# why is a companies implied rate of return the correct discount rate for projected cash flows

Let's say we wish to value a company using the DCF method. To determine which discount rate to use for the cash flows we choose to use the CAPM methodology. The estimated beta of the company can tell us how its price today relates to the expected value of its price in the next period. I am having trouble seeing why this implied rate of return is also applicable for discounting the projected cash flows. Why should a company´s cash flows have the same beta as the companie´s value?

• It is only true for projects whose risk is similar to the overall existing business(es) of the company. If a company is getting involved in a completely new business the discount rate to use may indeed be different from this. (But if a car company builds a new car factory, the Beta of the car company is probably the correct risk measure for the new project). – noob2 Jul 27 '20 at 2:26

# Discount Rate Matches the Cashflow Type

For DCF valuation, there is a simple rule: the type of cashflow dictates the type of discount rate to use. Dividends are discounted at the CAPM rate (although one can also use other equity factor models). Free cash flow to the firm is discounted using the WACC; and, free cash flow to equity is discounted using the CAPM (or other equity factor model) rate after correcting for firm leverage.

I'm going to assume (maybe incorrectly) that the cashflows in your question are dividends. I said we could use any equity factor model, but let's stick to the CAPM.

# How CAPM Discounting Affects the Value of Dividends

We use the CAPM for discounting future dividends because it gives us the equilibrium expected return for investing in that firm. If the firm pays us dividends, that money will not grow at the same rate as the firm (unless we reinvest dividends). In some cases, that is good and we will redeploy that money to earn more elsewhere; in some cases, that is bad and we will not want to redeploy that money since it will likely earn less elewhere.

It helps to think of the perpetuity form for a dividend discount model with dividend growth (the Gordon model). That form gives us the equity value by $$E=\frac{D}{k-g}$$ where $$k$$ is the CAPM-implied discount rate and $$g$$ is the dividend growth rate.

If we rewrite the growth rate and dividends to account for $$ROE$$ and some fraction $$b$$ of dividends being reinvested in the firm, we get that equity is worth $$E=\frac{(1-b)D}{k-b\cdot ROE}$$. If $$ROE, the optimal policy is to not reinvest dividends. If $$ROE>k$$, we can grow the firm value without bound as $$b\uparrow\frac{k}{ROE}$$. (This is unrealistic, but it does give us an upper bound on the optimal reinvestment fraction $$b$$.)

Therefore, firms with a low ROE (slow growing firms with a low beta) should not keep excess cash. Those firms should pay that cash out to investors who can do better redeploying the funds to other firms.

Firms with a high ROE (above $$k$$, fast growing firms with a high beta) should reinvest some of their excess cash. Now, this model breaks down because it may even make sense for a firm to pay out no dividends while the firm is growing rapidly (when $$ROE>k$$). Ostensibly, the firm will eventually grow less quickly and then begin paying out dividends. We saw this happen with Microsoft which paid no dividend from its IPO in 1986 until 2003, when the firm began paying dividends.

# Why Use the CAPM for Discounting?

As for why to use the CAPM to discount projected cashflows: the CAPM is a forward-looking expectation of the return on the firm's stock. When we are thinking about the opportunity cost of getting dividends instead of having that money invested in the firm\s stock, a forward-looking estimate of the firm's expected stock return is a good estimate of that opportunity cost.

This is why we could also use other equity factor models: those also yield model-driven estimates of the firm's expected stock return.

# Beta of Firm's Cashflows?

Why should a company´s cash flows have the same beta as the companie´s value?

Firm cashflows do not have a beta. I suppose you could compute a cashflow beta, but I have never seen that done and I'm not sure it is very informative.

We refer to beta to describe a firm's stock returns as a multiplier of "the market's" excess returns. (We could fill a whole topic with "What is 'the market,' but that is another question.)

• "The firm should not keep money and invest it in their company. Investors could do better redeploying those funds to other firms". This thinking seems off to me. In the CAPM world each company's returns are competitive at their specific beta. – robot112 Jul 27 '20 at 8:03
• It is easier to see this if you look at the Gordon DDM and express the growth rate as a function of ROE and the fraction of dividends reinvested $b$. Depending on ROE, there are different optimal reinvestment policies. Returns are competitive; that does not mean dividend policy is irrelevant. – kurtosis Jul 27 '20 at 14:21
• Updated the above to use the Gordon+ROE dividend reinvestment thinking. – kurtosis Jul 27 '20 at 14:53
• Thanks for the edit, your answer makes much more sense now to me. I guess this is the capital markets way of incentivizing company`s to pursue projects which will help diversify the market as a whole. – robot112 Jul 28 '20 at 11:49

To determine which discount rate to use for the cash flows we choose to use the CAPM methodology.

The determination of the discount rate to use when discounting cash flows depends on what you're valuing. If it's the entire company, and not just it's equity, the discount rate is the WACC (i.e., weighted average cost of capital), that accounts for both debt and equity financing. It is nothing more than a weighted average of the required return on debt and the required return on equity.

CAPM is properly used to estimate the required rate on equity. In other words, what return does an investor who invests in the company's equity demands. It is generally used as the discount rate when you're valuing the company's equity, and therefore, the cash flows are the Free Cash Flows to Equity (in contrast to the Free Cash Flows to the Firm).

• this really doesn't answer my question – robot112 Jul 26 '20 at 23:18