# Calculating the discount rate for Discounted Cash Flow Analysis

The discount rate is a financial phrase that can have two interpretations. When we read the discount rate in financial news, it generally refers to the rate of central banks charge commercial banks for overnight loans. In the USA, the board of governors of the Federal Reserve Bank approves the rates. In the UK, the Bank of England’s Monetary Policy Committee sets and approves the rate. The discount rate is one of the tools of the central bank’s tool to control the supply of money in a country to assure stability in the economy.

The second interpretation of the discount rate, which is widely used in capital budgeting and evaluating investments, is used to calculate what future cash flows are worth today. The discount rate is a critical part of Discounted Cash Flow (DCF), a valuation method used to estimate the value of an investment or project based on its future cash flows.

The central banks’ discount rate is a broad topic and involves numerous factors to be considered as it impacts a country’s overall economy. For this article, we will focus on calculating the discount rate to be used in DCF analysis.

## Why is the discount rate a critical part of any DCF Valuation?

The Discounted Cash Flow (DCF) analysis is a commonly used valuation method used to determine the value of an investment or company based on the company’s future free cash flows to firm. This method is based on the principle of the time value of money where the money available today is worth more than an identical sum in a future time due to its potential earning capacity. DCF assesses an investment or company’s viability by calculating the present value of future cash flows using the discount rate.

As mentioned earlier, the discount rate is a critical part of DCF analysis. To illustrate, take a look at the table below.

The table shows a set of cash flows, an upfront investment of \$1m that returns \$100,000 at the end of each year for 5 years and the original investment of \$1m is also returned at the end of the 5th year. Notice how a one percent change in the discount rate impacts the net present values.

The net present value for the cash flows at a discount rate of 10% is equal to \$0, what does this mean? The percentage rate earned on each dollar invested for each period that it is invested is exactly 10%. It simple terms, you are paying exactly what the investment or asset is worth. Notice also when the discount rate moves higher than 10%, the investment becomes less viable, you are losing money to the tune of \$33,296. At 11% and higher, you will essentially be paying more than what the asset is worth. Selecting the discount rate has a significant impact on a company or investment’s valuation. Therefore, accurately calculating the discount rate becomes crucial to obtain a precise DCF valuation result.

## Calculating the discount rate as the Weighted Average Cost of Capital (WACC)

A company uses financing from two main sources, equity, and debt. Using these financing sources comes at a cost and varies on the importance (or weight) placed on each type of source. Simply put, the Weighted Average Cost of Capital (WACC) is the average cost of these two sources of funding given each one’s appropriate weight in the company’s overall capital structure. WACC is calculated as:

Whereas

• Equity Weight % – Weight % of Equity Capital at Market Values
• Cost of Equity – Risk-Free Rate + ( Beta x Equity Risk Premium) + any other Premium
• Debt Weight % – Weight % of Financial Debt  at Market Values
• Cost of Debt – After-tax cost of Financial Debt

## Weight of Equity and Debt

To calculate the discount rate, we need to weight the two main components of financing sources:

• Equity Weight %: Values the equity capital at market values. The percentage is obtained when dividing the equity value by the total financing amount (equity + financial debt at market values). When you deal with publicly quoted companies, the equity value is equal to the market capitalization or market cap. It can be calculated by multiplying the market price per share by the number of outstanding shares.
• Debt Weight %: Simply put, the market value of debt is the amount that an investor would be willing to pay for a company’s financial debt. The debt weight is the financial debt divided by the total financing amount (equity + financial debt at market values). For non-listed debt instruments, the debt value equals the book value. In the case of publicly traded bonds, the market value can be found at the bond market.

Both, Equity and Debt weight, should total 100% together.

## Cost of Equity

The cost of equity reflects the return the company needs to offer to its investors in order that investors are compensated for the investment risk and provide the funding. The standard way to determine the cost of equity is by using the Capital Asset Pricing Model (CAPM). This model represents the relationship between the risk and the expected returns. In general, the higher the risk, the higher the return the investor needs to obtain to assume this risk.

