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**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.

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**User Contributed Comments**
7

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 |