Net Present Value Study Notes

Net Present Value Rule

Objective

  • Understanding the net present value (NPV) rule for project investment decisions in corporations.

  • Aim to convince the audience that the NPV rule maximizes corporate value.

  • Overview of how to calculate net present value.

Future Value (FV)

  • Future value defined as the sum of the initial deposit and the interest earned from it.

  • Example: Depositing $100 in a bank account with a 10% interest rate.

    • Calculation:

    • Future Value = Initial Deposit + Interest

    • Interest = 10% of $100 = $10

    • Future Value = $100 + $10 = $110

  • General formula for future value when interest rate is $r$:

    • FV=100imes(1+r)FV = 100 imes (1 + r)

  • Concept: Moving cash flow forward in time.

Present Value (PV)

  • Present value represents how much is needed today to meet a future cash requirement.

  • Example: Need $100 in one year.

    • Calculation:

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

    • Solving gives:

      • PV=rac1001+rPV = rac{100}{1 + r}

  • For an interest rate of $r = 10\%$:

    • PV=rac1001+0.1=rac1001.1extor90.91PV = rac{100}{1 + 0.1} = rac{100}{1.1} ext{ or } 90.91

  • Note: The concept of bringing the future cash flow back in time.

General Present Value Formula

  • For any cash flow $C$ in one year,

    • PV=racC1+RPV = rac{C}{1 + R}

  • Term: Present Discounted Value (PDV) is used because, with $R > 0$, the present value equals less than the future cash flow, hence discounted.

Considerations about the Interest Rate (R)

  • The reasoning for expecting $R o 0$:

    • Negative interest rates, such as -8%, imply that depositing $100 would yield only $92 next year. This is typically unattractive for individuals.

  • The expectation is that traditionally $R o 0$ or greater:

    • Holding money in a secure location (like a cookie jar) seems preferable than placing it in a poor-performing bank.

  • Historical Context: During the 2008 Financial Crisis,

    • $R$ approached $0$ or even negative values, leading to higher costs for safe storage solutions (e.g., safes).

    • Asset protection became a priority, leading to increases in safe and firearm sales.

Net Present Value (NPV)

  • NPV is calculated as follows:

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

    • Where:

    • $C_0$ is the cost of the investment (usually negative),

    • $C_1$ is the expected cash flow (positive).

  • Conceptual Framework: NPV emphasizes that the initial investment cost is included.

Example of Net Present Value Calculation

  • Scenario: Software development requiring an investment of $500,000 with an expected payoff of $540,000 next year.

  • Calculations:

    • NPV=−500,000+rac540,0001+0.05NPV = -500,000 + rac{540,000}{1 + 0.05}

    • For a discount rate ($R$) of $5 ext{%}$, the simplified calculation will show:

    • Convert $500,000 into millions: -0.5 million.

    • Discount future payoff:

      • Payoff in millions = 540,000.

      • Discounting gives:

      • NPV=−0.5+rac0.5401.05=−0.5+0.5142857extmillion=0.0142857extmillionNPV = -0.5 + rac{0.540}{1.05} = -0.5 + 0.5142857 ext{ million} = 0.0142857 ext{ million}

      • Conclusively,
        NPVextisapproximately14,300NPV ext{ is approximately } 14,300.

Conclusion

  • Understanding NPV is vital for financial decision-making regarding investment projects as it provides a methodology for determining the potential increase in corporate value.