Estimating Cost of Capital

To value Kleiner Perkins’ investment in Ideko, we need to assess the risk associated with Ideko and estimate an appropriate cost of capital.

Because Ideko is a private firm, we cannot use its own past returns to evaluate its risk, but must instead rely on comparable publicly traded firms.

Here, we use data from the comparable firms identified earlier to estimate a cost of capital for Ideko. First, we estimate the equity cost of capital for Oakley, Luxottica Group, and Nike. Then, we estimate the unlevered cost of capital for each firm based on its capital structure.

Once we have this estimate, we can use Ideko’s capital structure to determine its equity cost of capital or WACC, depending on the valuation method employed.

CAPM Based Estimation

To determine an appropriate cost of capital, we must first determine the appropriate measure of risk.

Kleiner Perkins’ investment in Ideko will represent a large fraction of its portfolio. As a consequence, Kleiner Perkins itself is not well diversified.

But Kleiner Perkins’ investors are primarily pension funds and large institutional investors, which are themselves well diversified and which evaluate their performance relative to the market as a benchmark.

Thus, you decide that estimating market risk using the CAPM approach is justified.

Using the CAPM, we can estimate the equity cost of capital for each comparable firm based on the beta of its equity. The standard approach to estimating an equity beta is to determine the historical sensitivity of the stock’s returns to the market’s returns by using linear regression to estimate the slope coefficient in the equation:

\[\begin{align*} & \text{Excess Return}_s = \alpha_s + \beta_s (\text{ Excess Return on Market Porfolio}) + \epsilon_s \end{align*}\] \[\begin{align*} R_s - r_f = \alpha_s + \beta_s * (R_{mkt} - r_f) + \epsilon_s \end{align*}\]

where,

\(R_s\) = return of the stock
\(r_f\) = risk free rate
\(R_{mkt}\) = return of the market portfolio
\(\alpha_s\) = intercept of the regression
\(\beta_s\) = slope of the regression
\(\epsilon_s\) = error (or residual) termk

As a proxy for the market portfolio, we use a value-weighted portfolio of all NYSE, AMEX, and NASDAQ stocks.

With data from 20X0 to 20X4, we calculate the excess return—the realized return minus the yield on a one-month Treasury security—for each firm and for the market portfolio. We then estimate the equity beta for each firm by regressing its excess return onto the excess return of the market portfolio. We perform the regression for both monthly returns and 10-day returns. The estimated equity betas, together with their 95% confidence intervals, are shown:


While we would like to assess risk and, therefore, estimate beta based on longer horizon returns (consistent with our investors’ investment horizon), the confidence intervals we obtain using monthly data are extremely wide. These confidence intervals narrow somewhat when we use 10-day returns. In any case, the results make clear that a fair amount of uncertainty persists when we estimate the beta for an individual firm.

Unlevering Beta

Given an estimate of each firm’s equity beta, we next “unlever” the beta based on the firm’s capital structure:

\[\begin{align*} \beta_U = ({\text{Equity Value} \over \text{Enterprise Value}}) \beta_E + ({\text{Net Debt Value} \over \text{Enterprise Value}}) \beta_D \end{align*}\]

We must use the net debt of the firm—that is, we must subtract any cash from the level of debt — so we use the enterprise value of the firm as the sum of debt and equity in the formula.


Above we show the capital structure for each comparable firm. Oakley has no debt, while Luxottica has about 17% debt in its capital structure. Nike holds cash that exceeds its debt, leading to a negative net debt in its capital structure.

Here, we have used an equity beta for each firm that falls within the range of the results from the first table shown further above this page. Given the low or negative debt levels for each firm, assuming a beta for debt of zero is a reasonable approximation. Then, we compute an unlevered beta for each firm according to the above equation.

The range of the unlevered betas for these three firms is large. Both Luxottica and Nike have relatively low betas, presumably reflecting the relative non-cyclicality of their core businesses (prescription eyewear for Luxottica and athletic shoes for Nike). Oakley has a much higher unlevered beta, perhaps because the high-end specialty sports eyewear it produces is a discretionary expense for most consumers.

Ideko’s Unlevered Cost of Capital

The data from the comparable firms provides guidance to us for estimating Ideko’s unlevered cost of capital.

Ideko’s products are not as high end as Oakley’s eyewear, so their sales are unlikely to vary as much with the business cycle as Oakley’s sales do. However, Ideko does not have a prescription eyewear division, as Luxottica does. Ideko’s products are also fashion items rather than exercise items, so we expect Ideko’s cost of capital to be closer to Oakley’s than to Nike’s or Luxottica’s. Therefore, we use 1.20 as our preliminary estimate for Ideko’s unlevered beta, which is somewhat above the average of the comparables shown above.

We use the security market line of the CAPM to translate this beta into a cost of capital for Ideko. In mid-20X5, one-year Treasury rates were approximately 4%; we use this rate for the risk-free interest rate.

We also need an estimate of the market risk premium. Since 1960, the average annual return of the value-weighted market portfolio of U.S. stocks has exceeded that of one-year Treasuries by approximately 5%. However, this estimate is a backward-looking number. Some researchers believe that future stock market excess returns are likely to be lower than this historical average. To be conservative in our valuation of Ideko, we will use 5% as the expected market risk premium.

Based on these choices, our estimate of Ideko’s unlevered cost of capital is:

\[\begin{align*} r_U = r_f + \beta_U ( E[R_{mkt}] - r_f) \end{align*}\] \[\begin{align*} = 4 \text{ % } + 1.20 * 5 \text{ % } \end{align*}\] \[\begin{align*} = 10 \text{ % } \end{align*}\]

Of course, this estimate contains a large amount of uncertainty (and why also including a sensitivity analysis with regard to the unlevered cost of capital can also be quite useful.

As with any analysis based on comparables, experience and judgment are necessary to come up with a reasonable estimate of the unlevered cost of capital. In this case, our choice would be guided by industry norms, an assessment of which comparable is closest in terms of market risk, and possibly knowledge of how cyclical Ideko’s revenues have been historically.