How are you approaching Exercise 1.2?  I was thinking NPV rule or rate of return Rule, but I think that's too much.  For part A are we just supposed to pick 1 project for each firm?  Wouldn't that just be the project with the highest yield? For part B I dont even know where to begin.

I agree with you in the first part: just choose the project with the highest yield rate (pretty simple).  In the second part I'm not sure.  For example, let's focus on firm W.  He will choose project yielding 11%, so, the rate of interest he will lend should be at least 11%.  If this is correct, company W will be willing to borrow $20 million to Z.  Y will be willing to borrow his $10 million to Z at a rate of interest of 11%.

So let's see what happens to each company:

• Company W:  will have in a year 20(1.11)=$22.1
• Company Y:   will have in a year 10(1.11)=$11.1
• Company Z:   at the beginning of the year will have 20+10+10=$40.  He will invest at 15% so after a year he will have 40(1.15)=46.  But after a year, he needs to pay back the loan, so he will return $22.1 to W and $11.1 to Y, so he has left: 46-22.1-11.1=$12.9.  And everybody is happy because W and Y got at least what they wanted and Z increased his profit by borrowing the money from W and Y, otherwise, he would only had at the end of the year 10(1.15)=$11.5, so he got $1.4 more

[NEAS: A firm can invest only once (for $10 million) in a project.  Firm Z can invest only $10 million in the 15% project, not $40 million.]

Wait a minute.  If you can only invest $10 million into each of these projects, company Z can't invest $40 million into the 15% yield project.  They would only be able to invest $10 million in that one, but they would still want to borrow at 11% from one of the other companies to invest in the 12% yield project.  Therefore, company W would lend $10 million at 11% to company Z, and invest their other $10 million in their own 11% yield project.  Company Y would keep their money and invest in the 11% yield project.

Maybe I'm looking at this wrong, but you can't invest in a project twice.  They only need the investment once.  [NEAS: Correct.  Suppose the project is to build a branch office in Chicago.  The firm can build one branch office; it can't build the branch office four times.]

On second thought, in the Homework thread someone asked about interest rate questions and the NEAS replied that they are just looking for a range. So could it simply be that Z invest $10mil in its own 15% project, Y invests $10mil in its own 11% project, and W invests $10 mil in its own 11% project and $10 mil in Z's 12% project, and therefore the interest rate is in the range 11%-15%?

[NEAS: A firm can invest in its own projects or lend money to other firms.  It can not invest in another firm's project.  If Firm W lends money to Firm Z, and Firm Z has only a 12% project left (after investing in the 15% project with its own $10 million), why would Firm Z pay more than 12% interest?]

Why wouldn't Y also want Z's project with 12%?

Because, as I understand it, each project costs $10 million and if one company invests $10 million in a project, then another company can't invest in it also.  So, you can't have 2 different companies each investing $10 million in the same project.  I suppose Y could invest in the 12% project instead of its own 11% project, but then W will still have an extra $10 million to invest so they will invest in Y's 11% project.  However you look at it, the 4 projects that get invested in are : 11%, 11%, 12%, and 15%.

Y would want to invest in Z's 12% projects.  Z, however would not want to borrow Y's money.

The reason being that once Z has invested 10 mil in the 15% project and W has invested 10 mil in their 11% project there is only 20 mil left to invest- W's 10 and Y's 10.

Y will only invest their 10 mil with Z if they get a return of over 11% (otherwise they would invest in their own 11% project). 

W will only invest their 10 mil in Z's 12% project as long as they get a return of over 8% (otherwise they would invest in their own 8% project).

Z having the choice will opt to borrow from W (because they can borrow at a lower rate since W's opportunity cost is lower) at a rate X such that 8%<X<12%

[NEAS: Close, but not exact]

I think we have to realize that Y cannot actually invest in Z's project... she can only lend the money to Z and try to get an interest rate higher than 11%.  However, I agree that with MattAR that Z will not borrow Y's money; she can get a lower interest rate by borrowing from W.  W will have invested in his own 11%-yield project and will only have the 8%-er left.  Thus he should be willing to lend money to Z at a rate anywhere above 8%.  So Z will borrow $10M from W at an interest rate between 8% and 11%, noninclusive.

[NEAS: Yes]

Wonder woman, I did it the same way you did, and it was nice to know there are other people taking the course now!  Quick question though, you said the interest would have to be between 8% and 11%, I think it can be between 8% and 12% non-inclusive.???

It would be between 8% and 11% non-inclusive because in order to get Z to borrow from X, X would outprice Y by lowering the interest rate below 11%.  Y would not lend at an interest rate below 11% because Y already has its own project which yields 11%.

[NEAS: Correct]