"DCF
and the Hubble Telescope", this is the provocative title to a
presentation by Rajeev Thakkar, CFA, in April 2018. Thakkar's
presentation is primarily about input sensitivity of Discounted Cash Flow (DCF)
models. Thakkar did not discuss the exact DCF model he used but provided enough
information to figure it out. The presentation starts off with a table showing input values and resulting DCF values for 3 scenarios - A, B, C.
B is the base case, most likely scenario. A is the optimistic scenario
and C is the pessimistic scenario. Each scenario uses the same starting
cash flow but different inputs for cash flow growth (g1, g2) and equity cost of
capital (CoC1, CoC2).
Thakkar makes references to Dr. Damodaran several
times during his presentation, so it seemed likely he used a model based on
Damodaran's teachings. Since the table included 2 growth rates, next 10
years and terminal value, it seemed logical he used Damodaran Two-Stage growth
model. Running Thakkar's numbers through the following Damodaran formula
validated the model used.
Damodaran Two-Stage Valuation Model:
DCF = Present Value of Stage 1 Cash Flows
+ Present
Value of Terminal Value
= (Starting
Cash Flow)(1+g1)(1-(((1+ge1)/(1+CoC1))^10))/(CoC1-g1)
+ (Starting
Cash Flow)(1+g2) (((1+ge1)/(1+CoC1))^10) /(Coc2-g2)
Varying g1, g2, CoC1, and CoC2 as shown in Thakkar table results in DCF of 306, 720, and 157 for the base, optimistic, and pessimistic
scenarios. What struck me odd was the use of a exacting formula with uncertain inputs. To me, Thakkar's presentation was more of a
statement about the art of valuation. Damodaran's Two-Stage valuation
model is mathematical correct, but unlikely to produce more useful results then simpler formulas. I think a more practical formula for valuation is the one used on
the Polaris
website, namely:
DCF = (Dividend)(10)
+ (Current
Sales)(1+gs2)((1+gs1)^10)((Future PM)/Future Shares))(Future PE)/((1+CoC1)^10)
The first part of the formula omits the growing of dividends and discounting back because they tend to cancel each other out.
The second part of the formula uses well known ratios - Profit Margin (PM)
and mean reverted Price/Earnings (PE). Future Shares accounts for stock buybacks. The formula is easily understood, add up dividends for the first 10 years and then add the present
value of future sales per share times PM times PE.
I wondered what Dr. Damodaran thoughts were on this topic,
so I discussed with him on 07/26/18. I recently meet Dr. Damodaran by
taking his Advanced Valuation Certification class. Unlike courses
offered by other universities, Dr. Damodaran was very accessible.
At the start of the video call, I could not
help but notice Dr. Damodaran was enjoying his sabbatical. He was in a
lounge chair with the Pacific Ocean in the background. Not to disrupt his
time off too much, I jumped right into discussing valuation. First off,
Dr. Damodaran did not agree with the "Hubble Telescope"
analogy. He said valuation inputs do not typically vary independently of
each other. Changes to input values tend to offset each other resulting
in a reasonable changes to DCF.
The rest of my conversation with Dr. Damodaran was primarily
about false precision, using exact formulas with inexact inputs. He said
the preferred way to do DCF is to determine explicit cash flows for the first
several years and add on a terminal value. He said his Two-Stage
valuation model is an approximation and the Polaris practical formula is a reasonable approximation as well. Polaris practical formula shifts the inputs
from cash flow growth and cost of capital to sales growth, PM, PE, and
approximating future shares.
There are defensible ways to forecast sales
growth (analyst consensus forecasts), PM (industry historical average), and PE
(McKinsey convergence), but approximating future shares is more
difficult. Dr. Damodaran referenced a blog he just posted the day
before titled “Share Count Confusion" on his "Musing with
the Markets" blog. In the blog he discusses an alternative to compute DCF by excluding negative cash flows and forecasting the
number of new shares to cover them, which is essentially what the Polaris
practical formula does. The blog suggests how to replace explicit
negative cash flows with newly issued shares.
Unfortunately, there was
not enough time to discuss how to forecast new shares when using an
approximation formula. In a comment to his blog, I suggested calculating
historical trend of shares growth to sales growth and multiplying by forecasted
sales growth. I hope to discuss this further with him.
This blog is a reminder that valuation is a craft consisting
of some science and art. It is important to keep the exactness of
formulas and inputs in balance in order to end up with useful accuracy.
