Can I confirm the answer as follow?

Ex 1.1
(A) The expected return = 18.75%
(B) NPV(Health Club) = 848,214
(C) NPV(Project) = 48,214

Ex 1.2
(Part A)
- W will invest in both projects
- Y will invest in project yielding for 11%
- Z will invest in project yielding for 15%

(Part B)
- W will lend to Z with interest rate 8-12%


Gordon

Since they presented the sell date as "one year later", the relative time at which they buy the club & equipment is t=0 and it is sold at t=1. This allows for one full period of discounting at the capitalization rate (which is assumed to be an annual rate).

If the information was presented as "In year one, they buy..." and then said "In year two, they sell..." then I believe an EOY or BOY assumption would be necessary.

[NEAS: Correct]

For 1.1C, should we assume that the purchase of the equipment and refurbishing of building occurs at the beginning, end, or over the course of the year? i.e. are they t=0, t=1, or t=0.5?

 

 

-Adam

Z wants to borrow at the lowest possible rate. Y can only profit by offering a rate over 11%. But W can offer any amount above 8%. Assume they want to avoid competition with Y, and you have your range of interest rates they could profitably offer.

I don't understand why it would be a range or how to go about finding the range for 1.2 part B.  I see it as Z invests $10 mil to get the 15%, then borrows $10 mil from W to invest in the 12%.  I would expect W to charge Z 8%, because W is giving up the right to receive the 8% from the project they don't invest in.  W would still invest $10 mil in the 11% project.  Y would invest $10 mil in its 11% project.  Or would it be like a give and take thing?  Like W is willing to lend Z $10 mil, but only if they receive at least an 8% return.  Z is willing to borrow $10 million from W as long as they have to pay less than a 12% interest rate.  So the range is 8% <= r < 12%?  Or maybe Z would want to borrow it at only 8% and W would want to lend it at 12%, so they meet the average and make it 10%?  Or do the other companies not know what the other's projected return percentages are?  There could be an argument made that Y would lend Z the $10 mil, but they would want at least 11% returned, so Z has more flexibility with the range from W.

Can we assume the following for these homework problems?

1. There is only one instance of each project. For example, Firm X cannot build two life insurance branch offices in Chicago that each cost $10 million and each yield 11%.
2. All projects are equally risky.

[NEAS: Assume projects can not be duplicated. If a $10 million branch office in Chicago yields 11%, building two $10 million branch offices in Chicago will not yield 11% each.

If not told otherwise, assume projects are equally risky. In later modules, the scenario specifies the beta of the project, which quantifies its systematic risk.]

is there any trick to problem 1.2B because W has only two possible projects? Intuition suggests that Z will borrow between the higher rate of other 2 companies' projects and 15% However, it's possible for Z to borrow just 10 million from W at rate between .08 to .11 because W will be better off than investing at 8% after investing 10 million in its 11% project.

[NEAS: After Z invests its $10 million in its 15% project, it has only a 12% project left.  It would not pay 15% for cash to invest in its 12% project.]

See the other thread in this folder. 

Basically:  a firm will lend money rather than investing in a project if it can get a greater interest rate on the loan than on the project.  A firm will borrow money and use it to invest in a project if it can borrow money at a lower interest rate than it will earn on the project.  So if you write down what rates each firm would be willing to lend and to borrow at, you can see which firms can make a deal with each other.

[NEAS: Correct]

  -- Mathochist

I'm having a little trouble with question 1.2. For Part A, I'm fairly certain that W would choose to invest $10 mill in each project (provided they cannot invest in the 11% project twice), Y would invest in the 11% project and Z in the 15% project.  I'm stuck with part B, though.  Is there a simple way to look at this?