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 - [[https://www.udemy.com/course/an-entire-mba-in-1-courseaward-winning-business-school-prof/learn/lecture/4301156#overview][S12:L66 course video]]
 
 * notes
+- easier way to do [[*Discounted Cash Flow (DCF)][DCF]]
+- [[*Net Present Value (NPV)][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
+   #+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