In-Depth Notes on Net Present Value and Financial Decision-Making

Net Present Value (NPV)

  • Definition: NPV compares the market value of a project to its cost. It measures how much value is created from undertaking an investment and is also known as Discounted Cash Flow (DCF) Analysis.

  • Formula:
    NPV=PVextofallbenefits−PVextofallcostsNPV = PV ext{ of all benefits} - PV ext{ of all costs}

    • Accept the project if NPV > 0 which indicates expected increase in the wealth of the owners.

  • Steps to Calculate NPV:

    1. Estimate expected future cash flows - critical with investment uncertainty.
    2. Determine required return for the project based on its risk to identify the appropriate discount rate.
    3. Compute present value (PV) of all cash flows, then subtract the initial investment.

  • Example Calculation:

    • Year 0: CF = -165,000
    • Year 1: CF = 63,120
    • Year 2: CF = 70,800
    • Year 3: CF = 91,080
    • Required return = 12%
    • NPV = rac{63,120}{(1.12)^1} + rac{70,800}{(1.12)^2} + rac{91,080}{(1.12)^3} - 165,000 = 12,627.42
    • Decision: Accept since NPV > 0.

Decision Criteria in NPV

  • Pros:

    • Adjusts for the time value of money.
    • Considers risk and shareholder value maximization.

  • Cons:

    • Expresses value in dollar terms rather than percentages, potentially misleading for project scales.
    • Ignores life of the project, biased towards longer-term projects.

Payback Rule

  • Definition: The payback rule measures how long it takes to recover the initial investment.

  • Implementation:

    1. Estimate future cash flows.
    2. Subtract cumulative cash flows from the initial cost until recovered.
    • Accept if the payback period is less than a preset threshold.

  • Example:

    • Recover Year 1: 165,000 - 63,120 = 101,880 remaining.
    • Recover Year 2: 101,880 - 70,800 = 31,080 remaining.
    • Recover Year 3: 31,080 - 91,080 = -60,000
    • Conclusion: Project pays back in Year 3.

  • Pros:

    • Easy to understand; emphasizes liquidity.

  • Cons:

    • Ignores time value of money and future cash flows beyond the cutoff date.

Discounted Payback Rule

  • Definition: Improves the payback rule using discounted cash flows.
  • Computation Steps:
    1. Estimate cash flows.
    2. Compute PVs of expected cash flows.
    3. Compare with initial investment to determine when it is recovered.

Internal Rate of Return (IRR)

  • Definition: The IRR is the discount rate at which the NPV equals zero. If IRR exceeds the required return, the project should be accepted.
  • Caution on IRR Pitfalls:
    • Multiple IRRs may occur with non-conventional cash flows (cash flows changing signs).
    • Comparing projects based solely on IRR can be misleading - it ignores project scale and the magnitude of returns.
  • Example of Non-Conventional Cash Flows:
    • Initial investment: -90,000; later cash flows: 132,000, 100,000, -150,000.
    • NPV: 1,769.54; IRRs: 10.11% and 42.66%, consider both cautiously.