📊 1. Net Present Value (NPV)

✅ What is NPV?

Net Present Value is the difference between the present value of cash inflows and the present value of cash outflows over the life of a project.

📘 Formula:

NPV=∑Ct(1+r)t−C0NPV = sum frac{C_t}{(1 + r)^t} – C_0

Where:

  • CtC_t = Cash inflow in year tt

  • C0C_0 = Initial investment (cash outflow)

  • rr = Discount rate (cost of capital)

  • tt = Time period

💡 Decision Rule:

  • NPV > 0 → Accept the project (adds value)

  • NPV < 0 → Reject the project

📈 Advantages:

  • Considers time value of money

  • Uses all cash flows

  • Directly relates to shareholder value

⚠️ Limitations:

  • Requires accurate cash flow forecasts and discount rate

  • Not suitable when comparing projects of unequal size/lifespan (use PI for that)

📉 2. Internal Rate of Return (IRR)

✅ What is IRR?

IRR is the discount rate that makes NPV = 0. It represents the project’s expected annual rate of return.

📘 Formula (solving for IRR numerically):

0=∑Ct(1+IRR)t−C00 = sum frac{C_t}{(1 + IRR)^t} – C_0

 

Decision Rule:

  • IRR > cost of capital → Accept

  • IRR < cost of capital → Reject

📈 Advantages:

  • Easy to interpret as a percentage

  • Useful for ranking multiple projects

⚠️ Limitations:

  • May produce multiple IRRs with unconventional cash flows

  • Can be misleading for mutually exclusive or non-standard projects

⏱️ 3. Payback Period and Discounted Payback Period

🔹 A. Payback Period

Time it takes for the project to recover its initial investment without discounting future cash flows.

📘 Formula:

Payback Period=Time when cumulative cash inflow = initial investmenttext{Payback Period} = text{Time when cumulative cash inflow = initial investment}

🔹 B. Discounted Payback Period

Same as Payback Period, but uses present value of cash flows.

💡 Decision Rule:

  • Shorter payback → more attractive (used as a liquidity/risk measure)

📈 Advantages:

  • Simple and quick

  • Useful when cash flow timing is critical (e.g., for startups or risky ventures)

⚠️ Limitations:

  • Ignores cash flows after payback

  • Doesn’t consider time value of money (unless discounted)

  • Not aligned with shareholder value maximization

📊 4. Profitability Index (PI)

✅ What is PI?

PI measures the value created per unit of investment. It’s the ratio of the present value of future cash inflows to the initial investment.

📘 Formula:

PI=PV of future cash inflowsInitial Investment=NPV+C0C0PI = frac{text{PV of future cash inflows}}{text{Initial Investment}} = frac{NPV + C_0}{C_0}

💡 Decision Rule:

  • PI > 1.0 → Accept

  • PI < 1.0 → Reject

📈 Advantages:

  • Useful when capital is limited (e.g., ranking projects under a budget)

  • Considers time value and relative efficiency

⚠️ Limitations:

  • Cannot always distinguish between projects of different scales (NPV is better for absolute value)

🧠 Summary Table: Key Financial Evaluation Metrics

Metric Key Feature Accept Rule Pros Cons
NPV Dollar value added NPV > 0 Considers all cash flows, TVM Requires discount rate
IRR Rate of return IRR > cost of capital Easy to compare Multiple IRRs possible
Payback Period Time to recover investment Lower is better Simple, useful for liquidity Ignores later cash flows, TVM
Discounted Payback Payback using PV of cash flows Lower is better More accurate than regular payback Still ignores post-payback cash flows
Profitability Index Value per dollar invested PI > 1 Good for capital rationing Less useful for large-scale comparisons

✅ Tools for Evaluation

Tool Usage
Excel NPV() =NPV(rate, cash_flows) + initial_investment
Excel IRR() =IRR(cash_flow_range)
NPV Sensitivity Tables Vary discount rate or cash inflows
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