#+title: Section 11 | Lesson 66 - valuing a company vs competition
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../_share/media/css/org-media-sass/categories/business.css" />
#+OPTIONS: H:6

* Links
- [[./../mba-main.org][TOC | Business]]
- [[https://www.udemy.com/course/an-entire-mba-in-1-courseaward-winning-business-school-prof/learn/lecture/4301156#overview][S12:L66 course video]]
- [[https://www.udemy.com/course/an-entire-mba-in-1-courseaward-winning-business-school-prof/learn/lecture/4321706#overview][S12:L67 course video]]

* notes
- easier way to do [[*Discounted Cash Flow (DCF)][DCF]]
- [[*Net Present Value (NPV)][NPV]]
** how do we look at companies
- www.sec.gov
- get the S1 - IPO filing document
- look at each line item as a percentage of revenue

** IPO prospectus
- number of shares on top
- firms involved
- inside says the use of proceeds
  - what the money will be used for
    - hiring people
    - general business purposes
    - opening new offices
    - aqcuiring new businesses

- every risk
- also referred to as an S1

- you can find it in sec.gov, look for an S1 on any company

* 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
   #+BEGIN_SRC text
   PV = Cash Flow in Year n / (1 + r)^n
   #+END_SRC
   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
   #+BEGIN_SRC text
   NPV = Σ [ Cash Flow_t / (1 + r)^t ] − Initial Investment
   #+END_SRC
   Where:
   - t = year iteration.  ie, 1, 2, 3... not the actual year
   - r = discount rate [[*Weighted Average Cost of Capital (WACC)][WACC]]
   - Cash Flow_t = cash flow at time t

*** Python Formula
#+BEGIN_SRC python
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
#+END_SRC

#+BEGIN_SRC python
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
#+END_SRC

#+BEGIN_SRC python
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
#+END_SRC

*** 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
#+BEGIN_SRC latex
WACC = \frac{E}{V} \times Re + \frac{D}{V} \times Rd \times (1 - Tc)
#+END_SRC

*** Variables
- \( Re \) = [[*Cost of Equity (Re)][Cost of Equity]]
- \( Rd \) = [[*Cost of Debt (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):
     #+BEGIN_SRC
     Re = Rf + β * (Rm - Rf)
     Rf = Risk-free rate
     β  = Beta (measure of stock's volatility vs. market)
     Rm = Expected market return
     #+END_SRC

** Cost of Debt (Rd)
   - The effective interest rate a company pays on its borrowed funds, adjusted for tax savings.
   - Formula:
     #+BEGIN_SRC
     Rd = Effective Interest Rate * (1 - Tc)
     #+END_SRC
   - Example:
     #+BEGIN_SRC
     If Effective Interest Rate = 6%
     Tc = 25%
     Rd = 0.06 * (1 - 0.25) = 0.045 (4.5%)
     #+END_SRC