Limitations:

Example: Investment = $100,000, Annual Cash Inflow = $20,000. Payback = $100,000 / $20,000 = 5 years.

Measures average annual profit as a percentage of initial or average investment.
Formula: $\text{ARR} = \frac{\text{Average Annual Profit}}{\text{Initial Investment (or Average Investment)}}$
Utility:
- Simple to calculate and understand.
- Uses easily available accounting profits.
- Provides a percentage for comparison.
Limitations:
- Ignores time value of money.
- Based on accounting profits, not cash flows.
- Does not consider project duration.
- Inconsistent with maximizing market value of shares.
Example: Investment = $200,000, Average Annual Profit = $40,000. ARR = $\frac{40,000}{200,000} \times 100 = 20\%$

Discount rate at which the Net Present Value (NPV) of an investment is zero. ($PV_{\text{inflows}} = PV_{\text{outflows}}$)
Considers time value of money.
Formula: $0 = \sum_{t=1}^{n} \frac{CF_t}{(1 + IRR)^t} - CF_0$ (where $CF_0$ is initial investment)
Utility:
- Considers time value of money.
- Provides a single percentage rate for comparison.
- Considers all cash flows.
Limitations:
- Tedious to compute manually (often requires calculator/software).
- Can give multiple IRRs for non-conventional cash flows.
- Assumes reinvestment at IRR, which may be unrealistic.
Interpretation: Positive IRR indicates return higher than cost of capital; Negative IRR indicates loss; Zero IRR means break-even.

Analyzes cash inflows and outflows over an asset's life, discounted to present value.
Formula: $PV = \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t}$ (where $r$ is the discount rate, often WACC)
Utility:
- Considers time value of money and returns after payback period.
- Provides a comprehensive view of project value.
Limitations:
- Requires accurate cash flow forecasts, which can be difficult.
- Selection of appropriate discount rate (WACC) can be subjective.
Example: Initial investment $11M, WACC 5%.
- Year 1 CF $1M \rightarrow DCF = \frac{1,000,000}{(1+0.05)^1} = 952,381$
- Sum of all DCFs minus initial investment gives NPV.

Difference between the present value of future cash inflows and the initial investment.
Formula: $NPV = \sum_{t=1}^{n} \frac{C_t}{(1 + r)^t} - C_0$
- $C_t$: Cash inflow at time $t$
- $r$: Discount rate (cost of capital)
- $t$: Time period
- $C_0$: Initial investment at time $0$
Utility:
- Accounts for time value of money.
- Directly measures value added to the firm.
- Considers all cash flows.