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Merton Model Formula

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Distance to the Default is a financial metric that measures how far a company's current value (assets) is from its default point (liabilities). Check FAQs

DD = \ln (\frac{V}{D M}) + \frac{(Rf + \frac{{(σ cav)}^{2}}{2}) \cdot T}{σ cav \cdot \sqrt{T}}

DD - Distance to the Default?V - Market Value of Company Assets?D_M - Market Value of Company Debt?Rf - Risk Free Interest Rate?σ_cav - Volatility of Company Asset Value?T - Time to Maturity?

Merton Model Example

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Here is how the Merton Model equation looks like with Values.

Here is how the Merton Model equation looks like with Units.

Here is how the Merton Model equation looks like.

126.1931 = \ln (\frac{20000}{10000}) + \frac{(5 + \frac{{(0.2)}^{2}}{2}) \cdot 25}{0.2 \cdot \sqrt{25}}

126.1931 = \ln (\frac{20000}{10000}) + \frac{(5 + \frac{{(0.2)}^{2}}{2}) \cdot 25}{0.2 \cdot \sqrt{25}}

126.1931 = \ln (\frac{20000}{10000}) + \frac{(5 + \frac{{(0.2)}^{2}}{2}) \cdot 25}{0.2 \cdot \sqrt{25}}

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Merton Model Solution

Follow our step by step solution on how to calculate Merton Model?

FIRST Step Consider the formula

DD = \ln (\frac{V}{D M}) + \frac{(Rf + \frac{{(σ cav)}^{2}}{2}) \cdot T}{σ cav \cdot \sqrt{T}}

Next Step Substitute values of Variables

∴

DD = \ln (\frac{20000}{10000}) + \frac{(5 + \frac{{(0.2)}^{2}}{2}) \cdot 25}{0.2 \cdot \sqrt{25}}

Next Step Prepare to Evaluate

∴

DD = \ln (\frac{20000}{10000}) + \frac{(5 + \frac{{(0.2)}^{2}}{2}) \cdot 25}{0.2 \cdot \sqrt{25}}

Next Step Evaluate

∴

DD = 126.19314718056

LAST Step Rounding Answer

∴

DD = 126.1931

Merton Model Formula Elements

Variables

Functions

Distance to the Default

Distance to the Default is a financial metric that measures how far a company's current value (assets) is from its default point (liabilities).

Symbol: DD

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Distance to the Default

Market Value of Company Assets

Market Value of Company Assets refers to the total value that investors in the open market would assign to all of the company's assets.

Symbol: V

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Market Value of Company Assets

Market Value of Company Debt

Market Value of Company Debt refers to the total value that investors in the open market would assign to all of the company's outstanding debt obligations.

Symbol: D_M

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Market Value of Company Debt

Risk Free Interest Rate

Risk Free Interest Rate is the theoretical rate of return of an investment with zero risks.

Symbol: Rf

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Risk Free Interest Rate

Volatility of Company Asset Value

Volatility of Company Asset Value refers to the degree of variation or fluctuations in the market value of the company's assets over a certain period.

Symbol: σ_cav

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Volatility of Company Asset Value

Time to Maturity

Time to Maturity is the time required to mature a bond.

Symbol: T

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Time to Maturity

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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C = \sqrt{\frac{2 \cdot b \cdot t}{R}}

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Z = 3 \cdot {(\frac{3 \cdot b \cdot σ}{4 \cdot \frac{R}{360}})}^{\frac{1}{3}}

Go Cash Coverage

Cash cov = \frac{EBIT}{Int}

How to Evaluate Merton Model?

Merton Model evaluator uses Distance to the Default = ln(Market Value of Company Assets/Market Value of Company Debt)+((Risk Free Interest Rate+(Volatility of Company Asset Value)^2/2)*Time to Maturity)/(Volatility of Company Asset Value*sqrt(Time to Maturity)) to evaluate the Distance to the Default, The Merton Model formula is defined as a financial model developed by economist Robert C. Merton. It provides a framework for assessing the credit risk of a company's debt by analyzing the relationship between the company's assets and liabilities. Distance to the Default is denoted by DD symbol.

How to evaluate Merton Model using this online evaluator? To use this online evaluator for Merton Model, enter Market Value of Company Assets (V), Market Value of Company Debt (D_M), Risk Free Interest Rate (Rf), Volatility of Company Asset Value (σ_cav) & Time to Maturity (T) and hit the calculate button.

FAQs on Merton Model

What is the formula to find Merton Model?

The formula of Merton Model is expressed as Distance to the Default = ln(Market Value of Company Assets/Market Value of Company Debt)+((Risk Free Interest Rate+(Volatility of Company Asset Value)^2/2)*Time to Maturity)/(Volatility of Company Asset Value*sqrt(Time to Maturity)). Here is an example- 126.1931 = ln(20000/10000)+((5+(0.2)^2/2)*25)/(0.2*sqrt(25)).

How to calculate Merton Model?

With Market Value of Company Assets (V), Market Value of Company Debt (D_M), Risk Free Interest Rate (Rf), Volatility of Company Asset Value (σ_cav) & Time to Maturity (T) we can find Merton Model using the formula - Distance to the Default = ln(Market Value of Company Assets/Market Value of Company Debt)+((Risk Free Interest Rate+(Volatility of Company Asset Value)^2/2)*Time to Maturity)/(Volatility of Company Asset Value*sqrt(Time to Maturity)). This formula also uses Natural Logarithm (ln), Square Root (sqrt) function(s).

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Merton Model Formula

Merton Model Example

Merton Model Solution

Merton Model Formula Elements

Other formulas in Cash Management category

How to Evaluate Merton Model?

FAQs on Merton Model

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