Which of the following is the correct calculation for Project Sigma's Internal Rate of Return (IRR)?

• A. The rate at which Project Sigma's initial investment is divided by its total future cash inflows.
• B. The discount rate that makes the net present value (NPV) of Project Sigma's cash flows equal to zero.
• C. The average annual return of Project Sigma divided by its initial investment.
• D. The interest rate used to discount Project Sigma's future cash flows to their present value at the company's cost of capital.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the concept of Internal Rate of Return (IRR). IRR is the discount rate that makes the Net Present Value (NPV) of all cash flows from a project equal to zero. It is a measure of the profitability of an investment.
2. Step 2: Identify the formula for NPV. The NPV formula is: \( \text{NPV} = \sum_{t=1}^{n} \frac{C_t}{(1 + r)^t} - C_0 \), where \( C_t \) is the cash inflow at time \( t \), \( r \) is the discount rate, and \( C_0 \) is the initial investment.
3. Step 3: Recognize that IRR is the value of \( r \) that makes \( \text{NPV} = 0 \). This means solving the equation \( \sum_{t=1}^{n} \frac{C_t}{(1 + r)^t} - C_0 = 0 \) for \( r \).
4. Step 4: Note that IRR is not calculated by dividing the initial investment by total future cash inflows, nor is it the average annual return divided by the initial investment. These are incorrect definitions.
5. Step 5: Clarify that IRR is also not the interest rate used to discount future cash flows to their present value at the company's cost of capital. Instead, it is the rate that equates the present value of cash inflows to the initial investment, making NPV zero.