 # How to Calculate the Discount Rate in a DCF

In this second free tutorial, you’ll learn what the Discount Rate means intuitively, how to calculate the Cost of Equity and WACC, and how to use the Discount Rate in a DCF analysis to value a company’s future cash flows.

• 0:39: Intuitive Explanation of the Discount Rate and WACC
• 5:53: Discount Rate Assumptions
• 11:43: How to Calculate the Cost of Equity
• 21:05: How to Calculate and Use WACC
• 24:55: Summary and Preview

## Discount Rate Meaning and Explanation

The Discount Rate goes back to that big idea about valuation and the most important finance formula: The Discount Rate represents risk and potential returns, so a higher rate means more risk but also higher potential returns.

The Discount Rate also represents your opportunity cost as an investor: if you were to invest in a company like Michael Hill, what might you earn by investing in other, similar companies in this market?

Normally, you use something called WACC, or the “Weighted Average Cost of Capital,” to calculate the Discount Rate.

The name means what it sounds like: you find the “cost” of each form of capital the company has, weight them by their percentages, and then add them up.

“Capital” just means “a source of funds.” So, if a company borrows money in the form of Debt to fund its operations, that Debt is a form of capital.

And if it goes public in an IPO, the shares it issues, also called “Equity,” are a form of capital.

## How to Calculate Discount Rate: WACC Formula

The formula for WACC looks like this:

WACC = Cost of Equity * % Equity + Cost of Debt * (1 – Tax Rate) * % Debt + Cost of Preferred Stock * % Preferred Stock

Finding the percentages is basic arithmetic – the hard part is estimating the “cost” of each one, especially the Cost of Equity. The Cost of Equity represents potential returns from the company’s stock price and dividends, and how much it “costs” the company to issue shares.

For example, if the company’s dividends are 3% of its current share price, and its stock price has increased by 6-8% each year historically, then its Cost of Equity might be between 9% and 11%.

The Cost of Debt represents returns on the company’s Debt, mostly from interest, but also from the market value of the Debt changing – just like share prices can change, the value of Debt can also change.

For example, if the company is paying a 6% interest rate on its Debt, and similar companies are as well, meaning the market value of Debt is close to its value on the Balance Sheet, then the Cost of Debt might be around 6%.

Then, you also need to multiply that by (1 – Tax Rate) because Interest paid on Debt is tax-deductible. So, if the Tax Rate is 25%, the After-Tax Cost of Debt would be 6% * (1 – 25%) = 4.5%.

The Cost of Preferred Stock is similar because Preferred Stock works similarly to Debt, but Preferred Stock Dividends are not tax-deductible and overall rates tend to be higher, making it more expensive.

So, if the Preferred Stock Coupon Rate is 8%, and its market value is close to its book value because market rates are also around 8%, then the Cost of Preferred Stock should be around 8%.

## Discount Rate Meaning: WACC in One Sentence

WACC represents what you would earn each year, over the long term, if you invested proportionally in the company’s entire capital structure.

So, let’s say this company uses 80% Equity and 20% Debt to fund its operations, and that it has a 25% effective tax rate.

You decide to invest \$1,000 in the company proportionally, so you put \$800 into its Equity, or its shares, and \$200 into its Debt.

We said before that the Cost of Equity was between 9% and 11%, so let’s call it 10%.

We know the After-Tax Cost of Debt is 4.5% as well.

So, WACC = 10% * 80% + 4.5% * 20% = 8.9%, or \$89 per year.

That does not mean we will earn \$89 in cash per year from this investment; it just means that if we count everything – interest, dividends, and eventually selling the shares at a higher price in the future – the annualized average might be around \$89.

WACC is more about being “roughly correct” than “precisely wrong,” so the rough range, such as 10% to 12% vs. 5% to 7%, matters a lot more than the exact number.

## How to Calculate Discount Rate in Excel: Starting Assumptions

To calculate the Discount Rate in Excel, we need a few starting assumptions: The Cost of Debt here is based on Michael Hill’s Interest Expense / Average Debt Balance over the past fiscal year. That’s 2.69 / AVERAGE(35.213,45.034), so it’s 6.70%. here.

This is a “rough estimate,” and there are some problems with it (e.g., What if the market value of Debt changes? What if that doesn’t represent the cost to issue *new* Debt?) but we’ll go with it for now in this quick analysis.

