Showing posts with label dicounted cash flow. Show all posts
Showing posts with label dicounted cash flow. Show all posts

Aug 30, 2009

DCF: Discounted Crash Flow

I remember in a 2007 client panel discussion I was chocked to hear that three large company CFOs of name and fame, without blinking an eye, stated that they were running their company on basis of a narrow quarterly time schedule, no longer. Long term investments? Out of the question. Pension obligations? Rather not, please... Project payback periods: 3-6 months, in exceptional cases a maximum of a year.

What was happening?
How come, CFOs have become that short term focused?

It's easy to come up with answers that pass the buck:
  • Extraordinary shareholder demands
  • Bonus Structure,
  • Greed, Grab Culture
However, despite and behind all this, there is a deeper cause.

Thinking concept
This short term focus, that is not limited to CFOs, is the logical consequence of the way our thinking and modeling has developed during the last decades:
  • we try to exclude risk at any price, instead of managing it.
  • we struggle and sometimes even fear to transform long term cash flows into discounted cash values or NPVs

According to a 2002 survey, more than 85% of the CFOs say they use NPV-analysis in at least three out of four decisions.
As actuaries we're also part of this family of Discounted Cash Flow (DCF) Experts. Some of us might even have thought there's nothing more to learn about DCF...

Of course we understand every technical detail of our DCF-model, but let's take a look at some classical aspects of the DCF technique from a different angle. I'll call this angle the I-View, with the I of Important.....

DCF properties
As we know the value of a future cash flow (cf ) , depends strongly on the choice of the discount rate (r) and the moment in time (t) of the cash flow. The further away (in time) the cash flow and the higher the discount rate, the lower the DCF value.

From an I-View perspective one might say that in the DCF of a constant cash flow, the contribution of the cash flow in year 10 is ruffly half as Important (UnImportant-effect) as a cash flow in year one, assuming a discount rate of 7%.

Another way of saying: This one off cash flow is only of 51% Importance to us.

Although this might not surprise you, a often heavy underestimated effect is that the UnImportant-effect rapidly increases in case a particular discounted cash flow in year (t) is part of and expressed as a percentage of a discounted fixed term (or perpetual) cash flow stream. This is illustrated in the next graph (base: r= 10% discount rate).

De relative contribution of a cash flow t, soon loses more and more Importance when it's part of a constant cash flow stream. As the term of this cash flow increases to infinity, the relative contribution of any 'one year cash flow' becomes rapidly UnImportant.

I-View 1: Discount Rate Adjustments
As we know, the choice of the discount rate depends on the type of cash flow. Cash flows with substantial risks are often discounted with an adjusted (higher) r, according to the (CAPM) formula:
r = rf + β×(rm - rf)
with: rf = risk free rate, rm = expected return on the market and β = (beta) a measure of the (opposed to the market) cash flow risk.

It's obvious this CAPM-method amplifies the mentioned 'UnImportant-effect' of long term cash flows.

In times of financial crisis, when we're inclined to become more risk averse, the 'UnImportant-effect' grows even more, as we are inclined to adjust r for fear:

r = rfear + rf + β×(rm - rf)

Moreover in general, the longer the cash flow term, the higher the (compound) expected risk, and therefore the higher the discount rate (r). Instead of a constant r, there's a need for a variable r, rt, that increases in time, intensifying the 'UnImportant-effect'.

I-View 2: Discount Rate of Liabilities
Another DCF example: A pension fund has extremely long term liabilities. A cash flow of - let's pick - 50 years ahead, is no exception, but only accounts for about 14% of its cash flow in the discounted liabilities of the pension fund (abstracting from mortality and assuming a discount rate of 4%), and is therefore implicit considered (rated) less Important compared to more recent cash flows. Because there's no real or substantial market for long term cash flow pension obligations, r is even harder to define. Increasing r for this risk is like putting the cart before the horse: The UnImportance effect will increase. For internal valuation r should be decreased instead of increased, but how.....?

I-View 3: Short term Ruin Probability Nonsense
A third effect is that a 0.5% yearly ruin probability sounds safe, but nevertheless compounds up to a risk of 14% over a period of 30 years and even more on the long term.
Years Cum.Ruin Risk
1 0.5%
10 4.9%
20 9.5%
30 14.0%
40 18.2%
50 22.2%
60 26.0%
70 29.6%
80 33.0%
90 36.3%
100 39.4%
FCLTOS, Financial Companies with Long Term Obligations, like banks, insurance companies or pension funds are by definition companies that have to stay ruin proof on the long term. Managing these kind of companies on short term ruin and certainty models is completely nonsense.

