FRIDAY'S KILLER QUESTION: A question involving interest rates and EPS
On alternate Friday afternoons we're posting cryptic questions from 7city Learning. Add your answers in the comments box at the bottom of the page. We'll add the official answer to the bottom of this article on Monday afternoon. The first correct answer will not win a prize, but will attract the admiration of the community.
Bob has done a lengthy study of the economy and a particular stock and has decided that he thinks the probability of an interest rate rise is 0.3. If rates don't rise, they'll stay the same. If rates rise, the EPS of the company has a 25% probability of being $4.00, and a 75% of being $4.40. If rates stay the same, there is a 33% chance that EPS is $4.80 and a 67% chance of them being $5.20. What is the expected value of EPS?
A $4.15
B $4.68
C $4.84
ANSWER
Correct Answer: C
A probability tree needs to be drawn. The probability of the four states of EPS are: Interest rate rise and lower EPS - p($4) = 0.3x0.25 = 0.075 Interest rate rise and higher EPS - P($4.40) = 0.3x0.75 = 0.225 Interest rate steady and lower EPS - p($4.80) = 0.7x0.33 = 0.231 Interest rate steady and higher EPS - p($5.20) = 0.7x0.67 = 0.469 So the expected value is the probability of each event multiplied by the value: Expected EPS = 0.075x$4 + 0.225x$4.40 + 0.231x$4.80 + 0.469x$5.20 Expected EPS = $4.84
