Net Present Value Rule Overview

Net Present Value Rule

  • Introduction to the Net Present Value Rule

    • Purpose: To determine which projects are worth investing in within a corporation.

    • Aim of the Section: Convince that the net present value (NPV) rule is the optimal criterion for project selection.

    • Importance of Calculating NPV: It increases the value of the corporation.

Future Value

  • Definition: The future value (FV) is the total amount of money an investment will grow to over a period at a specified interest rate.

    • Example: If $100 is deposited in a bank account at a 10% interest rate, the future value calculation is as follows:

    • Calculation:

      • Future Value = Deposit + Interest

      • Future Value = $100 + ($100 imes 0.10) = $110

    • General Formula:

    • FV=Cimes(1+r)FV = C imes (1 + r)

    • Where:

      • CC = initial cash flow

      • rr = interest rate

    • Note: This represents moving cash flow forward in time.

Present Value

  • Definition: The present value (PV) is the current worth of a future sum of money or stream of cash flows given a specified rate of return.

    • Question: If one needs $100 in one year, what should be set aside today?

    • Rearranging the future value equation:

      • 100=PVimes(1+r)100 = PV imes (1 + r)

    • Solving for Present Value:

    • PV=racC1+rPV = rac{C}{1 + r}

    • If rr = 10%, then:

      • PV=rac1001.10=90.91PV = rac{100}{1.10} = 90.91

    • General Formula for Present Value:

    • If CC is the cash flow in one year, then:

      • PV=racC1+rPV = rac{C}{1 + r}

    • Concept of Present Discounted Value:

    • Refers to the property that if r > 0, then PV < C.

    • Implications of a Zero Interest Rate:

    • If rr = 0, then PV=CPV = C.

    • Example of Negative Interest Rates:

    • If a bank offers a rate of -8%, depositing $100 yields only $92 next year, leading to a preference for holding cash instead of investing.

    • Impediments for Negative Rate:

    • Storing cash might become more appealing than negative return accounts.

    • Historical Context: During the 2008 financial crisis, interest rates dropped to zero or below.

Net Present Value (NPV)

  • Definition: Net Present Value is a method for capital budgeting that calculates the difference between the present value of cash inflows and outflows over a period.

    • Formula:

    • NPV=C<em>0+racC</em>11+rNPV = C<em>0 + rac{C</em>1}{1 + r}

    • Where:

      • C0C_0 = Initial cost of investment (usually negative)

      • C1C_1 = Cash inflow in one year (usually positive)

    • Purpose: Emphasizes both the upfront cost and the anticipated returns.

Example of NPV Calculation

  • Scenario: A software developer invests $500,000 to create software.

    • Initial Investment:

    • C0=−500,000C_0 = -500,000

    • Future Cash Inflow:

    • C1=540,000C_1 = 540,000

    • Calculation Steps:

    • NPV in millions:

      • NPV=−0.5+rac0.541+rNPV = -0.5 + rac{0.54}{1 + r}

      • If rr = 5%:

      • NPV=−0.5+rac0.541.05NPV = -0.5 + rac{0.54}{1.05}

      • Calculate:

        • NPVext(approximately)=14,300NPV ext{ (approximately) } = 14,300

    • Insight: Positive NPV indicates a profitable investment decision.