To calculate the Cost of Equity, we’ll need the Risk-Free Rate, the Equity Risk Premium, and Levered Beta.

Cost of Equity = Risk-Free Rate + Equity Risk Premium * Levered Beta

The Risk-Free Rate (RFR) is what you might earn on “safe” government bonds in the same currency as the company’s cash flows – Michael Hill earns in CAD, NZD, and AUD, but reports everything in AUD, so we’ll use the yield on 10-Year Australian government bonds, which was 2.10% at the time of this case study.

You can find up-to-date data on Australian government bond yields here, and you can do simple Google searches to find them for other countries.

The Equity Risk Premium (ERP) is the amount the stock market is expected to return each year, on average, above the yield on “safe” government bonds. We link it to the stock market of the country the company operates in (mostly Australia here).

You can find estimates for this number in different countries online; Damodaran’s data on the ERP is the best free resource for this.

At the time of this case study, the Australian ERP was 5.96% based on this data.

Levered Beta tells us how volatile this stock is relative to the market as a whole, factoring in intrinsic business risk and risk from leverage (Debt).

If it’s 1.0, then the stock follows the market perfectly and goes up by 10% when the market goes up by 10%; if it’s 2.0, the stock goes up by 20% when the market goes up by 10%.

## How to Calculate the Cost of Equity

We could use the company’s historical “Levered Beta” for this input, but we usually like to look at peer companies to see what the overall risks and potential returns in this market, across different companies, are like.

We could look up “Beta” for each company and take the median, but Beta on sites like Google Finance, Capital IQ, Bloomberg, etc. reflects both inherent business risk and risk from leverage.

So, we must “un-lever Beta” for each company to determine the “average” inherent business risk for these types of companies:

Unlevered Beta = Levered Beta / (1 + Debt/Equity Ratio * (1 – Tax Rate) + Preferred/Equity Ratio)

This formula ensures that Unlevered Beta is always less than or equal to Levered Beta since we’re removing the risk from leverage.

We use VLOOKUP in Excel to find the Debt, Equity, and Preferred Stock for each company in the “Public Comps” tab, but you could find these figures on Google Finance and other sources if you don’t have the time/resources to extract them manually.

You can see the Unlevered Beta formula and output for each company below: Michael Hill, like most companies, has more than just “inherent business risk” since it also carries Debt, so now we need to “re-lever” this median Unlevered Beta based on the company’s current or targeted capital structure to reflect that additional risk from leverage.

To do that, we can reverse the formula for Unlevered Beta:

Unlevered Beta = Levered Beta / (1 + Debt/Equity Ratio * (1 – Tax Rate) + Preferred/Equity Ratio)

We multiply both sides by the denominator to isolate Levered Beta on the right side:

Unlevered Beta * (1 + Debt/Equity Ratio * (1 – Tax Rate) + Preferred/Equity Ratio) = Levered Beta

Levered Beta = Unlevered Beta * (1 + Debt/Equity Ratio * (1 – Tax Rate) + Preferred/Equity Ratio)

When re-levering Beta, we like to use both the company’s current capital structure and the median capital structure of the peer companies, to get different estimates and see the range of potential values.

Once we have that, we can then plug this Levered Beta number into the formula for Cost of Equity to calculate that:

Cost of Equity = Risk-Free Rate + Equity Risk Premium * Levered Beta

You can see the results of these slightly different Cost of Equity calculations below: Here, the Cost of Equity is always between 9% and 10% regardless of the exact number we use for Levered Beta, which is good since we want a range – but a relatively narrow range.

## How to Calculate Discount Rate: Putting Together the Pieces for WACC

Once again, the main question here is “Which values do we for the percentages Equity, Debt, and Preferred Stock? The company’s current percentages, or those of peer companies?”

There’s no definitive answer, so we use different approaches here – one based on peer companies and two based on the company’s current percentages – and average them: This result tells us that WACC for Michael Hill is most likely between 8.50% and 9.50%.

## How to Discount the Cash Flows and Use the Discount Rate in Real Life

Finally, we can return to the DCF spreadsheet, link in this number, and use it to discount the company’s Unlevered FCFs to their Present Values using this formula:

Present Value of Unlevered FCF in Year N = Unlevered FCF in Year N /((1+Discount_Rate)^N)

The denominator gets bigger each year, so the Present Value is a lower and lower percentage of the Future Value as time goes by.

You can see that illustrated in the screenshot below: #### Excel Files  