Discounted Cash Flows
By Adam Bozman in Theme Features R
June 3, 2024
Understanding Cash Flows in Financial Modeling
Types of Cash Flows
Cash flows are crucial for evaluating a company’s financial health and investment potential. They can be categorized into three main types:
Operating Cash Flows (OCF)
 Generated from the core business operations.
 Includes cash receipts from sales and cash payments for expenses.
 Formula: [ \text{OCF} = \text{Net Income} + \text{Noncash Expenses} + \text{Changes in Working Capital} ]
Investing Cash Flows (ICF)
 Associated with the purchase and sale of longterm assets.
 Includes capital expenditures and proceeds from asset sales.
 Formula: [ \text{ICF} = \text{Capital Expenditures}  \text{Proceeds from Sale of Assets} ]
Financing Cash Flows (FCF)
 Related to borrowing, repaying debt, and equity transactions.
 Includes dividends paid and proceeds from issuing stock or debt.
 Formula: [ \text{FCF} = \text{Proceeds from Issuance of Debt or Equity}  \text{Repayments} + \text{Dividends Paid} ]
Cash Flows to Firm vs. Cash Flows to Equity
Cash Flows to the Firm (FCFF)
 Represents the cash flow available to all capital providers (both debt and equity holders).
 FCFF is used in enterprise valuation.
 Formula: [ \text{FCFF} = \text{Net Income} + \text{Noncash Expenses} + \text{Interest} \times (1  \text{Tax Rate})  \text{Changes in Working Capital}  \text{Capital Expenditures} ]
Cash Flows to Equity (FCFE)
 Represents the cash flow available to equity shareholders.
 FCFE is used in equity valuation.
 Formula: [ \text{FCFE} = \text{FCFF}  \text{Interest} \times (1  \text{Tax Rate}) + \text{Net Borrowing} ]
The Math Underpinning Cash Flows
Time Value of Money (TVM)
Fundamental concept stating that money available now is worth more than the same amount in the future due to its earning potential.
Net Present Value (NPV)
 The value of all future cash flows (both incoming and outgoing) over the entire life of an investment discounted to the present.
 Formula: [ \text{NPV} = \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t}  \text{Initial Investment} ]
 (CF_t) is the cash flow at time (t), (r) is the discount rate, and (n) is the number of periods.
Discounted Cash Flow (DCF) Processes
Generic DCF Process

Forecast Future Cash Flows:
 Project the company’s future operating cash flows, capital expenditures, and changes in working capital.

Determine the Discount Rate:
 Use the Weighted Average Cost of Capital (WACC) for FCFF or the Cost of Equity for FCFE.

Calculate the Terminal Value:
 Estimate the value of the company beyond the forecast period.
 Formula: [ \text{Terminal Value} = \frac{FCF_{n+1}}{(r  g)} ]
 Where (FCF_{n+1}) is the cash flow in the first year after the forecast period, (r) is the discount rate, and (g) is the growth rate.

Discount Cash Flows to Present Value:
 Discount the forecasted cash flows and terminal value back to present value using the discount rate.

Summing Up:
 Sum the present value of the forecasted cash flows and the terminal value to get the total enterprise value or equity value.
DCF in Excel

Set Up Your Spreadsheet:
 Create columns for each year of the forecast period.
 Include rows for revenues, expenses, taxes, changes in working capital, capital expenditures, and resulting cash flows.

Calculate Each Component:
 Use Excel formulas to project revenues and expenses.
 Calculate free cash flows for each year.

Discount Cash Flows:
 Use the NPV function to discount cash flows back to the present value.
 Formula in Excel:
=NPV(discount_rate, cash_flows_range)

Calculate Terminal Value:
 Use the formula for terminal value.
 Include the terminal value in your NPV calculation.
 Formula in Excel:
=Terminal_Value / (1 + discount_rate)^years

Sum the Present Values:
 Add the NPV of the forecast period and the discounted terminal value.
 Example Spreadsheet Setup:
 Column A: Year
 Column B: Cash Flows
 Column C: Discounted Cash Flows (
=B2/(1+$B$1)^A2
)
DCF in Python Jupyter Notebooks
import numpy as np
# Define cash flows and discount rate
cash_flows = np.array([100000, 20000, 30000, 40000, 50000, 60000])
discount_rate = 0.1
# Calculate NPV
npv = np.npv(discount_rate, cash_flows)
print(f"Net Present Value (NPV): {npv}")
# Calculate Terminal Value
fcf_next_year = 60000
growth_rate = 0.02
terminal_value = fcf_next_year / (discount_rate  growth_rate)
terminal_value_pv = terminal_value / (1 + discount_rate) ** len(cash_flows)
print(f"Terminal Value (Present Value): {terminal_value_pv}")
# Total Value
total_value = npv + terminal_value_pv
print(f"Total Value: {total_value}")