# Natural log computation

In problem 3, page 363 of Quant, we are given a regression model for number of analysts who follow a company: AF_i = b0 + b1 SIZE_i + b2 (D/E)_i SIZE is the natural log of market cap, and we are told that market cap is \$100 million. If you are told that b0 = 0.20, b1=0.30, b2=0.4, and D/E = 0.75, how would you calculate AF_i?

AF_i= .2+.3(ln100)+.4(.75)

Why ignore the million part?

Another question concerning the p value. They show that p-value =0.00236 for the D/E ratio variable. So, is D/E a significant variable in this model or not? p-value always confuses me!

1st question: In the af_i question - they would have told you that the size is in units of Millions of \$. 2nd question: p-value is the minimum probability that the variable would be significant. In this case - the minimum value is 0.2% --> so definitely significant, even if you took a Level of significance of 1%.

Thanks cpk. on the first question they do say it is \$100 million, but they compute it as only \$100, and in another example it is \$1 billion, and they calculate it as 1000. This makes a difference in the answer. See page 363.

I think this is a bit tricky as you should not include the millionth part if it says size is in millions of dollars!

Problem 3 -> pg 363 --> they do tell you that sizet is in millions of Dollars.

Problem 3 -> pg 363 --> they do tell you that sizet is in millions of Dollars. so for Company A-> 100 Company B -> where it is 1 Billion \$ -> it is 1000 Million to be used.

If units of MarketCap in the formula is millions of dollars , then be careful to put in given values divided by 1 miliion. That is the ONLY catch in the problem e.g. if company cap is \$ 1 Billion then put in 1000 ( i.e. \$1 Billion/\$1Million = 1000 )

I had issues with this ? too.

I believe they are wrong, but we’ll just do what they expect. Whenever you take out the zeros from intermediate calculations, you have to put them back in in the final answer. They don’t do that though!

I had a question like this to that did NOT specify millions of dollars, and it was a market cap of \$500 million, but the answer took ln(500) rather than ln(500,000,000). I am fairly certain in the absence of a “units are in “x” amount” qualifier, this is an erroneous question.

I am a little confused about this. I understand that we are to use ln(500) for 500 million. In the CFA books one of the solutions is showing that ln(1000) is used for 1 billion however in another question ln (900000) is used for 900 million. Shouldn’t it be ln (900). I am having a really hard time understanding the logic behind this. Any thoughts?

Please give the volume and page references for these two examples.

Thank you for your response and my apologies in not proving references. Here it is;

CFA Level 2 Volume 1, Reading 10, Practice Problem Solutions for Question number 4 (page 200) is the one where the solution uses ln (900,000).

please read the last line of the question : it says Company size is measured by the natural logarithm of the book value of company’s assets in thousands of Canadian dollars.

please correct me if am wrong.

That makes sense… Thank you for your help.