However, there's nothing much FCLTOS can do about it. A long-term certainty level of 99.5% (0.5% ruin risk) over a period of 40 years would imply a yearly certainty level of 99.9875% (0.0125% ruin risk). Even if it would be possible to minimize the technical risks to such a low level, it would be overshadowed by unquantifiable external outside risks (e.g. nature disasters). Anyhow, government regulators should define a target with regard to an appropriate choice of a long-term certainty level and should distinguish between short term and long term certainty in their models.

These examples illustrate that the management FCLTOS, giving these DCF-like methods, do not have another choice than to focus on the near future (5-10 years) and - by method - are not obliged and therefore also not will focus on the long term effects.

Managing FCLTOS, is like navigating an oil tanker from A to B between the ice floes. You have to avoid the short term (nearby)
risks (the ice floes) while at the same time keep sight and hold direction on your long term target (port B) in order to succeed.

Translated to a pension fund: manage your liquidity on the short term and your solvency and coverage-ratio on the long term. Any captain of an oil tanker would certainly be discharged immediately when he would make a dangerous change in course today to avoid an actual clear, but in the future certainly changing (moving targets) ice floe situation 50 km ahead. Yet, government regulators and supervisors are forcing pension fund 'captains' to undertake such ridiculous actions.

Steering on short term recovery plans , publishing and publicly discussing coverage-ratios and finally 'valuing pension funds' solely on market value (given that the market for extreme {> 30 years} long term assets and liabilities is extremely 'thin' and volatile), is therefore dangerous and apparently wrong (nonsense) and leads to discounted crash situations.

But there's more that contributes to discounted crash management......

One off negative cash flow in the future
Let's compare two (almost) equal cash flows, CFa and CFb:
- CFa: 30 year constant cash flow of yearly $1,
- CFb: like CFa, but in year 25 a one off negative cash flow : -$1

Although a negative cash flow of $1 in year 25 will probably ruin the activities an cash flows in later years, the NPV of the two cash flows only differ slightly and the calculated IRR of CFb (9.76%) is also just slightly lower than the IRR of CFa (10%).

One might argue that because CFb is obviously a more risky cash flow, the adjusted r has to be raised. This is true, but nevertheless intensifies the so called UnImportant-effect: the relative weight of the 'year 25 cash flow' in the NPV decreases.

Last but not least, what explains the short term attitude and those extreme short periods of several years or months, some CFOs practice as a time frame to run and control their company ?

Certainty Erosion
These extreme short periods are the consequence of the No. 1 concern for CFOs:

The fundamental and increasing lack of ability to forecast results

Let's do some rule of thumb exercise....

Assume the certainty level of calculating a sound financial forecast in the next period (year, quarter, month) is estimated by a CFO at C%.

Now take a look at the next table (on the right) that shows the average extrapolated certainty level (AC) over a number of periods P.

In formula:

Some examples from the table:
  • A CFO that estimates the 'next quarter result' with a certainty level of 70% (C=0.7), will probably not burn his fingers by presenting a full year forecast with an average expected certainty level of 44%.
  • A CFO of a company hit by the current financial crisis, estimates the certainty of his companies January results at 60%. The board announces it's not able to estimate the full year result. Right they are, with a 60% monthly certainty level, the full year result would have a certainty level of only 12%.....
  • Even a CFO with a superb forecast certainty level of 90%, will be cautious with a 5-year forecast (certainty level 74%).
  • A 'best of class actuary' that estimates the certainty level of his data at 90% on a yearly basis, will have a hard time in answering question about the certainty level of his projections over 14 years (50%?).

The I-View consequence of this 'compound certainty development' is that even at high levels of (yearly) certainty, the (average) certainty of cash flows after already a few years in the future, erodes.

The effects of Certainty Erosion are enormous. The wall of haziness that is created in a few years - at even high levels of certainty - is astonishing. Never 'believe' a long term one point forecast. Always request variance and certainty level(s) of presented forecasts.

We may conclude that DCF is a superb technique as such to analyze and value cash flows. To prevent ending up in a 'crash flow', DCF has to be implemented by professionals who realize that the essential point of DCF is not just the technique itself, but the way the parameters, used in the DCF-models, are defined.

In order to be able to really take responsibility in managing a company, the Board of a company should be involved in the selection and consequences of the deeper and underlaying DCF-parameters. Enough work for actuaries it seems....

Related Links:
- Some comments on QIS3, (Long term certainty levels)
- Quantifying Unquantifiable Risks