## What is the Discount Rate?

The **Discount Rate** represents the minimum return expected to be earned on an investment given its specific risk profile. In practice, the present value (PV) of the future cash flows generated by a company is estimated using an appropriate discount rate that should reflect the risk profile of the underlying company, i.e. the opportunity cost of capital.

## How to Calculate Discount Rate (Step-by-Step)

In corporate finance, the discount rate is the minimum rate of return necessary to invest in a particular project or investment opportunity.

The discount rate, often called the “cost of capital”, reflects the necessary return of the investment given the riskiness of its future cash flows.

**Conceptually, the discount rate estimates the risk and potential returns of an investment – so a higher rate implies greater risk but also more upside potential.**

In part, the estimated discount rate is determined by the “time value of money” – i.e. a dollar today is worth more than a dollar received on a future date – and the return on comparable investments with similar risks.

Interest can be earned over time if the capital is received on the current date. Hence, the discount rate is often called the opportunity cost of capital, i.e. the hurdle rate used to guide decision-making around capital allocation and selecting worthwhile investments.

When considering an investment, the rate of return that an investor should reasonably expect to earn depends on the returns on comparable investments with similar risk profiles.

Calculating the discount rate is a three-step process:

**Step 1 →**First, the value of a future cash flow (FV) is divided by the present value (PV)**Step 2 →**Next, the resulting amount from the prior step is raised to the reciprocal of the number of years (n)**Step 3 →**Finally, one is subtracted from the value to calculate the discount rate

## Discount Rate Formula

The discount rate formula is as follows.

**Discount Rate =**(Future Value

**÷**Present Value)

**^**(1

**÷**n)

**–**1

For instance, suppose your investment portfolio has grown from $10,000 to $16,000 across a four-year holding period.

- Future Value (FV) = $16,000
- Present Value (PV) = $10,000
- Number of Periods = 4 Years

If we plug those assumptions into the formula from earlier, the discount rate is approximately 12.5%.

- r = ($16,000 / $10,000) ^ (1/4) – 1 = 12.47%

The example we just completed assumes annual compounding, i.e. 1x per year.

However, rather than annual compounding, if we assume that the compounding frequency is semi-annual (2x per year), we would multiply the number of periods by the compounding frequency.

Upon adjusting for the effects of compounding, the discount rate comes out to be 6.05% per 6-month period.

- r = ($16,000 / $10,000) ^ (1/8) – 1 = 6.05%

## Discount Rate vs. Net Present Value (NPV)

The net present value (NPV) of a future cash flow equals the cash flow amount discounted to the present date.

With that said, a higher discount rate reduces the present value (PV) of the future cash flows (and vice versa).

**Net Present Value (NPV) =**

**Σ**Cash Flow

**÷**(1

**+**Discount Rate)

**^**n

In the formula above, “n” is the year when the cash flow is received, so the further out the cash flow is received, the greater the reduction.

Moreover, a fundamental concept in valuation is that incremental risk should coincide with greater returns potential.

- Higher Discount Rate → Lower NPV (and Implied Valuation)
- Lower Discount Rate → Higher NPV (and Implied Valuation)

Therefore, the expected return is set higher to compensate the investors for undertaking the risk.

If the expected return is insufficient, it would not be reasonable to invest, as there are other investments elsewhere with a better risk/return trade-off.

On the other hand, a lower discount rate causes the valuation to rise because such cash flows are more certain to be received.

More specifically, the future cash flows are more stable and likely to occur into the foreseeable future – hence, stable, market-leading companies like Amazon and Apple tend to exhibit lower discount rates.

**Learn More →** Discount Rate by Industry (Damodaran)

## How to Determine the Discount Rate

In a discounted cash flow (DCF) model, the intrinsic value of an investment is based on the projected cash flows generated, which are discounted to their present value (PV) using the discount rate.

Once all the cash flows are discounted to the present date, the sum of all the discounted future cash flows represents the implied intrinsic value of an investment, most often a public company.

The discount rate is a critical input in the DCF model – in fact, the discount rate is arguably the most influential factor to the DCF-derived value.

One rule to abide by is that the discount rate and the represented stakeholders must align.

The appropriate discount rate to use is contingent on the represented stakeholders:

- Weighted Average Cost of Capital (WACC) → All Stakeholders (Debt + Equity)
- Cost of Equity (ke) → Common Shareholders
- Cost of Debt (kd) → Debt Lenders
- Cost of Preferred Stock (kp) → Preferred Stock Holders

## WACC vs. Cost of Equity: What is the Difference?

**WACC → FCFF**: The weighted average cost of capital (WACC) reflects the required rate of return on an investment for all capital providers, i.e. debt and equity holders. Since both debt and equity providers are represented in WACC, the free cash flow to firm (FCFF) – which belongs to both debt and equity capital providers – is discounted using the WACC.**Cost of Equity → FCFE**: In contrast, the cost of equity is the minimum rate of return from the viewpoint of only equity shareholders. The free cash flow to equity (FCFE) belonging to a company should be discounted using the cost of equity, as the represented capital provider in such a case are common shareholders.

Thereby, an unlevered DCF projects a company’s FCFF, which is discounted by WACC – whereas a levered DCF forecasts a company’s FCFE and uses the cost of equity as the discount rate.