Final answer:
Using the expected value formula and substituting the provided sustainable and non-sustainable values, the assumed probability of the company being sustainable is calculated to be approximately 4.26% over a 9-year horizon.
Step-by-step explanation:
To find the assumed probability of being sustainable, we have to compare the expected value of the company if it is sustainable versus if it is not. Given that the value of sustainable investing is $175.1, and the value of non-sustainable investing is $12.61, we need to calculate the probability that the company is sustainable based on its expected value of $19.53 over a 9-year horizon, using a discount rate of 9.2%.
The formula to calculate the expected value (EV) considering two scenarios (sustainable and non-sustainable) is:
EV = (Probability of Sustainability) * (Value of Sustainable Investing) + (1 - Probability of Sustainabilty) * (Value of Non-Sustainable Investing)
We know the EV is $19.53. Substituting the known values:
$19.53 = (Probability of Sustainability) * $175.1 + (1 - Probability of Sustainability) * $12.61
Solving this equation for the Probability of Sustainability (p), we get:
$19.53 = p * $175.1 + (1 - p) * $12.61
p * $175.1 + $12.61 - p * $12.61 = $19.53
p * ($175.1 - $12.61) = $19.53 - $12.61
p = ($19.53 - $12.61) / ($175.1 - $12.61)
p = $6.92 / $162.49
p ≈ 0.0426 or 4.26%
Therefore, the assumed probability of the company being sustainable is approximately 4.26%.