The capital asset pricing model measures risk in relation to how a stock behaves to the overall stock market by multiplying the beta with the equity risk premium on top of a risk-free return. There are three main parameters needed to calculate the cost of equity under CAPM:

• Equity Risk Premium (ERP) – This premium represents the extra return available to shareholders for investing in the stock market and taking on a relatively higher risk as opposed to investing in a risk-free investment such as Treasury Bills (T-bills) or Treasury Bonds.  To calculate for the ERP, calculate the long-term stock market return and subtract a long-term risk-free rate from the market’s expected rate of return. Estimated Equity Risk Premiums normally range between 4.5% – 7.0%.
• Beta – A measure of sensitivity (correlation) of a stock’s return in comparison to the overall stock market returns. The market’s beta is set at 1, if a stock has a beta greater than 1 then it is more volatile and is therefore riskier. It is also called the beta coefficient and is represented by ß symbol. Beta is a function of business risk (risk related to running a business such as loss, missing sales targets, etc.) and financial risk (risk related to borrowing or debt such as defaulting on a loan, taking on high levels of debt, etc.). The beta used for the CAPM Model is the levered beta. When using betas from comparable companies we first need to get their unlevered betas and then adjust for the different capital structures.
• Levered Beta (Equity Beta) – Measures the company’s risk with debt and equity in its capital structure.
• Unlevered Beta (Asset Beta) – Assumes the company has zero debt and measures its risk solely on company assets. If a company has debt, this will require a commitment to more cash flows to service the debt thereby increasing its financial risk.

There are different formulas to adjust asset beta to obtain the levered beta. For our purposes, we stick to the levered beta to keep it simple.

• Risk-Free Rate – This is the yield an investor can obtain from a risk-free or zero risk investment. In practice, this will be the yield of a long-term government bond or Treasury bill (T-bill). For countries which do not have an excellent credit rating, one can also work around this problem by taking the yield of a US Bond and add a country risk premium as per one of the rating agencies Standards & Poors, Moodys or Fitch. The term of the government bold should correspond to the average weighted cash flow duration of a company’s business plan, therefore should normally lie between 10 and 20 years.

The CAPM model can easily be enhanced by additional risk premiums such as e.g. a small cap premium, a key man premium or any other premium which can reasonably be justified.

## Cost of Debt

The cost of debt refers to the after-tax cost of debt as the following illustration shows:

• Average interest rate: We calculate the weighted average interest rate charged to all financial debt used by the company. Please note, the interest itself has two components: i) the risk-free rate and ii) the debt premium. The debt premium compensates lenders to take more than the risk of a government bond yield as a company normally is viewed as a less quality lender. The debt premium itself also reacts to the financing structure of the company. If the company uses a high degree of leverage, the debt premium normally increases, if the leverage is low, the debt premium will be lower.
• Tax Shield: Taxes become lower the more interest expenses the company can deduct. Therefore, a high tax rate actually creates a higher tax shield than a low tax rate and helps to reduce the after-tax cost of debt.

## Conclusion: Calculating the discount rate

The Weighted Average Cost of Capital is a very important concept in finance and has two components – the cost of equity and the cost of debt. The WACC reflects the opportunity cost of investing in a company with similar risk and therefore requires the return which is required to compensate for the risk.

When conducting a DCF analysis, the WACC is a key factor which determines the outcome of the DCF valuation as any change in the WACC as the discount rate normally has a big impact on the valuation outcome. For a more detailed discussion on DCF valuation, please refer to the article Discounted Cash Flows for Valuation Analysis.

The WACC can also be used as a minimum hurdle rate when analyzing IRR calculations which base on the Free Cash Flow to Firm. If the IRR is higher than the WACC, one should pursue the project.

Calculating the discount rate can be complex when done detailed and requires a variety of financial data and careful analysis. However, very often the discount rate is simply estimated to avoid too many complex calculations. A good DCF valuation stands and falls with how the discount rate can be justified.

Please refer here to a WACC model for calculating the discount rate as well as DCF Models which you can browse below.