- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 4. The Discrete Uniform Distribution

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**CFA Practice Question**

A company is in breach of a covenant in the lending facility if the interest coverage ratio, EBITDA/Interest, falls below 3. You forecast interest of $30 million. You estimate EBITDA to be between $50 and $75 million. Assuming the outcomes for EBITDA are equally likely, what is the probability that the coverage ratio will fall below 1.8?

A. 12%

B. 15%

C. 16%

**Explanation:**You forecast interest of $30 million. You estimate EBITDA to be between $50 and $75 million. Assuming the outcomes for EBITDA are equally likely, the probability is 16%, and the coverage ratio will fall below 1.8.

EBITDA/Interest is a continuous uniform random variable because all outcomes are equally likely. The coverage ratio can have a range of values as follows:

EBITDA/Interest = 50/30 = 1.667 and EBITDA/Interest = 75/30 = 2.5.

Range = 2.5 - 1.667 = 0.833

The distance between 1.8 and 1.667 is 0.133.

The value of 0.133 as a percentage of 0.833 is 0.133/0.833 = 0.16 = 16%.

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**User Contributed Comments**
10

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

dimos |
Any comments on my approach? 1.8*30m=54m. EBITDA must be below 54m which means between 50m and 54m. The probability is 4/25=16% |

eddeb |
exactly the same approach. |

DAS11 |
Same here...hope its right and not just a coincidence. |

dimanyc |
Also can use cont distr formula: (x-a)/(b-a)=(54-50)/(75-50)=0.16. but it's pretty much the same thing |

apiccion |
@dimos I used the exact same approach. |

zzhumanov |
thanks for all |

Gooner7 |
I assume the key words are "both scenarios equally likely" ? |

atemple315 |
I took the same approach, then read the wording so that the ratio had to be "below" 1.8. And recalculated so that the EBITDA was below 54m and got it wrong. Very frustrating, sometimes they use this word play to trip you up. This time there was no word play and I tripped myself up!! |

Rosalind |
This question is very sensitive to whether you consider 'between' to include 50 and/or 75 or not |

CWade10 |
could you calculate a z score here? i did (.5-.25)/(.25) and got 1 which has the 68% probability related to it then the lower tail probability .32/2 = 16% |