03 Economic Financial Analysis/Evaluation

The Internal Rate of Return (IRR) is the discount rate at which the Net Present Value (NPV) of an investment project equals zero.

In other words, it is the rate at which the present value of the cash inflows (revenues) equals the present value of the cash outflows (expenses and initial investment).

1. IRR > WACC: The project is profitable and should be undertaken.

2. IRR = WACC: The project just covers the cost of capital; decision depends on other factors.

3. IRR < WACC: The project is not profitable and should be rejected.

1. Rj​ = Revenue in year j

2. Dj​ = Expense in year j

3. Cn = Residual value (or terminal value) at the end of the project

4. C0 = Initial investment (cost at time 0)

5. ir = Internal rate of return

6. n = Total number of periods

NPV (Net Present Value) is used to assess the profitability of an investment by comparing the present value of expected cash inflows to the present value of cash outflows.

1. Positive NPV: The investment is profitable and should be considered.

2. Negative NPV: The investment is not profitable and should be avoided.

The formula compares the present value of cash inflows (revenues) and the present value of cash outflows (expenses and initial investment) to determine the NPV.

1. Rj​ = Revenue in year j

2. Dj​ = Expense in year j

3. Cn​ = Residual value (or terminal value) of the investment at the end of the project

4. C0​ = Initial investment (cost at time 0)

5. i= Discount rate (rate of return)

6. n = Total number of periods

The Payback Period (Recovery Period) is the time required for an investor to recover their initial investment through net cash flows from the project.

The formula calculates the cumulative net cash flow over time, discounted at the given interest rate, until it equals the invested capital.

1. T = Recovery time (Payback Period)

2. FLCj​ = Net cash flow (Exploration Cash Flow) in period j

3. Cj = Capital invested in period j

4. n = Total term of the investment

5. I = Interest rate adopted

   
   

Payback Period < Project Lifetime: The investment is recovered within the project's duration, making it a viable project.

Payback Period = Project Lifetime: The investment is fully recovered by the end of the project, but no profit is made beyond that.

Payback Period > Project Lifetime: The investment is not recovered during the project's life, making it unprofitable.

The Profitability Index (PI), also known as ROI (Return on Investment), is a measure of the profitability of an investment project, calculated by comparing the present value of future cash flows to the initial investment.

• CFEp​ = Exploitation cash flows from the project at period p

• Ip​ = Value of the investment at period p

• Cn​ = Residual value or terminal value of the project

• i = Discount rate (interest rate)

• n = Total number of periods (investment duration)

• PI (Profitability Index) or ROI (Return on Investment) = The ratio of the present value of future cash flows to the present value of the investment.

Key Points:

• PI > 1: The project is profitable, as future cash flows exceed the investment.

• PI = 1: The project breaks even, with cash flows equal to the investment.

• PI < 1: The project is not profitable, as the investment outweighs the returns.