An approach to leverage a stochastic (Monte Carlo) model of a business for risk-adjusted valuation and hurdle rates

1. RISK ADJUSTED
BUSINESS VALUATION
Leveraging Stochastic Models to Price Businesses
and Calculate Hurdle Rates
Damon Levine, CFA, CRCMP

2. PRELIMINARIES
• We consider a single line of business (LOB) for illustrative purposes
• A stochastic model1 is assumed to exist with capabilities including simulation, on an
annual basis, of:
• Financial results with dynamic accounting logic and many model years (e.g. 20 or 30
years)
• Earnings (GAAP, STAT or some other basis)
• Free cash flows or (in the case of an insurer) distributable earnings
1: see http://www.ermsymposium.org/2016/ERM_Additional_Papers/Levine.pdf

3. MODEL ATTRIBUTES
• The model captures the company risk profile including both internal and external
risks
• Risks or risk scenarios manifest randomly in the model and reflect appropriate
probability and correlation assumptions
• Economic scenarios are a subset of the macro scenarios captured in the model
• The final model year (e.g. year 20 or 30) includes a terminal value calculation to
reflect future earnings or cash flows

4. SIMULATION OUTPUT
• Each simulation contains many years of earnings, free cash flows or what ever is
desired as the key input for valuation (henceforth called “earnings”)
• The general approach is to take the present value of the earnings as a measure of
company value
• So each simulation will have a unique vector of earnings and we calculate the
present value of earnings (called “PV” on subsequent slides)
• The interest rate used for the PV calculation is up for debate and could be WACC, a
risk free rate or some other choice

5. RUNNING MANY SIMULATIONS
• Let us assume on Monday we run 10,000 simulations and on each simulation we
calculate the PV; we therefore have 10,000 different values of PV
• We run 10,000 simulations again on Tuesday and observe that there is stability in
the results; i.e., the average, median, and various percentiles of the simulated PVs
are approximately the same as on Monday
• The number 10,000 may need to be bigger; the important thing is to find a
minimum number that ensures we have such stability in results from one run to the
next

6. LOB VALUATION
• We may then define the business’s value, V, as the average of the simulated PVs
• Note that this is a probability weighted average or statistical expectation (“expected
value”)
• The use of expectation to value an uncertain quantity is a standard approach in
finance and investments (e.g. valuation of a derivative or expected return of an asset
can be determined in this manner)

7. RISK ADJUSTED HURDLE RATE
• Consider the financial Plan for the LOB and work with Finance and the LOB to
extend this forecast to the full model time horizon
• This is a “baseline” or best-estimate forecast
• Solve for the interest rate, r, such the present value of earnings in the baseline
forecast is equal to V
• The rate r is a risk-adjusted rate and reflects the volatility of earnings for the LOB;
the difference between r and the WACC (or other reference rate) may be regarded
as a (risk based) spread for the business

8. ABOUT THE AUTHOR
Damon Levine is a published enterprise risk management thought leader, cyber risk consultant,
and industry speaker. He is the winner of the Actuarial Foundation's ERM Research Excellence
Award for his whitepaper "Enterprise Risk-Reward Optimization: Two Critical Approaches" and the
Joint CAS/CIA/SOA award for practical risk management applications for the paper "Growth in
Stock Price as the ERM Linchpin".
He is a frequent speaker at RIMS, the Enterprise Risk Management Symposium, Insurance Nexus,
ISO's ERM Forum, Actuarial Society of NY and Marcus Evans conferences. He has taught actuarial
mathematics at Columbia University and is published in The Actuary and included in Society of
Actuaries' exam syllabus. Recently, he authored the cover article for the March 2017 issue of the
CAS/CIA/SOA Joint Risk Management journal. Mr. Levine holds a Masters in Mathematics, and is a
Chartered Financial Analyst (CFA), and Certified Risk and Compliance Management Professional
(CRCMP) with over 20 years experience in risk management, insurance, asset management, and
consulting.
https://www.linkedin.com/in/damon-levine-cfa-crcmp-40722714/