# Expected Return on Investment.

Hi,

just doing some last minute questions here and i was a bit stumped on how this answer is being derived.

Appreciate any help on this. Thanks!

An investor is considering purchasing XYZ. There is a 30% probability that XYZ will be acquired in the next two months. If XYZ is acquired, there is a 40% probability of earning a 30% return on the investment and a 60% probability of earning 25%. If XYZ is not acquired, the expected return is 12%. What is the expected return on this investment?

E® = (0.70 × 0.12) + (0.30 × 0.40 × 0.30) + (0.30 × 0.60 × 0.25) = 0.165.

It’s just splitting up the possibility of it being acquired into two separate expected returns.

So 70% chance of it not being acquired is a 12% return. 70% * 12%.

30% chance of it being acquired, but that probability is split into:

A) 40% chance of 30% return (so 30% * 40%) * 30%

B) 60% chance of 25% return (so 25% * 60%) * 30%

You’re multiplying the last 2 expected returns by 30% because you’re essentially splitting that 30% chance into smaller “sub chances”.

So in effect, the chance of earning a 30% return on investment DUE TO being acquired is (30% * 40%). Same for the 25% return, it’s (30% * 60%).

I know that was confusing, hopefully it helped explain a little bit.

Draw a binomial tree. Once you do that, the calculations are clear and easy.