AEM 424
PS #1 Answer Key
1. Software marketing.
a. See attached decision tree. You have already developed the software, so that $2 million
is a sunk cost (assuming you can’t see the software). Forget about it. The expected value
of marketing the software is $3,350,000, which is greater than the expected value of not
marketing, which is $0. So, not knowing whether or not Linux will succeed, the best you
can do is to get $3,350,000 on average.
Now suppose you know whether or not Linux will succeed. If Linux does succeed, a
situation you will face with probability 0.7, you will chose to market with a profit of
$5,000,000. If Linux does not succeed, a situation you will face with probability 0.3, you
will chose not to market with a payout of $0. So, on average, you will get
0.7($5,000,000)+0.3($0)=3,5000,000.
The value of knowing the information is thus the difference between the best you can do
knowing and the best you can do not knowing: $3,500,000-$3,350,000=$150,000.
If you could go back in time and reconsider the decision to develop the software, the
value of the information would increase to $750,000. Use the same procedure to see this.
2. VC Decision Tree
a. See attached decision tree. The highest EV is to prepare lightly with an average
outcome of $12,000.
b. The question asks what the option value of waiting to see the outcome of the first
meeting before deciding how much to prepare for the second meeting. Obviously, if you
prepare heavily for the first meeting, then there is no option value (nothing gained from
delaying). So, you need to consider only the case in which you prepare lightly, and then
prepare heavily if the first meeting fails. To do this, just change the probabilities and
payouts in the “prepare light” VC#2 decision branch to the same as that of the “prepare
heavy” VC#2 branch. The expected outcome of the VC#2 branch then rises from zero to
$5,000 and the “light preparation” decision rises from $12,000 to $15,500
(0.3*$40,000+0.7*$5,000). Hence, you would pay up to $3,500 for the option to have the
second meeting a week later.
3. Acme Steel Research
(a)
See figure 3a.
(b)
For the project to be successful, each of the three independent steps must be
completed. Since the probability of success in each stage is 0.8 and the probabilities are