DCF Analysis: Calculating The Discount Rate
  1. DCF Analysis: Introduction
  2. DCF Analysis: The Forecast Period & Forecasting Revenue Growth
  3. DCF Analysis: Forecasting Free Cash Flows
  4. DCF Analysis: Calculating The Discount Rate
  5. DCF Analysis: Coming Up With A Fair Value
  6. DCF Analysis: Pros & Cons Of DCF
  7. DCF Analysis: Conclusion

DCF Analysis: Calculating The Discount Rate


By Ben McClure
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Having projected the company's free cash flow for the next five years, we want to figure out what these cash flows are worth today. That means coming up with an appropriate discount rate which we can use to calculate the net present value (NPV) of the cash flows.

So, how do we figure out the company's discount rate? That's a crucial question, because a difference of just one or two percentage points in the cost of capital can make a big difference in a company's fair value.

A wide variety of methods can be used to determine discount rates, but in most cases, these calculations resemble art more than science. Still, it is better to be generally correct than precisely incorrect, so it is worth your while to use a rigorous method to estimate the discount rate.

A good strategy is to apply the concepts of the weighted average cost of capital (WACC). The WACC is essentially a blend of the cost of equity and the after-tax cost of debt. (For more information, see Investors Need A Good WACC.) Therefore, we need to look at how cost of equity and cost of debt are calculated.

Cost of Equity
Unlike debt, which the company must pay at a set rate of interest, equity does not have a concrete price that the company must pay. But that doesn't mean that there is no cost of equity. Equity shareholders expect to obtain a certain return on their equity investment in a company. From the company's perspective, the equity holders' required rate of return is a cost, because if the company does not deliver this expected return, shareholders will simply sell their shares, causing the price to drop.

Therefore, the cost of equity is basically what it costs the company to maintain a share price that is satisfactory (at least in theory) to investors. The most commonly accepted method for calculating cost of equity comes from the Nobel Memorial Prize-winning capital asset pricing model (CAPM), where: Cost of Equity (Re) = Rf + Beta (Rm-Rf).

Let's explain what the elements of this formula are:

Rf - Risk-Free Rate - This is the amount obtained from investing in securities considered free from credit risk, such as government bonds from developed countries. The interest rate of U.S. Treasury bills or the long-term bond rate is frequently used as a proxy for the risk-free rate.

ß - Beta - This measures how much a company's share price moves against the market as a whole. A beta of one, for instance, indicates that the company moves in line with the market. If the beta is in excess of one, the share is exaggerating the market's movements; less than one means the share is more stable. Occasionally, a company may have a negative beta (e.g. a gold mining company), which means the share price moves in the opposite direction to the broader market. (To learn more, see Beta: Know The Risk.)

(Rm – Rf) = Equity Market Risk Premium - The equity market risk premium (EMRP) represents the returns investors expect, over and above the risk-free rate, to compensate them for taking extra risk by investing in the stock market. In other words, it is the difference between the risk-free rate and the market rate. It is a highly contentious figure. Many commentators argue that it has gone up due to the notion that holding shares has become riskier.

Barra and Ibbotson are valuable subscription services that offer up-to-date equity market risk premium rates and betas for public companies.

Once the cost of equity is calculated, adjustments can be made to take account of risk factors specific to the company, which may increase or decrease the risk profile of the company. Such factors include the size of the company, pending lawsuits, concentration of customer base and dependence on key employees. Adjustments are entirely a matter of investor judgment and they vary from company to company.

Cost of Debt
Compared to cost of equity, cost of debt is fairly straightforward to calculate. The rate applied to determine the cost of debt (Rd) should be the current market rate the company is paying on its debt. If the company is not paying market rates, an appropriate market rate payable by the company should be estimated.

As companies benefit from the tax deductions available on interest paid, the net cost of the debt is actually the interest paid less the tax savings resulting from the tax-deductible interest payment. Therefore, the after-tax cost of debt is Rd (1 - corporate tax rate).

Finally, Capital Structure
The WACC is the weighted average of the cost of equity and the cost of debt based on the proportion of debt and equity in the company's capital structure. The proportion of debt is represented by D/V, a ratio comparing the company's debt to the company's total value (equity + debt). The proportion of equity is represented by E/V, a ratio comparing the company's equity to the company's total value (equity + debt). The WACC is represented by the following formula: WACC = Re
x E/V + Rd x (1 - corporate tax rate) x D/V.

A company's WACC is a function of the mix between debt and equity and the cost of that debt and equity. On the one hand, in the past few years, falling interest rates have reduced the WACC of companies. On the other hand, corporate disasters like those at Enron and WorldCom have increased the perceived risk of equity investments.

Be warned: the WACC formula seems easier to calculate than it really is. Rarely will two people derive the same WACC, and even if two people do reach the same WACC, all the other applied judgments and valuation methods will likely ensure that each has a different opinion regarding the components that comprise the company's value.





Widget Company WACC
Returning to our example, let's suppose The Widget Company has a capital structure of 40% debt and 60% equity, with a tax rate of 30%. The borrowing rate (Rd) on the company's debt is 5%. The risk-free rate (Rf) is 5%, the beta is 1.3 and the risk premium (Rp) is 8%. The WACC comes to 10.64%. So, rounded up to the nearest percentage, the discount rate for The Widget Company would be 11% (see Figure 1).

WACC for The Widget Company

Cost of Debt Cost of Equity

0.40 [Rd x (1-.30)] +
0.40 [5.0 x 0.7)] +
0.40 [3.5] +
1.40 +
WACC
Rounded WACC

0.60 [RF + b(RP)]
0.60 [5.0 + 1.3(8)]
0.60 [15.4]
9.24
10.64%
11%

Figure 1

In the next section of the tutorial, we'll do the final calculations to generate a fair value for the Widget Company.

DCF Analysis: Coming Up With A Fair Value

  1. DCF Analysis: Introduction
  2. DCF Analysis: The Forecast Period & Forecasting Revenue Growth
  3. DCF Analysis: Forecasting Free Cash Flows
  4. DCF Analysis: Calculating The Discount Rate
  5. DCF Analysis: Coming Up With A Fair Value
  6. DCF Analysis: Pros & Cons Of DCF
  7. DCF Analysis: Conclusion
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