Home Value Investing Aswath Damodaran – Stare into the Abyss: Facing up to uncertainty with simulations

# Aswath Damodaran – Stare into the Abyss: Facing up to uncertainty with simulations

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Apple Inc. (NASDAQ:AAPL) Aswath Damodaran – Stare into the Abyss: Facing up to uncertainty with simulations

Published on May 23, 2016
In conventional financial analysis, you make point estimates for variables to arrive at an expected value. In a simulation, you assume probability distributions for input variables to derive a distribution of values, yielding a much richer set of data to make decisions with. In this webcast, I use Apple in May 2016 to illustrate the process.

## Apple – more info

Slides: http://www.stern.nyu.edu/~adamodar/pd…
Valuation of Apple: http://www.stern.nyu.edu/~adamodar/pc…

The Origins of Financial Analysis In both corporate finance and valuation, much of what we do is built around point estimates, made with the data that we have at the time of estimation. ¨ The reality is that what are estimating are distributions, with an expected value (that should be the point estimate) but also a substantial possibility of error. ¨ Our defense for using point estimates was that we lacked the data to estimate probability distributions and/or that doing valuations with distributions would require machine power that we did not have access to (at a reasonable price).
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A Big Picture View of Simulations ¨ In a simulation, you estimate probability distributions for each variable that goes into an analysis. ¨ In each simulation, you draw an outcome from each of the distributions and estimate the end result with those outcomes. Since these outcomes can come from the low end or high end of the distributions, they will be different. ¨ You run as many simulations as you can and come up with a distribution of the outcomes, which you then use for decision making. Step 1: Base Case Valuation Terminal Value= 38,110/(.08-.015) = \$586,304 Cost of capital = 10.59% (.892) + 1.% (.108) = 9.63% ERP 6.66% Beta 1.31 Cost of Debt Bond rating: AA- (1.9%+0.7%)(1-.35) = 1.69% Cost of Equity 10.59% Stable Growth g = 1.5%; Cost of capital = 8% ROC= 12%; Reinvestment Rate=1.5%/12% = 16.67% Weights E = 89.2% D = 10.8% + X In May 2016, Apple was trading at \$93 a share. Cost of capital decreases to 8% from years 6-10 Apple: Base Case Valuation (May 2016 Simulation Slides: http://www.stern.nyu.edu/~adamodar/pd…
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