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Discount Rate

Value used in DCF (Discounted Cash Flow) analysis to adjust the future value of earnings into present-day dollars

## What Is A Discount Rate?

The discount rate refers to a value used in DCF (Discounted Cash Flow) analysis to adjust the future value of earnings into present-day dollars. For the interest rate set by the Federal Reserve, see Federal Discount Rate.

Contrary to what you might think, this discount rate does not represent that 15% off label on your favorite brand of cheese-filled danishes.

Instead, the one we’re talking about applies to businesses and investments, where it helps investors determine the profitability of a planned project. Depending on the type of investment, the value used will vary.

DCF analysis helps us compare the invested inputs into a project with the predicted outputs it will generate. However, the time value of money varies between the inputs, which are paid today, and the outputs, which are to be gained in the future.

To resolve this discrepancy, the discount rate is used to find the present value of future cash flows. In other words, it allows you to solve for the value of a sum of money in the future in today’s terms.

## Key Takeaways

- The discount rate, essential in Discounted Cash Flow (DCF) analysis, is used to convert future earnings into present-day value, serving as a key metric for evaluating project profitability.
- The discount rate's formula, like compound interest in reverse, determines present value from future value. Applying this to specific investments allows calculation, aiding in decision-making.
- In Discounted Cash Flow (DCF) analysis, the discount rate is pivotal, helping ascertain the current value of expected future cash flows. Positive net present value deems a project feasible.

## Discount Rate Formula

Firstly, let’s compare it to compound interest, which is its inverse. This would make the concept more clearer.

For example, take a savings account that earns 5% a year, compounded annually. If it has a principal of $1,000, here’s how much it would have in ten years:

*1000 x (1.05) ^{10} = 1628.89*

More generally, this formula can be simplified to:

*A = P(1 + (r/n)) ^{nt}*

Where

**P**is principal, also known as the initial amount**r**is the interest rate**n**is the number of times the interest is applied per period, e.g., four times if it was quarterly**t**is the number of periods, typically in years**A**is the resulting amount

Conversely, you can find the discount rate if you have the future and the present value:

*(1628.89/1000) ^{0.1} - 1 = 0.05*

Here is the more general formula:

*Discount Rate = (FV/PV) ^{1/n} - 1*

Where

**FV**stands for future value**PV**stands for the present value**n**is the number of times interest is applied per period

## Calculating The Discount Rate

To calculate the discount rate, you can use the formula:

*Discount Rate = (FV/PV) ^{1/n} − 1*

Let’s take an example to illustrate how the discount rate works. Suppose you want to find the discount rate for a specific investment with the following details:

- Future value: $8,000
- Present value: $6,200
- Number of Years: 8

Now, let’s apply the formula:

*DR = ($8,000/$6,200) ^{1/8} − 1*

*DR = 1.29 ^{1/8 }− 1*

*DR = 1.03679 − 1*

*DR = 0.03679*

So, here, the discount rate is approximately 3.679%.

## Types of Discount Rates

It is used to find the present value of future free cash flows in DCF analysis. Depending on the project being evaluated, the value used can vary.

Let’s look at some commonly used values:

**Weighted average cost of capital (WACC)**

The WACC uses a company’s capital structure to balance the weighted average between the cost of equity and the cost of debt. This value measures the average cost for a company when attracting monetary capital.

The equity portion of the calculation reflects the demand from shareholders for a sufficient return on their investment, while the debt portion represents the bondholders’ demand.

The overall value measures the amount of return both parties require to supply the company with capital. To calculate this value, follow the formula below:

*WACC = [(E/V) * Re] + [(D/V) * Rd * (1 - Tc)]*

Where

**E**is the market value of the company’s equity**D**is the market value of the company’s debt**V**is the sum of E and D**Re**is the cost of equity**Rd**is the cost of debt**Tc**is the corporate tax rate

While other components of the formula are fairly straightforward, the cost of equity and the cost of debt require further discussion. The former measures the amount of return that the company must issue to incentivize investors to buy shares of its stock.

However, stocks are inherently unpredictable. As a result, this value is often estimated through the CAPM (Capital asset pricing model).

In contrast, the cost of debt is simply the amount that the company must pay for its debt financing, specifically through bonds.

