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**CFA Practice Question**

A venture capital investment is expected to yield of payoff of $100 million in five years if it survives. The initial cost is $20 million and the appropriate discount rate is 20%. What is the average annual probability of failure that makes the investment's NPV = 0? In other words, what is the maximum annual average probability of failure before the investment is not acceptable?

A. 13%

B. 17%

C. 20%

**Explanation:**The NPV is equal to zero when:

Discounted expected payoff = Initial cost

[(1 - Average prob)

^{5}$100 million] / (1.20)

^{5}= $20 million

Average annual probability = 0.1303, or 13%

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**User Contributed Comments**
8

User |
Comment |
---|---|

chamad |
More details? Anyone? with BAII if possible? Thanks |

chamad |
Ok Got it. Discounted expected payoff = PAY OFF * prob of succes each year (p1*p2*p3*p4*p5). Since we are considering an average=p5. Remember we're looking for prob of failure and not success so use (1-p)5 |

azramirza |
Solve for opp |

maria15 |
Can someone please explain? Thanks |

bluejazzy1 |
NPV = 0 when initial cost = pv of cf for the project to happen, it must not fail in 5 years, therefore it faces a probability of surviving (we can call that X) every year. The probability of it surviving 5 years would be x^5. The probability of it not surviving 5 years is (1-X)^5 |

mynotes1 |
This answer ignores the impact to NPV under the 'Failure' scenario. The NPV is the weighted ave of the 'success' and 'failure' scenarios. in this case, prob fail = 50.15% that the 20M outlay is lost, so total NPV actually = -10.03M |

ebola |
bluejazzy1 - you got it backwards. It's asking for prob of failure. 1-prob failure = success. Therefore, the threshold of failure is prob of failure and you set the two equal to know the limit of success. 1-x in this case is prob of success. |

Chl4072 |
How to calculate by BA II...?thanks. no understand |