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f. calculate the value of a private company using free cash flow, capitalized cash flow, and/or excess earnings methods;

g. explain factors that require adjustment when estimating the discount rate for private companies;

h. compare models used to estimate the required rate of return to private company equity (for example, the CAPM, the expanded CAPM, and the build-up approach);
CFA Program Curriculum (2015), Volume 4, Page 546.

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The income approach methods determine fair market value by multiplying future income/cash flows by a discount or capitalization rate. The discount or capitalization rate converts the future economic benefits into a present value.

There are three forms of income approach. They all involve estimating the required rate of return.

Required Rate of Return

Some issues when estimating the required rate of return:

  • Size premium: Should a smaller company's earnings or cash flow be discounted or capitalized at a higher rate (which results in a lower value) just because the private company is smaller than most public companies?

  • CAPM: E(R) = Rf + β x RPM, where Rf is the risk-free rate, and RPM is the risk premium for the market.

    CAPM uses past prices of an asset to estimate its risk parameters (β). However, private companies are not traded, and thus do not have past prices. Many appraisers argue risk estimation has to be based upon an approach that does not require past prices.

  • Expanded CAPM: E(R) = Rf + β x RPM + RPS + RPU, where RPS is the risk premium for the "small" stocks, RPU is the risk premium for company-specific risk attributable to the specific company.

  • Build-up approach: E(R) = Rf + RPM + RPS + RPi + RPU, where RPi is the industry risk premium.

  • Cost of debt: Private firms generally have limited access to public debt markets, and are therefore not rated. Most debt on the books is bank debt, and the interest expense on this debt might not reflect the rate at which they can borrow (especially if the bank debt is old.)

  • Discount rates in an acquisition context: The seller's (not the acquirer's) WACC should be used.

  • Discount rate adjustment for projection risk: When forecasting future financial performance of a private company, management may be biased or less experienced and outside appraisers may not have enough information - adjustments to the projected discount rate may be necessary.

Free Cash Flow Method

The method is similar for private and public companies: project the future free cash flows and discount them to present dollars to estimate their present value. The discount rate should be the company's WACC. A terminal value needs to be calculated when a stable growth rate is expected. The method is covered extensively in level 1.

Capitalized Cash Flow Method

It is often used for the valuation of small private companies that are expected to grow at a constant rate.

  • To value a firm: Vf = FCFF1/(WACC - gf), where gf is the sustainable growth rate of free cash flow to equity.
  • To value a firm's equity: V = FCFE1/(r - gf), where r is the required rate of return on equity and gf is the sustainable growth rate of free cash flow to equity.
In both equations the denominator is known as the capitalization rate, which is the rate to convert an income/cash stream into a present value lump sum.

Do they look familiar? Recall that in the dividend discount model (DDM), the value of stock is D1/(r - g), where D1 is the dividend of next period, r is the required rate of return on equity, and g is the dividend growth rate.

Excess Earnings Method

This method basically values a company in two pieces - the tangible value and the intangible value.

  • The tangible value of the company is simply calculated as the value of the company's net worth (i.e., working capital + fixed assets).
  • The intangible part is calculated by capitalizing those earnings that are calculated to be in "excess" of what a reasonable amount of earnings would be on the company's tangible net worth.
  • Adding the tangible and intangible values of the company together results in the value of the entire company.
Assume a company has a $1 million in tangible equity and net profits of $150,000 per year. Its return on tangible equity is then 15%. Now assume that a "normal" company in the business earns only a 10% return on tangible equity. Our company should therefore be expected to earn a net profit of $100,000. The "excess earnings" of $50,000 indicate the existence of intangible value at the company.

We need to capture the value that the $50,000 in excess earnings represents. Assume a 20% capitalization rate is used, $50,000/ 20% = $250,000.

Adding the tangible value of $1 million to the intangible value of $250,000 gives us the total value of the company of $1,250,000.

Generally, the EEM has been used to value intangible assets and very small businesses. The problem with the method is that significant judgment is associated with many of these estimates.