Hi,
kindly help to to explain the below calculus for expected NPV.
An investment of 2.5 million in a venture capital has the following probablilities of failure over the next 4 years: 60%, 55%, 45%, 30%.
If the cash projects succeeds at the end of the 4th year the investor can exit with 13.5 million. Given the risk of the investment the discount rate is 40%. Should the investment undertaken?
Solution: No, expected NPV -2.26 mln.
The probability of success over the 4 years is the product of probabililies of the 4 years:
Prob(S) = (1-60%) * (1-55%) * (1-45%) * (1.30%) = 0.069
Prob(F) = 1 - 0.0696 = 0.931
Prob(F) is the probability of ONE failure over the next 4 years. PV of CF after 4 years: 13.3/1.4^4 = 3.51 mln
Expected NPV = 0.069 * 3.51 + 0.931 * 0 - 2.5 = -2.26 < 0 - project should be turned down