risk-free interest rate is the theoretical return on an investment assumed to have no default risk over the relevant period.

In practice, government securities are commonly used as a proxy because governments issuing securities in their own currency are generally considered to have relatively low credit risk.

For ESOP valuation in India, the yield on an appropriate Government of India security may be used as a reference, considering the currency and expected life of the option.

For example, if the relevant government security yield is 6.5% per annum, the risk-free interest rate input may be estimated at 6.5%, provided that the rate is appropriate for the option’s expected life and the valuation methodology.

The rate should not be selected arbitrarily. Its maturity, currency and measurement-date relevance must be considered.

How does the Risk-Free Interest Rate Work in the Black-Scholes Model?

The Black-Scholes Model estimates the theoretical fair value of a call option using several inputs, including the current share price, exercise price, expected life, volatility, risk-free interest rate and expected dividend yield.

The risk-free interest rate affects the model through the present value of the exercise price.

Consider an employee who can purchase a share for ₹100 after three years. The employee does not need to pay the exercise price until exercising the option, subject to the scheme’s terms.

A higher risk-free interest rate reduces the present value of that future ₹100 payment. This generally increases the theoretical value of a call option, assuming all other inputs remain unchanged.

The relationship can be expressed through the Black-Scholes call option formula:

C = S₀e⁻ᵠᵀN(d₁) − Ke⁻ʳᵀN(d₂)

Here, r represents the risk-free interest rate. The formula discounts the exercise price to its present value and incorporates the probability-weighted outcomes associated with the option.

Why does a Higher Risk-Free Interest Rate Generally Increase Call Option Value?

Suppose an employee has the right to purchase a company’s share for ₹100 after three years.

When the risk-free interest rate is higher, the present value of the ₹100 exercise payment is lower.

This benefits the call option holder because the employee retains the right to purchase the share at the predetermined price in the future. The option’s theoretical value therefore generally increases when the risk-free interest rate rises, assuming all other inputs remain unchanged.

Conversely, a lower risk-free interest rate generally reduces the value of a call option.

This relationship is specific to the relevant option-pricing assumptions; other types of financial instruments may respond differently to interest-rate changes.

Practical Example: Impact on ESOP Fair Value and Compensation Cost

Suppose a company grants 1,000 equity-settled ESOPs to its employees. The current share price, exercise price, expected life, volatility and dividend yield remain unchanged.

Only the risk-free interest rate differs between the two scenarios.

Note: The fair values shown are hypothetical figures used only to demonstrate the relationship. They are not calculated Black-Scholes outputs.

What does this mean?

Under Scenario A, the total compensation cost is ₹65,000. Under Scenario B, it is ₹70,000.

The illustrative difference is ₹5,000. The higher risk-free interest rate increases the assumed fair value per option, resulting in a higher total compensation cost.

The actual impact depends on the complete set of valuation inputs and the option-pricing model.

How does the Risk-Free Interest Rate Affect ESOP Expense Under Ind AS 102?

For a typical equity-settled ESOP, the grant-date fair value is used to determine the compensation cost. This cost is generally recognised over the applicable vesting period as employees provide the required services.

Assume the options vest over four years and straight-line expense recognition is appropriate.

Scenario A:

Total compensation cost = ₹65,000

Annual expense = ₹65,000 ÷ 4 = ₹16,250

Scenario B:

Total compensation cost = ₹70,000

Annual expense = ₹70,000 ÷ 4 = ₹17,500

The difference in annual compensation expense is ₹1,250.

The typical annual journal entry for Scenario A would be:

Employee Compensation Expense A/c Dr. ₹16,250

To ESOP Outstanding Reserve A/c ₹16,250

For Scenario B, the corresponding annual expense would be ₹17,500, subject to the actual vesting conditions and applicable accounting requirements.

For equity-settled awards, the grant-date fair value is generally not remeasured for subsequent movements in the risk-free interest rate. The rate is an input used to determine the initial fair value rather than a recurring adjustment to that value.

Cash-settled share-based payment arrangements follow different measurement requirements and are generally remeasured at each reporting date until settlement.

How Should Companies Select the Risk-Free Interest Rate?

Companies should use a consistent and supportable approach when selecting the risk-free interest rate for ESOP valuation.

Key considerations include:

• Expected life of the option: Select a rate with a maturity that reasonably corresponds to the option’s expected life, rather than automatically using the longest available government security.
• Currency: The interest rate should be consistent with the currency in which the exercise price and underlying share value are denominated.
• Valuation date: Use relevant market data as of the appropriate measurement date.
• Government security yields: Consider suitable government bond yields as a reference for the risk-free rate.
• Valuation consistency: Ensure the rate is applied consistently with the assumptions and methodology used in the option-pricing model

Conclusion

The risk-free interest rate is an important input in the Black-Scholes Model because it affects the present value of the exercise price and, consequently, the theoretical fair value of a call option.

Generally, a higher risk-free interest rate increases the fair value of a call option, while a lower rate reduces it, assuming all other factors remain unchanged.

For companies applying Ind AS 102, selecting an appropriate rate helps ensure that ESOP options are valued using relevant market information and that the resulting compensation expense is determined appropriately.