The WACC is typically used as the discount rate by investors, who expect a return equal to the WACC when investing.

**Risk-free rate**

The risk-free rate corresponds to the rate of return on an asset with zero risk. Although zero risk is unattainable, a fair approximation typically used for this value is the three-month U.S. Treasury bill.

## Note

Even the three-month US Treasury bill holds risk, however, as there is always the chance of a government default.

The risk-free rate can be adjusted to match the time frame of the planned project for greater accuracy. For example, if you are using the discounted cash flow model to determine the viability of a ten-year project, then you should use a ten-year Treasury bill as the risk-free rate.

**Hurdle rate**

A hurdle rate is a broader term that refers to the minimum return on a project to make it viable. Think of it as a hurdle—only if the company can earn a specified level of compensation could it move forward with the project.

The hurdle rate reflects several considerations, such as the cost of the project, its relative riskiness, and potential value compared to other projects.

## Note

To determine if the project's cost makes it worthwhile, companies use discounted cash flow analysis to calculate the NPV (net present value) while using the hurdle rate as the discount rate.

The risk of the project is also factored into the hurdle rate. When the project bears more risk, the hurdle rate rises to compensate for the increased risk. This risk premium can mean the difference between an undertaken project and one that is not.

Finally, if there are alternative projects that could yield the same return, the hurdle rate reflects the difference in execution costs. If one project has a higher net present value of future cash flows, it would be chosen over the others.

**Cost of equity**

The cost of equity was previously discussed in the WACC, but it can also stand alone as the discount rate. So, for example, companies solely financed by equity would use this value instead.

## Note

For investors, the cost of equity represents a value that will rightfully compensate them for undertaking additional risk by investing in a specific company.

Under the CAPM model, the formula for calculating the cost of equity follows:

*E(R _{i}) = R_{f} + 𝛽_{i}(E(R_{m}) - R_{f})*

Where

**E(R**is the expected return on the asset, also the cost of equity_{i})**R**is the risk-free rate of return_{f}**𝛽**is the beta, representing the volatility of the market_{i}**E(R**is the expected market return_{m})

The cost of equity evaluates an asset’s viability by calculating the expected return of an asset from its volatility and expected market returns. As a discount rate, this value uses the volatility of an asset to adjust for the present value of future cash flows.

**Cost of debt**

The cost of debt was also discussed previously, and just like the cost of equity, it can function independently. Specifically, this term refers to the interest payments on a company’s total debt from debt financing.

Companies heavily funded by debt will have a higher cost of debt, which can drag down the DCF-adjusted returns.

## How The Discount Rate Works In Cash Flow Analysis

The discount rate is a term also employed in discounted cash flow (DCF) analysis, a method for gauging the worth of an investment based on its anticipated future cash flows.

Grounded in the time value of money, DCF analysis evaluates project or investment viability by determining the current value of expected future cash flows by applying a discount rate.

The analysis starts with estimating the investment required for a proposed project and considering its anticipated future returns.

One can compute the present value of forthcoming cash flows by utilizing the discount rate. A project is deemed feasible if the net present value (PV) is positive; otherwise, the investment is not advisable.

In DCF analysis, the discount rate denotes the interest rate used to ascertain present value.

To illustrate, consider investing $100 today in a futuristic venture, the Quantum Growth Fund, which promises a 15% yield.

Consequently, that initial $100 investment would equate to $115 in the future. In simpler terms, applying the 15% discount rate to the future value (FV) of $115 aligns with a present value of $100 today.

With a good understanding or reasonable predictions about all future cash flows, like knowing the expected future value of $115, you can figure out the current investment value using the chosen discount rate.

## Issues with the Discount Rate

Some of the issues when using discount rates are:

- Estimating the discount rate involves assumptions that can complicate financial analyses.
- The common practice of using a uniform discount rate for all future cash flows oversimplifies the dynamic nature of interest rates and risk profiles, potentially leading to inaccurate valuations.
- This approach may be less suitable for short-term investments, as a static discount rate might not capture the nuances of quicker returns.
- The focus on long-term value creation may overlook the adaptability required in rapidly changing economic conditions and financial markets.
- The discount rate’s rigidity may not align well with varying economic landscapes, limiting its effectiveness in addressing short-term market fluctuations or tactical investment decisions.

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