1. (10 pts.) Suppose that The Salt River Project (SRP) has a acquired a large amount of land on the outskirts of the Phoenix Metropolitan Area and is deciding between i) constructing a large-scale solar farm or ii) creating a nature preserve. The solar farm would generate 500 megawatts of electricity but would take 2 years to construct and generate considerable traffic, noise, and air pollution for nearby residents during that time. The nature preserve would plant a variety of native vegetation to provide provide new habitat for local wildlife. Currently, the land is vacant but lacks any vegetation. If SRP decides to build the solar farm (instead of the preserve) what is included in the opportunity cost? Explain 2. (25 pts.) Supply and demand analysis. a) Suppose the market for Nissan’s electric cars is currently in equilibrium. Suddenly, Tesla announces that they will drop the price of all their electric cars by 20%. What happens to the price and quantity of Nissan’s electric cars in the new equilibrium? Draw a graph with the initial equilibrium price and quantity and the new equilibrium price and quantity. Explain your answers. Document Preview:

SOS 325S 2018Problem Set #2Answer all questions and turn in by the end of class on February 22nd. You may also submit yourassignment via Blackboard, but it must be uploaded before the end of class on the 22nd. Do NOT emailyour problem set to me or the TA. Make sure that your answers are clear, legible, and concise.1. (10 pts.) Suppose that The Salt River Project (SRP) has a acquired a large amount of land on the outskirtsof the Phoenix Metropolitan Area and is deciding between i) constructing a large-scale solar farm or ii) creating anature preserve. The solar farm would generate 500 megawatts of electricity but would take 2 years to constructand generate considerable trac, noise, and air pollution for nearby residents during that time. The nature preservewould plant a variety of native vegetation to provide provide new habitat for local wildlife. Currently, the land isvacant but lacks any vegetation. If SRP decides to build the solar farm (instead of the preserve) what is includedin the opportunity cost? Explain2. (25 pts.) Supply and demand analysis.a) Suppose the market for Nissan’s electric cars is currently in equilibrium. Suddenly, Tesla announces thatthey will drop the price of all their electric cars by 20%. What happens to the price and quantity of Nissan’selectric cars in the new equilibrium? Draw a graph with the initial equilibrium price and quantity and the newequilibrium price and quantity. Explain your answers.1b) Suppose the market for Apple Watches is currently in equilibrium. Then, workers at Apple’s factories goon strike and demand a wage increase. This raises the cost of producing each Apple Watch. What happens toprice and quantity for Apple Watches in the new equilibrium? Draw a graph with the initial equilibrium price andquantity and the new equilibrium price and quantity. Explain your answers.c) Suppose ASU increases the price of admission to ASU Basketball games. How does this aect the demandfor basketball tickets?…

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1. (10pts)Explain the benefits from asset securitization as outlined in Riddiough (2011). For full credit, you’ll need more detail than was provided in my bullet

2. (10pts)In the following example assume that the MBS has total collateral of $1,000, the CDO collateral is $150 worth of MBS mezzanine bonds, and the MBS collateral has suffered a 7% default loss. Fill in the principal losses for each of the MBS and CDO tranches below (show calculations on a separate page.

MBS

Tranche

Attachment

Detachment

Principal Loss

Senior (AAA)

20%

100%

Mezzanine

3%

20%

Residual

0%

3%

CDO

Attachment

Detachment

Principal Loss

Senior (AAA)

30%

100%

Mezzanine

5%

30%

Residual

0%

5%

3. (20pts) In July 2008, KKR announced a revision to its plans to go public. The plan called for KKR to acquire its subsidiary KKR Private Equity Investors (“KPE”) that currently was publicly traded on Euronext. KKR would then reorganize the entire firm as a public corporation and list on the NYSE.[1] At closing, the new KKR would have 975,708,333 shares.

The plan called for KPE’s current shareholders to exchange their shares for 21% of the new firm’s common equity, or 204,898,750 shares. KKR’s current principals would retain the remaining (770,809,583) shares. To demonstrate their commitment to the long-term performance of KKR, the principals also proposed to grant Contingent Value Interests (“CVIs”) to KPE shareholders that would transfer up to an additional 6% of the new firm’s shares to KPE shareholders depending on the firm’s share price three years from closing. The relevant terms of the CVI (per KPE share turned in) are as follows:

If on the 3rd anniversary of the closing the new firm’s shares trade at or above $22.25 per share, the CVIs granted to the KPE shareholders would expire worthless.[2]

If the shares trade at or below $17.31 per share, KKR’s principals would transfer an additional 6% of the firm’s market value to the CVI shareholders.

