Hi everyone,

I know when calculating the WACC for a DCF model usually the cost of equity (in %) is multiplied with the market value of equity, not the book value, right?
But when valuing a stock with the residual income model, usually the cost of equity (in %) is multiplied with the book value of equity. Here is the equation for the residual income model (same as in the image)...

Value (today) = Book Value (totay) + (Earnings for period 1 - (cost of equity x book value of equity)

Can you please tell me, why we use book value of equity here instead of market value, which I think makes more sense?
Thank you!

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Read either of Bennett Stewart's two books for more details. The idea here has to do with how you are going about the valuation. The Residual Income (or EVA or Excess Profits) calculation uses more of a replacement cost concept for the Invested Capital, which is what the Book Value of Equity represents in your equation above. Let's look at this simple example. Suppose you have one shareholder who puts in \$100 in the firm and you bought a machine for \$100. Now suppose the market value of the machine drops to \$50. At the end of one year, the investor still expects a return equal to r*\$100. If the investor only demanded a return of r*\$50, then you are basically being rewarded for poor performance because the hurdle (i.e., capital charge or r*B) is going to be lower everytime you perform worse.

There are also many little assumptions so that the valuation generated by FCFF/WACC and EVA/Residual Income end up being equal (many of which are easily violated in practice). A good discussion of this is by Damodaran. You can Google that document.

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Thank you for your time! That has helped me!

Thank you for your time! That has helped me!

Best Response

Residual income model just uses book value as a starting point. If the stock's ROE is the same as its cost of equity, then it is worth 1x book value. If ROE exceeds cost of equity then it is worth more than 1x, vice versa if ROE is lower.

So in the formula you posted the r*B is sort of like an imaginary interest payment - it's the cost of using equity capital to generate those earnings.

You don't use market value of equity because that's a measure of what other people think the stock is worth - by using residual income model or DCF you're trying to figure out an intrinsic value.

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