In the last four posts, I laid our alternatives to the CAPM beta, but all of them were structured around adjusting the discount rate for risk. Having made this pitch many times in the past, I know that there are some of you who wonder why I don't risk adjust the cash flows instead of risk adjusting the discount rate. The answer to that question, though, depends on what you mean by risk adjusting the cash flows. For the most part, here is what the proponents of this approach seem to mean. They will bring in the possibility of bad scenarios (and the outcomes from these scenarios) into the expected cash flows and thus risk adjust them. As I will argue below, that is not risk adjustment.

It is true that there are two ways in which you can adjust discounted cash flow value for risk. One is to estimate expected cash flows across all scenarios, essentially multiplying the probability of each scenario by the likelihood of that scenario unfolding, and then to discount those expected cash flows using a risk adjusted discount rate. The other is to take the expected cash flows and replace them with "certainty equivalent" cash flows and discounting those certainty equivalent cash flows at the riskfree rate.

But what are certainty equivalent cash flows? To illustrate, let me provide a simple example. Assume that you have an investment, where there are two scenarios: a good scenario, where you make $ 80 instantly and a bad one, where you lose $ 20 instantly. Assume also that the likelihood of each scenario occurring is 50%. The expected cash flow on this investment is $30 (0.50*$80 + 0.50*- $20). A risk neutral investor would be willing to pay $ 30 for this investment but a risk averse investor would not. He would pay less than $ 30, with how much less depending upon how risk averse he was. The amount he would be willing to pay would be the certainty equivalent cash flow.

Applying this concept to more complicated investments is generally difficult because there are essentially a very large number of scenarios and estimating cash flows under each one is difficult to do. Once the expected cash flow is computed, converting it into a certainty equivalent is just as complicated. There is one practical solution, which is to take the expected cash flow and discount it back at just the risk premium component of your discount rate. Thus, if your expected cash flow in one year is $ 100 million, and your risk adjusted discount rate is 9% (with the risk free rate of 4%), the certainty equivalent for this cash flow would be:

Risk premium component of discount rate = (1.09/1.04)-1 = 4.81%

Certainty equivalent cash flow in year 1 = $ 100/ 1.0481 = $95.41

Value today = Certainty equivalent CF/ (1 + riskfree rate) = $95.41/1.04 = $91.74

Note, though, that you would get exactly the same answer using the risk adjusted discount rate approach:

Value today = Expected CF/ (1 + risk adjusted discount rate) = 100/1.09 = $91.74

Put differently, unless you have a nifty way of adjusting expected cash flows for risk that does not use risk premiums that you have already computed for your discount rates, there is nothing gained in this exercise.

There is two practical approaches to certainty equivalent cash flows that I have seen used by some value investors. In the first, you consider only those cash flows from a business that are "safe" and that you can count on, when you do valuation. If you do so, and you are correct in your assessment, you don't have to risk adjust the cash flows. The next time you are told that Buffett does not risk adjust his valuations, take a look at whether this is in fact what he is doing. The second variant is an interesting twist on dividends and a throw back to Ben Graham. To the extent that companies are reluctant to cut dividends, once they initiate them, it can be argued that the dividends paid by a company reflects its view of how much of its earnings are certain. Thus, a firm that is very uncertain about future earnings may pay only 20% of its earnings as dividends whereas one that is more certain will 80% of its earnings. An investor who buys stocks, based upon their dividends, thus has less need to worry about risk adjusting those numbers.

Alternatives to the CAPM: Part 1: Relative Risk Measures

Alternatives to the CAPM: Part 2: Proxy Models

Alternatives to the CAPM: Part 3: Connecting cost of equity to cost of debt

Alternatives to the CAPM: Part 4: Market-implied costs of equity

Alternatives to the CAPM: Part 5: Risk adjusting the cash flows

Alternatives to the CAPM: Wrapping up

It is true that there are two ways in which you can adjust discounted cash flow value for risk. One is to estimate expected cash flows across all scenarios, essentially multiplying the probability of each scenario by the likelihood of that scenario unfolding, and then to discount those expected cash flows using a risk adjusted discount rate. The other is to take the expected cash flows and replace them with "certainty equivalent" cash flows and discounting those certainty equivalent cash flows at the riskfree rate.

But what are certainty equivalent cash flows? To illustrate, let me provide a simple example. Assume that you have an investment, where there are two scenarios: a good scenario, where you make $ 80 instantly and a bad one, where you lose $ 20 instantly. Assume also that the likelihood of each scenario occurring is 50%. The expected cash flow on this investment is $30 (0.50*$80 + 0.50*- $20). A risk neutral investor would be willing to pay $ 30 for this investment but a risk averse investor would not. He would pay less than $ 30, with how much less depending upon how risk averse he was. The amount he would be willing to pay would be the certainty equivalent cash flow.