At any price between $17.31 and $22.25 per share, the principals would transfer an additional percentage share of the firm’s market value such that each KPE shareholder would receive the difference between $22.25 and the firm’s share price.

1. (2pt) Assuming that KPE shareholders retain their initial KKR share grant and the CVIs attached to that grant, what is the maximum number of shares held after three years by KPE shareholders?

2. (2pt) What is the total payoff for a KPE shareholder who is granted one share of KKR stock and one unit of the CVI at closing if the KKR share price is $17.31 after three years?

3. (2pt) What is the total payoff for this KPE shareholder if the share price is $22.25 after three years?

4. (2pt) What is the total payoff for this KPE shareholder if the share price is $24.75 after three years?

5. (4pts) Draw and label the payoff diagram for a KPE shareholder who is granted one share of KKR stock and one unit of the CVI at closing. (see last page for graph template)

6. (3pts) On a separate graph, draw and label the payoff diagram for one unit of the CVI. (see last page for graph template)

7. (5pts) What combination of options, stock, and/or risk-free bonds would replicate the payoff from one unit of the CVI?

4. (10pts)Compare and contrast bookbuilding with Hambrecht’s Dutch auction for IPOs. Your response should include discussion of the fundamental incentive distortion they aim to resolve, how they go about doing so, and their relative strengths and weaknesses.

5. (5pts) Suppose “dirty” auctions became the norm for IPOs. What is a dirty auction and why might it be inferior to bookbuilding? You may wish to tie your response to your response to the preceding question.

6. (15pts)In what sense did Rural Metro’s board breach its fiduciary duty to shareholders? How did RBC “aid and abet” the Board’s breach of fiduciary duty? A strong response to these questions will evidence a good understanding of the economic tradeoffs and incentive conflicts facing sell-side boards and bankers as well as the legal standards for behavior.

7. (5pts)According to Holmstrom (2015), what is the primary purpose of the money markets and how is that purpose served by “over-collateralized” debt?

8. (10pts)Explain why repurchase agreements fit Holmstrom’s notion of over-collateralized debt and why repos were at the core of the 2008 financial crisis. Your response should evidence understanding of how repo financing contributed to a liquidity crisis that effectively led to a run on the shadow banking system.

9. (15pts) Several boutique investment banks already have gone public and Parella Weinberg Partners (PWP) has considered this option. Given that the founders of most of these firms have spoken of the benefits of being narrowly focused private partnerships, why would they want to go public? Your response should include a critical review of the costs and benefits from operating as a partnership, the tradeoffs facing a boutique that is considering going public, and should connect these ideas with PWP’s thoughts on organizational structure and culture.

---

[1] KPE was essentially a publicly-traded mutual fund that enabled unitholders (shareholders) to participatein some of KKR’s private equity investments.

[2]The payoff actually depended on the 30-day average price at the end of year three but we will ignore that for the purposes of this problem.

 

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1234567Number of baskets per hourPriceTotal RevenueTotal CostTotal profitPriceMarginal costA0—0$10.00-$10.00——B1$13.00$13.0015.00-    2.00$13.00$5.00C213.0026.0022.00+   4.0013.007.00D313.0039.0031.00+   8.0013.00  9.00E4

13.00

52.0044.00+   8.0013.0013.00F513.0065.0061.00+   4.0013.00

17.00

Graph information to show price or cost per basket and quantityof baskets of fish per hour.How many fish should be harvested at amarket price of $ 17, $13, and $9. How much total revenue iscollected at each price? How much profit does the farmer make ateach of these prices?

 

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1. 1.(2 pt.)The aptly-named Average Hotel has 100 rooms, each belonging to one of 100 guests. After an evening soiree, all of the guests (not thinking straight) randomly select a room to sleep in for that night. Multiple guests might end up in the same room.

   (a) (1 pt.) What is the expected number of guests that end up returning to their own hotel room?

   [We are expecting: A number, and please show your work.]

   (b) (1 pt.) What is the expected number of guests that end up in a room with exactly one other person? (Hint: you may find it easier to count by rooms instead of guests.)
   [We are expecting a mathematical expression like(6)(8)or a number like48, and please show your work.]

