Dcf model principles for fundamental guide

What is a Discounted Cash Flow Model? Components of DCF Model Mathematical Framework of DCF Terminal Value Calculation Analytical Derivation of DCF R Implementation Applications and Takeaways

Discounted Cash Flow Model

Principles, Analysis, and Implementation

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Outline

What is a Discounted Cash Flow Model?

Components of DCF Model

Mathematical Framework of DCF

Terminal Value Calculation

Analytical Derivation of DCF

R Implementation

Applications and Takeaways

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What is a Discounted Cash Flow Model?

Discounted Cash Flow (DCF) is a valuation method used to esti- mate the value of an investment based on its expected future cash flows:

> Foundational valuation technique in finance

> Based on the time value of money principle

> Estimates intrinsic value rather than market value

DCF serves as a comprehensive valuation tool that:

> Quantifies the present value of future cash flows

> Enables comparison between different investment opportunities

_ CF: _

> Provides a simple formula: Value = So}, Gary + chy

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Components of DCF Model

A complete DCF model consists of three essential components:

1 Cash Flow Projections: Forecasting future free cash flows

P Based on revenue growth, margins, capital expenditures, and working capital

> Typically projected for 5-10 years explicitly

2 Terminal Value: Capturing value beyond the forecast period

Pm Perpetuity growth method: TV = ret

> Exit multiple method: TV = FCF, x “Multiple

3 Discount Rate: Reflecting the time value of money and risk

> Often uses Weighted Average Cost of Capital (WACC): WACC =

txEze+xrazx(1—t)

> Must reflect the specific risk profile of cash flows

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Mathematical Framework of DCF

The general formula for a DCF model is:

Value = -q " net Gan ain (1) Where:

> CF; is the expected cash flow in period t

> ris the discount rate (typically WACC)

> nis the forecast period

> TV is the terminal value

Properties

> Higher discount rates lead to lower present values

> Cash flows further in the future have less impact on present value

> Terminal value often represents 60-80% of total value

> Sensitivity to discount rate and growth assumptions increases with time

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Terminal Value Calculation

Terminal value captures all cash flows beyond the explicit forecast period:

— FCFny1 FCFy x (1+) (2)

Key considerations for terminal value:

> Growth rate (g) must be sustainable in perpetuity

> Typically limited to long-term GDP growth (2-3%)

> Assumes the company reaches steady state

> For stable businesses, g should not exceed r

Limitations:

> High sensitivity to small changes in inputs

> Assumes going concern with infinite life

> Challenging to estimate for cyclical businesses

> May overvalue companies with unsustainable returns

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Analytical Derivation of DCF - Part 1

Starting Point: Present Value Formula

FV

Step 1: Extending to Multiple Cash Flows

¬ CF,

Step 2: Incorporating Terminal Value

"CF;

Analytical Derivation of DCF - Part 2

Step 3: Deriving the Terminal Value

For the perpetuity growth model, we start with an infinite sum:

If cash flows grow at a constant rate g, then:

Step 4: Deriving the Gordon Growth Model

CFạ.+ - CFạ.i(1+g) , CFa¿i(1+g}?

= Cy x ĐT

1

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Analytical Derivation of DCF - Part 3

Step 5: Putting It All Together

Value — Laat +"

=> mm (l+r)" x r—g

n

CF, CFax<(1+g)

Step 6: Sensitivity Analysis

The sensitivity of value to the discount rate:

+? Grn On x (rep This shows the high sensitivity of DCF to discount rate changes, particu- larly for the terminal value component

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R Implementation - Example

# Example company parameters

tax_rate <- 0.25 # 25% tax rate

# DCF parameters

# Generate financial projections

financials <- simulate_financials(

initial_revenue, projection_years,

growth_rates, ebitda_margins,

capex_percent, nwc_percent, tax_rate

)

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R Implementation - Example

# Calculate DCF valuation

dcf_result <- dcf_valuation(financials$FCF, terminal_growth, discount_rate)

print (paste("PV of Projected FCF:", round(dcf_result$pv_cf, 2)))

[1] "PV of Projected FCF: 140.78”

print (paste("PV of Terminal Value:", round(dcf_result$pv_terminal, 2)))

[1] "PV of Terminal Value: 774.62”

print (paste("Enterprise Value:", round(dcf_result$enterprise_value, 2)))

[1] "Enterprise Value: 915.4”

print (paste("Terminal Value Percentage:", round(dcf_result$pv_terminal_percent

[1] " Terminal Value Percentage: 84.62”

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Sensitivity Analysis Visualization

DCF Sensitivity Analysis 0.030

0.025

0.020

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Enterprise Value ($M)

1400

1200

1000

= 800

Discount Rate (WACC)

The heatmap shows enterprise value sensitivity to changes in discount rate and growth rate

The white dot represents the base case scenario (discount rate = 10%, growth rate = 2%)

Values increase (lighter colors)) with lower discount rates and higher growth rates

The contour lines represent equal enterprise value levels

Note the non-linear relationship: values increase exponentially as the growth rate approaches the discount rate

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Scenario Analysis Visualization

1600

1200

800

400

Enterprise Value by Scenario

$1487M

Component | PV of Terminal Value | | PV of Cash Flows The chart shows enterprise value breakdown for three scenarios: Bear, Base, and Bull

In all scenarios, terminal value (light blue) represents the majority of enterprise value

The Bear case shows 52% decrease in value from Base case due to the combined impact of higher discount rate, lower growth rate, and lower cash flows The Bull case shows 73% increase in value from Base case due to the combined impact of lower discount rate, higher growth rate, and higher cash flows Note the exponential relationship: small changes in inputs create large valuation differences

Monte Carlo Simulation Analysis

Monte Carlo Simulation of Enterprise Value 1,000 simulations with varying inputs

1 1

I I

I I

I I

I I

I I

Cc

oO I I

2 I

Q

iL I

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Enterprise Value ($M)

> Monte Carlo simulation with 1,000 runs, varying growth rates, discount rates, and cash flow levels

> The distribution is right-skewed, reflecting the non-linear relationship between inputs and valuation

> The median value of $867M is less than the mean value of $894M due to this skewness

> 95% confidence interval: $590M to $1284M

> Wide distribution emphasizes the uncertainty inherent in DCF valuation and the importance of range estimates

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Applications and Takeaways

Key Applications

> Investment Valuation: Determining intrinsic value of stocks and businesses

> M&A Analysis: Supporting pricing decisions in acquisition scenarios

> Capital Budgeting: Evaluating potential investment projects

> Equity Research: Informing buy/sell recommendations

Takeaways

> DCF provides a theoretically sound approach to valuation based on future cash generation

> Quality of inputs significantly affects reliability of results

> Sensitivity analysis is crucial due to high impact of small changes in key inputs

> Monte Carlo simulation offers a more robust way to incorporate un- certainty

> DCF should be used alongside other valuation methods, not in isola-