- author: The Finance Storyteller

# Understanding the Difference between Weighted Average Cost of Capital and Internal Rate of Return

When it comes to analyzing investment opportunities, there are various metrics that investors use to evaluate the potential profitability, such as net present value (NPV), weighted average cost of capital (WACC), and internal rate of return (IRR). While WACC and IRR are both essential components when calculating the net present value, they are distinct concepts and serve different purposes.

## What is Weighted Average Cost of Capital (WACC)?

WACC is a calculation that reflects a company's cost of capital in which each type of capital - equity, debt, and preferred stock - is proportionately weighted. It is used to determine the minimum required return that investors should expect when investing in a company. The higher the risk or uncertainty of the project or company, the higher the WACC rate will be.

To calculate the WACC of a project, it is essential to know the different types of capital and their costs. The formula for WACC is:

WACC = (E/V x Re) + (D/V x Rd x (1-Tc)) + (P/V x Rp)

- E: Market value of the company's equity
- D: Market value of the company's debt
- P: Market value of the company's preferred stock
- V: Total capital invested in the company (E + D + P)
- Re: Cost of equity
- Rd: Cost of debt
- Tc: Corporate tax rate
- Rp: Cost of preferred stock

## What is Internal Rate of Return (IRR)?

IRR is the discount rate at which the net present value of all cash flows generated by a project equals zero. In other words, IRR is a rate that makes the net present value of all cash flows equal to their initial investment. The IRR reflects the profitability of an investment and represents the average annual growth rate of the investment over the project's intended life.

To calculate the IRR of a project, the following formula is used:

0 = sum of (CFn / (1+r)^n)

Where:

- CFn: Cash flow for each year of the project
- r: the IRR
- n: the number of years

## How are WACC and IRR used in Net Present Value (NPV) Calculation?

WACC and IRR are both used in the calculation of net present value (NPV). NPV is the difference between the present value of the expected cash inflows and the present value of the expected cash outflows over a specific period. It is calculated using the following formula:

NPV = CF0 + (CF1 / (1+r)^1) + (CF2 / (1+r)^2) +…+ (CFn / (1+r)^n)

Where:

- CF0: Initial cash outflow
- CF1 to CFn: future cash inflows
- r: the discount rate

To use WACC in the NPV formula:

- Identify the nominal cash flows for the project
- Use the WACC as an input variable to calculate the present value of the future cash flows
- Calculate NPV by adding the discounted cash flows.

To use IRR in the NPV formula:

- Identify the nominal cash flows for the project
- Set NPV to zero
- Calculate IRR as the output variable

## Example Calculation of WACC and IRR

Let's assume that your company is considering investing $1000 in a project that will bring $400 benefits each year for the next four years. The nominal cash flows of the project would be as follows:

| Year | Cash Flow | |------|-----------| | 0 | ($1000) | | 1 | $400 | | 2 | $400 | | 3 | $400 | | 4 | $400 |

To calculate the WACC, let's consider a rate of 20%, according to the company's finance department. The present value of the project's future cash flows would be:

| Year | Cash Flow | Discount Factor | Present Value | |------|-----------|----------------|---------------| | 0 | ($1000) | 1.000 | ($1000) | | 1 | $400 | 1.200 | $333.33 | | 2 | $400 | 1.440 | $277.78 | | 3 | $400 | 1.728 | $231.48 | | 4 | $400 | 2.074 | $193.80 |

The sum of the present value of the cash flows equals $35, which is the project's NPV. Considering the positive NPV value, the project creates value for the company, and it's worth pursuing.

To calculate the IRR for the same project, you can set the NPV to zero. To find the rate at which the NPV equals zero, we can either use a trial-and-error approach or use the IRR formula in Excel. In this case, the IRR for the project is 22%, which is higher than the WACC of 20%. So, the project is profitable and should be considered for investment.

## Conclusion

WACC and IRR are valuable tools used in investment evaluation. While they both relate to the NPV formula, they serve distinct functions. WACC is the discount rate used to determine the required return of a project, while the IRR is the rate at which the NPV equals zero. Understanding the differences between WACC and IRR can help investors make informed investment decisions that are more likely to be profitable.