   2.(3 pt.)LetUkbe the universe of all strings consisting ofknumeric digits. (0000,0123, and9898are part of universeU4butb000,012,9!9!are not.) Letuidenote theithdigit of a stringu?Ukwhere 0=i

   LetHkbe a family ofkhash functions mapping universeUkto values{0,1,2, . . . ,9}whereh0?Hk hashes all strings according to their first digit. (For all stringsuwhereu0= 0,h0(u) = 0; for all strings uwhereu0= 1,h0(u) = 1; for all stringsuwhereu0= 9,h0(u) = 9.) Likewise,h1?Hkhashes all strings according to their second digit. Generally, for all stringsu?Ukwhereui=x,hi(u) =xfor 0=i

   1. (a) (1 pt.) What is an example of a maximally-sized subsetU3such thatH3is universal for the subset?

      [We are expecting: An example subset.]

   2. (b) (2 pt.) WouldHkbe a good family of hash functions (where “good” is defined as universal) to useforUkfork=3?
      [We are expecting: A short explanation (2-3 sentences) that answers the question.]

2. 3.(Plagiarism detection) (5 pt.)Hash functions are extremely good at what they do. Unsurprisingly, there are many fancier data structures that can be built on top of them. In this problem we will motivate and explore the idea of a “Bloom Filter,” which is one example of a fancier structure built on top of hash functions.

   Suppose you are hired by someone to make a plagiarism detection software for internal use so as to avoid any potentially embarrassing allegations of plagiarism. Specifically, your goal is to make a lightweight (i.e. fast, and relatively low-memory) piece of software that will take a sentence and output one of the following messages: 1) “potentially problematic, please rewrite”, or 2) “fresh like an ocean breeze.” Suppose your goal is the following: if the input sentence is something that you have already seen, you output “potentially problematic” (with probability 1), and if the input is something new, you want to output “fresh” with probability at least 0.99 (its alright if you have a few false-alarms).

1. (a) (1 pt.) First, you decide to use a hash table. You will make a has table that maps a piece of text to a bucket, then scrape the web for all English sentences, and hash each one to your table. Given a new sentence, you will check to see if it hashes to an empty bucket—if so, you will output option “fresh” otherwise you will output “potential plagiarism.” Suppose there are 1 billion unique sentences online. How many buckets will your hash table need to have to have the desired functionality?

   [We are expecting: A number (to the nearest order of magnitude) and one to two sentences of justification.]

2. (b) (2 pt.) You decide that is a little too much space usage, and consider the following approach: you choose 10 hash functions,h1,…,h10that each map sentences to the numbers 1 though 10 billion. You initialize an arrayAof 10 billion bits, initially set to 0. For each sentencesthat you encounter, you computeh1(s),h2(s),…,h10(s), and set the corresponding indices ofAto be 1 (namely you setA[h1(s)]?1, A[h2(s)]?1, . . .). Argue that after processing the 1 billion unique sentences, you expect a (1-1/(10 billion))10 billion˜0.37 fraction of the elements to be 0.

   For this part, feel free to assume that thehiare “idealized” hash functions that map each keys to a uniformly random bucket.
   [We are expecting: A paragraph with your argument.]

(c) (2 pt.) Now, given a sentences, to check if it might be plagiarized, you compute the 10 hashes of s, and check ifA[h1(s)] =A[h2(s)] =. . .=A[h10(s)] = 1. If so, you output “potential problem,” otherwise you output “fresh.” Prove that ifsis actually in your set of 1 Billion sentences, that you will output “potential problem” with probability 1, and that ifsisnotin your set of 1 Billion sentences, you will output “fresh” with probability˜1-(1-0.37)10˜0.99.

Again, feel free to assume that the hash functions are “idealized,” and that the claim of the previous part holds, namely that after processing the 1 Billion sentences, there are 3.7 billion indices in the arrayAwith value 0.
[We are expecting: Informal mathematical justifications for each of the bounds.]

 

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1.3 If a household’s income falls from R20 000 to R17 000 and its consumption falls from R18 000 to R15 000, then its: a) marginal propensity to consume is –0,67. b) marginal propensity to consume is 0,88. c) marginal propensity to consume is 0,20. d) marginal propensity to save is zero. e) marginal propensity to save is 0,12.

 

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