Applying this concept to more complicated investments is generally difficult because there are essentially a very large number of scenarios and estimating cash flows under each one is difficult to do. Once the expected cash flow is computed, converting it into a certainty equivalent is just as complicated. There is one practical solution, which is to take the expected cash flow and discount it back at just the risk premium component of your discount rate. Thus, if your expected cash flow in one year is $ 100 million, and your risk adjusted discount rate is 9% (with the risk free rate of 4%), the certainty equivalent for this cash flow would be:

Risk premium component of discount rate = (1.09/1.04)-1 = 4.81%

Certainty equivalent cash flow in year 1 = $ 100/ 1.0481 = $95.41

Value today = Certainty equivalent CF/ (1 + riskfree rate) = $95.41/1.04 = $91.74

Note, though, that you would get exactly the same answer using the risk adjusted discount rate approach:

Value today = Expected CF/ (1 + risk adjusted discount rate) = 100/1.09 = $91.74

Put differently, unless you have a nifty way of adjusting expected cash flows for risk that does not use risk premiums that you have already computed for your discount rates, there is nothing gained in this exercise.

There is two practical approaches to certainty equivalent cash flows that I have seen used by some value investors. In the first, you consider only those cash flows from a business that are "safe" and that you can count on, when you do valuation. If you do so, and you are correct in your assessment, you don't have to risk adjust the cash flows. The next time you are told that Buffett does not risk adjust his valuations, take a look at whether this is in fact what he is doing. The second variant is an interesting twist on dividends and a throw back to Ben Graham. To the extent that companies are reluctant to cut dividends, once they initiate them, it can be argued that the dividends paid by a company reflects its view of how much of its earnings are certain. Thus, a firm that is very uncertain about future earnings may pay only 20% of its earnings as dividends whereas one that is more certain will 80% of its earnings. An investor who buys stocks, based upon their dividends, thus has less need to worry about risk adjusting those numbers.

__Bottom line__. There are no short cuts in risk adjustment. It is no easier (and often more difficult) to adjust expected cash flows for risk than it is to adjust discount rates for risk. If you do use one of the short cuts - counting only safe cash flows or just dividends - recognize when these approaches will fail you (as they inevitably will) and protect yourself against those consequences.**The series on alternatives to the CAPM**Alternatives to the CAPM: Part 1: Relative Risk Measures

Alternatives to the CAPM: Part 2: Proxy Models

Alternatives to the CAPM: Part 3: Connecting cost of equity to cost of debt

Alternatives to the CAPM: Part 4: Market-implied costs of equity

Alternatives to the CAPM: Part 5: Risk adjusting the cash flows

Alternatives to the CAPM: Wrapping up

## 7 comments:

Professor,

I am guessing the aim of such an exercise by adjusting the cash flows is to arrive at some sort of "true expected cash flow" as opposed to most likely cash flow that we use in DCF (Mind you the latter is sometimes is wrongly dubbed as EXPECTED, whereas it's not.)

Another problem that I have getting my head around is how can the expected cash flow be assigned a lot of relevance by an investor when he is well and truly aware that EXPECTED cash flow is not to be expected in real life due to that cash flow not physically occurring ie In your above example $30 will not happen no matter what the case.

And in your opinion should risk adjustment be consistently applied to a valuation just like any other metric e.g. change in leverage will affect both cash flows and discount rate OR only one measure from either Discount rate or cash flow needs adjustment to account for the risk.

Thanks in advance.

Vinny,

That is actually not true. The cash flow in a DCF valuation is supposed to be the expected cash flow, not the most likely cash flow. The best description for the cash flow I am computing here is that it is a risk adjusted cash flow. If investors were risk neutral, that would be the expected cash flow... but they are not.

Professor,

Thanks for your input there. I stand corrected on the 1st point, but there are definitely some references out there where a central or most likely scenario is used in developing cash flow forecasts rather than an expected value specifically arrived at by probability weighting the cash flows.

And following on from that if I recall it right, then in your catastrophic events post you mentioned that unless one adjusts both the cash flow and discount rate for an un-diversifiable source of risk, one is not correctly adjusting for risk.

But for security specific risk, would one use the same approach or adjust only one of the variables out of cash flow/discount rate to account for that risk.

Thanks!

Dear Professor Damodaran,

Thank you very much for your very instructive posts. I have a question regarding the example you give, and the conclusion you draw:

"Put differently, unless you have a nifty way of adjusting expected cash flows for risk that does not use risk premiums that you have already computed for your discount rates, there is nothing gained in this exercise."

In the first year, the values of the discounted cash flows using the Risk-Adjusted Discount Rate (RADR) and the Certainty Equivalent (CE) methods are the same ($91.74 in your example). But if you were to extend this example for 10 years, would this still be the case?

Unless you compound the risk premium each year, the certainty equivalent cash flow each year would be $95.41, and the risk-free discount rate would be applied to that.

Then, the net present value of the expected cash flows using the RADR would be approximately $642, whereas the net present value of the certainty equivalent cash flows using the risk-free discount rate would be approximately $774. This is quite a big difference.

My underlying assumption is that the risk premium is not compounded, and this is what creates the discrepancy. Does it really make sense to compound the risk premium? (which is effectively what you are doing when you use a RADR)

Thank you in advance for your response.

Best regards,

Andreas

Hi Professor,

What if the expected Cash Flow is negative?

One of the assumptions that underlies the dcf model is that risk grows in a constant and controlled manner. One of our observations in the mining industry is that metal price risk in base metals initially grows quickly, but then slows - reflecting reversionary price expectations and other market factors. One of the problems with dcf is that use of a single "market" discount rate over values short life mines and under values long life mines. Wondering what you think of adjusting key sources of risk like metal price to certainty equivalents and then applying a lower dcf discount rate to calculate npv - where the dcf discount rate is rfr plus a residual premium. For all other risks?

rc

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