### CFA Practice Question

An investment of 2.5 million in a venture capital project has the following probabilities of failure over the next four years:

Year 1: 60%; Year 2: 55%; Year 3: 45%; Year 4: 30%

If the project succeeds at the end of the fourth year, the investor can exit with 13.5 million cash. Given the risk of the investment, the discount rate is 40%. Should this investment be undertaken?
A. No. Expected NPV is -2.26 million.
B. Yes. Expected NPV is 1.01 million.
C. No. Expected NPV is -0.06 million.
Explanation: The probability of success over four years is the product of probabilities of success in each year. Thus,

Prob(S) = (1 - 0.60) x (1 - 0.55) x (1 - 0.45) x (1 - 0.30) = 0.069
Prob(F) = 1 - 0.069 = 0.931

Prob(F) is the probability of ONE failure over the next four years.
PV of cash flow after four years = 13.5 / (1.4)4 = 3.51 million
Expected (NPV) = 3.51 x 0.069 + 0 x 0.931 - 2.5 = -2.26 million < 0

Since the expected NPV is negative, the investment should be turned down.

User Comment
staudinger you have to decide if with the high discount rate this project justifiable ...
dwalasinski Alternatively, you could simply start with the expected payoff of the project, ignoring discounting:

.069 x \$13.5mm = \$931k expected payout.

\$931k < \$2.5mm so the project is clearly -NPV
Friso Isn't the unlikelihood of payout already captured in the 40% discount rate? In my opinion, you have 2 options:
1) you calculate expected pay off (based upon the 60%, 55% etc) and discount at the regular WACC, or
2) calculate possible outcome (13.5) and discount at a higher rate (40%) to account for riskiness.
This question 'punishes' the project twice for risk. Who agrees/why am I incorrect?
Knapp Dwalaslnskl is correct, thinking about it in terms of EV (Expected Value) is the easiest.
pablofor Frisco I see it the same way, the question is how do the CFA want us to put in the exam?
GBolt93 Frisco/Pablo, consider that most investors are risk averse a would still discount a project with 96% of failure higher than regular even if you adjust for EV. Alternatively consider that you'd have a much higher Cost of Capital for a project like that, on top of having a 96% chance of no payout in the end.
harrybay Still agree with Friso