business-haroun/mba/ch66.org

Section 11 | Lesson 66 - valuing a company vs competition

• Links
• notes
• definitions
  • Discounted Cash Flow (DCF)
    • Basic Steps
    • Formula
    • Key Insight
  • Net Present Value (NPV)
    • Purpose
    • Formula
    • Python Formula
    • Steps
    • Interpretation
    • Key Difference from DCF
  • Weighted Average Cost of Capital (WACC)
    • Formula
    • Variables
    • Notes
  • Cost of Equity (Re)
  • Cost of Debt (Rd)

Links

• TOC | Business
• S12:L66 course video

notes

• easier way to do DCF
• NPV

definitions

Discounted Cash Flow (DCF)

In finance, DCF is a method used to estimate the value of an investment, company, or project based on its expected future cash flows, adjusted for the time value of money.

Basic Steps

1. Forecast future cash flows (e.g., for the next –10 years)
2. Choose a discount rate (often Weighted Average Cost of Capital, WACC)
3. Discount each year’s cash flow to its present value
4. Sum the present values to get the total estimated value

Formula

PV = Cash Flow in Year n / (1 + r)^n

Where:

• r = discount rate
• n = year number
• PV = present value

Key Insight

The result represents the estimated worth of the investment today based on its future cash-generating potential.

Net Present Value (NPV)

NPV is a financial metric used to determine the profitability of an investment or project by comparing the present value of cash inflows with the present value of cash outflows

• https://www.investopedia.com/ask/answers/021115/what-formula-calculating-net-present-value-npv-excel.asp

Purpose

• Shows whether an investment will add value to a business
• Helps compare different investment opportunities

Formula

NPV = Σ [ Cash Flow_t / (1 + r)^t ] − Initial Investment

Where:

• t = year iteration. ie, 1, 2, 3… not the actual year
• r = discount rate WACC
• Cash Flow_t = cash flow at time t

Python Formula

def present_value(t, cash_flow, wacc):
    """
    Calculate the present value of a future cash flow.

    Parameters:
    t          : int   -> Year index (0 for present year, 1 for next year, etc.)
    cash_flow  : float -> Cash flow amount for year t
    wacc       : float -> Weighted Average Cost of Capital (as decimal, e.g., 0.08 for 8%)

    Returns:
    float -> Present value of the given cash flow
    """
    # Discount factor = (1 + WACC)^t
    # The factor by which a future value is reduced to account for time & cost of capital
    discount_factor = (1 + wacc) ** t

    # Present Value = Future Cash Flow / Discount Factor
    return cash_flow / discount_factor

def npv_formula(cash_flow_list, wacc):
    """
    Calculate Net Present Value (NPV) for a series of cash flows.

    Parameters:
        cash_flow_list (list[float]): List of cash flows for each period,
            where index 0 is the first period's cash flow.
        wacc (float): Weighted Average Cost of Capital (discount rate)
            expressed as a decimal (e.g., 0.08 for 8%).

    Returns:
        float: Net Present Value (NPV) of the given cash flows.

    Notes:
        Uses the present_value() function for discounting each cash flow.
        Assumes cash flows occur at the end of each period.
    """
    net_value = 0
    for index, cash_flow in enumerate(cash_flow_list):
        net_value += present_value(t=index, cash_flow=cash_flow, wacc)

    return net_value

def npv_value(cash_flow_list, initial_outlay, wacc):
    """
    Calculate Net Present Value (NPV) by subtracting the initial investment
    from the present value of future cash flows.

    Parameters:
        cash_flow_list (list[float]): List of future cash flows for each period,
            where index 0 is the first period's cash flow.
        initial_outlay (float): The initial investment or project cost.
        wacc (float): Weighted Average Cost of Capital (discount rate)
            expressed as a decimal (e.g., 0.08 for 8%).

    Returns:
        float: Net Present Value (NPV).

    Notes:
        This function calls net_pv() to calculate the sum of discounted
        cash flows, then subtracts the initial_outlay.
    """
    return net_pv(cash_flow_list, wacc) - initial_outlay

Steps

1. Identify each expected cash inflow for future periods.
2. Discount each inflow using the discount rate \( r \) and period \( t \).
3. Add the discounted values together.
4. Subtract the initial investment cost.

Interpretation

• NPV > 0 → Investment is profitable
• NPV = 0 → Break-even
• NPV < 0 → Investment will lose money

Key Difference from DCF

• DCF is the method of valuing future cash flows
• NPV is the result after subtracting the initial cost from the DCF

Weighted Average Cost of Capital (WACC)

Formula

WACC = \frac{E}{V} \times Re + \frac{D}{V} \times Rd \times (1 - Tc)

Variables

• \( Re \) = Cost of Equity
• \( Rd \) = Cost of Debt
• \( E \) = Market value of the firm's equity
• \( D \) = Market value of the firm's debt
• \( V \) = \( E + D \) (Total market value of financing)
• \( \frac{E}{V} \) = Percentage of financing that is equity
• \( \frac{D}{V} \) = Percentage of financing that is debt
• \( Tc \) = Corporate tax rate

Notes

• WACC represents the average rate that a company is expected to pay to finance its assets.
• It is used as the discount rate in DCF calculations.

Cost of Equity (Re)

• The return required by equity investors for investing in a company.

• Often estimated using the Capital Asset Pricing Model (CAPM):

  Re = Rf + β * (Rm - Rf)
  Rf = Risk-free rate
  β  = Beta (measure of stock's volatility vs. market)
  Rm = Expected market return

Cost of Debt (Rd)

• The effective interest rate a company pays on its borrowed funds, adjusted for tax savings.

• Formula:

  Rd = Effective Interest Rate * (1 - Tc)

• Example:

  If Effective Interest Rate = 6%
  Tc = 25%
  Rd = 0.06 * (1 - 0.25) = 0.045 (4.5%)