Merton Model Calculator

✖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.ⓘ Market Value of Company Assets [V]			+10% -10%
✖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.ⓘ Market Value of Company Debt [D_M]			+10% -10%
✖Risk Free Interest Rate is the theoretical rate of return of an investment with zero risks.ⓘ Risk Free Interest Rate [Rf]			+10% -10%
✖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.ⓘ Volatility of Company Asset Value [σ_cav]			+10% -10%
✖Time to Maturity is the time required to mature a bond.ⓘ Time to Maturity [T]			+10% -10%

✖Distance to the Default is a financial metric that measures how far a company's current value (assets) is from its default point (liabilities).ⓘ Merton Model [DD]

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Formula

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Merton Model

Formula

`"DD" = ln("V"/"D"_{"M"})+(("Rf"+("σ"_{"cav"})^2/2)*"T")/("σ"_{"cav"}*sqrt("T"))`

Example

`"126.1931"=ln("20000"/"10000")+(("5"+("0.2")^2/2)*"25")/("0.2"*sqrt("25"))`

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Merton Model Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
DD = ln(V/D_M)+((Rf+(σ_cav)^2/2)*T)/(σ_cav*sqrt(T))
This formula uses 2 Functions, 6 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., 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., sqrt(Number)

Variables Used

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).
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.
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.
Risk Free Interest Rate - Risk Free Interest Rate is the theoretical rate of return of an investment with zero risks.
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.
Time to Maturity - Time to Maturity is the time required to mature a bond.

STEP 1: Convert Input(s) to Base Unit

Market Value of Company Assets: 20000 --> No Conversion Required
Market Value of Company Debt: 10000 --> No Conversion Required
Risk Free Interest Rate: 5 --> No Conversion Required
Volatility of Company Asset Value: 0.2 --> No Conversion Required
Time to Maturity: 25 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

DD = ln(V/D_M)+((Rf+(σ_cav)^2/2)*T)/(σ_cav*sqrt(T)) --> ln(20000/10000)+((5+(0.2)^2/2)*25)/(0.2*sqrt(25))

Evaluating ... ...

DD = 126.19314718056

STEP 3: Convert Result to Output's Unit

126.19314718056 --> No Conversion Required

FINAL ANSWER

126.19314718056 ≈ 126.1931 <-- Distance to the Default

(Calculation completed in 00.004 seconds)

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BMS College of Engineering (BMSCE), Bangalore

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Merton Model

Go 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))

Baumol's Model

Go Cost of Providing a Service = sqrt((2*Cost of Conversion*Total Requirement of Cash)/Interest Rate)

Cash Conversion Cycle

Go Cash Conversion Cycle = Days Inventory Outstanding+Days Sales Outstanding-Days Payables Outstanding

Miller Orr Model

Go Miller Orr Model = 3*((3*Cost of Conversion*Variance)/(4*Interest Rate/360))^(1/3)

Cash Surrender Value

Go Cash Surrender Value = mod(Enhanced Accumulated Value,Surrender Charges)

Cash Coverage

Go Cash Coverage = Earnings before Interest and Taxes/Interest Expense

Cash Burn Rate

Go Net Burn = Total Monthly Cash Sales-Total Monthly Cash Expenses

Implied Cash Runway

Go Implied Cash Runway = Cash Balance/Net Burn

Cash Budget

Go Cash Budget = Total Receipts-Total Payments

Merton Model Formula

What is Merton Model?

The Merton Model, also known as the Structural Credit Risk Model, is 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. The model is based on the idea that a company defaults on its debt when the value of its assets falls below a certain threshold relative to its liabilities.
Assumptions:
The company's assets follow a geometric Brownian motion, similar to stock prices in the Black-Scholes model for options pricing.
The company has a single, risk-free debt obligation with a fixed maturity.
The company's liabilities are assumed to be constant and known.
The default threshold represents the point at which the value of the company's assets falls below its liabilities, leading to default. This threshold can be expressed as the ratio of the company's liabilities to its assets.

How to Calculate Merton Model?

Merton Model calculator 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 calculate 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 calculate Merton Model using this online calculator? To use this online calculator 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. Here is how the Merton Model calculation can be explained with given input values -> 126.1931 = ln(20000/10000)+((5+(0.2)^2/2)*25)/(0.2*sqrt(25)).

FAQ

What is Merton Model?

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 and is represented as DD = ln(V/D_M)+((Rf+(σ_cav)^2/2)*T)/(σ_cav*sqrt(T)) or 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)). 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, 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, Risk Free Interest Rate is the theoretical rate of return of an investment with zero risks, 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 & Time to Maturity is the time required to mature a bond.

How to calculate Merton Model?

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 is calculated using 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 calculate Merton Model, you need 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). With our tool, you need to enter the respective value for Market Value of Company Assets, Market Value of Company Debt, Risk Free Interest Rate, Volatility of Company Asset Value & Time to Maturity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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