Question 1.                                                                                                  [Total 100 marks]

1A. In December 2030, a US-based cryptocurrency miner Coins-R-Mine (CRM) is considering expanding its crypto-mining capacity by installing a new mining rig, which requires an upfront  investment  $260,000.  Intensive  computing  and  fast  technological  advances together mean that the new mining rig invested will no longer be viable after the end of

2035. See below for the additional information for CRM to consider:

•   A block of cryptocurrency, if mined, is worth $2,000,000. The competition across the world affects the probability that the CRM’s new rig can succeed in mining a crypto block. There is a seasonality in the competition and thus the probability of success: In the “Hot” period, from May through August each year, the probability is estimated to be 0.7% each month, whereas it is 1.2% in the remaining months (“Cold” period).

•   Although cryptocurrency is currently banned in India, a discussion is underway to make it legitimate. The ruling party BJP is in favor of legalizing crypto markets, whereas the opposition party INC is against it. Therefore, the election outcome at the end of 2031 will affect this decision and the global competition for crypto-mining. If BJP wins the election, hence creating a crypto boom in India, then the competition for crypto-mining will increase and thus lower the aforementioned success probabilities to 0.4% (May– August) and 0.9% (the remaining months), respectively, from the beginning of 2032. If INC wins, the probabilities will remain as 0.7% and 1.2%, respectively.

•    Operating the new rig requires the recalibration of mining algorithms at a cost of $2,000 at the beginning of each month and 100 megawatts (MWh) of electricity per month. The cost of electricity will be $140 per MWh in years of high energy prices; otherwise, it will be $100 per MWh. The probability of high energy price is 50% each year.

•    Once the recalibration is completed, the rig continues to run until the end of that month. However, at the beginning of each month, CRM can decide not to operate the rig if a temporary shutdown is justified in that month.

For simplicity, assume that the investment decision must be made either at the end of 2030 (today) or at the end of 2031.

Required:

i)      Suppose that (1) the electricity cost is high in 2031. Calculate mining profits per month for “Hot” and “Cold” periods, respectively, with the probabilities of success 0.7% and 1.2%, respectively, and determine whether it is optimal to temporarily shut down the new rig in each period. Now, assuming that (2) the electricity cost is low in 2031, conduct the same analysis and determine.

[10% of marks]

ii)      By taking into account the optimal decisions and associated monthly profits for “Hot” and “Cold” periods, determine the expected profit per annum for year 2031 (Recall: the probability of high energy price is 50% each year).

[10% of marks]

iii)      Suppose that the probabilities of success have declined to 0.4% and 0.9%, respectively, for “Hot” and “Cold” periods in 2032. Find the expected profit per annum for year 2032 (*Hint: Repeat the analyses equivalent to parts i and ii).

[20% of marks]

iv)     There is a security traded in the market whose payoff depends solely on the India’s election outcome at the end of 2031. The security will pay $100 if BJP wins the election and zero otherwise. The price of the election security is $71.4286 today (31 December 2030). Assume that the risk-free rate is 5%. Calculate (1) the probability that justifies the current price of the security in a risk-neutral world. In addition, find (2) the expected NPV from investing now (at the end of 2030) and from investing in one year (at the end of 2031), respectively. Explain (3) the sources of the difference in the NPV between the two cases.

[30% of marks]

1B. Consider two firms, say, firm A and B, that generate the same EBIT each year, are subject to the same effective tax rate and have managers whose interest is perfectly aligned with each firm’s shareholders. Firm A, however, maintains a much higher leverage ratio than does firm B.

Required:

Discuss possible theoretical justification(s) for the relatively high leverage ratio for firm A. [30% of marks]

Question 2.                                                                                                  [Total 100 marks]

2A. A grocery supermarket chain All Foods Market, Inc. is considering opening several new stores. The CFO believes that the success of the new stores and thus the value of the firm will depend critically on the state of economy in the future. The expansion requires an investment cost of €90 million. The company currently has a bond outstanding with a face value of €250 million that is due in one year. The debt contract includes a covenant that prohibits the issuance of additional debt. The table below summarizes the estimated value of the firm in each state  of economy next year. Assume that the discount rate is zero.

Firm value                  Firm value

State of economy      Probability      without expansion       with expansion     

Weak                      0.3                        180                            240

Normal                     0.5                        340                            460

Strong                     0.2                        430                            540

Required:

i)      Determine (1) the expected value of the firm in one year, with and without expansion. Determine (2) the value creation from the expansion if undertaken.

[10% of marks]

ii)      Determine (1) the value of the bond in one year, with and without expansion. Determine

(2) the incremental value from the expansion that is expected to benefit bondholders. [20% of marks]

iii)      Determine (1) the value of equity in one year, with and without expansion. In addition,

(2) explain why or why not the shareholders would be willing to provide the €90 million needed for the expansion (carefully discuss the relevant theoretical ground).

[30% of marks]

2B. It is well known that some corrupted government officials force companies to pay them privately in return for issuing operating license, building permit, government contract, etc. An empirical analysis shows that firms operating in the cities with more cases of corrupted government officials tend to have a lower cash to asset ratio (and a higher leverage ratio) than do firms in less corrupt cities.

Required:

i)      Explain, using relevant economic justification, why the strong presence of corrupted government officials in a region (e.g., city or province) can cause an incentive for local firms to reduce their cash holding and increase leverage.

[20% of marks]

ii)      Discuss some potential challenges in interpreting the empirical relationship described above. That is, explain why a negative (positive) correlation between corruption and cash (leverage) may not necessarily be the evidence that the corruption has affected firms’ choice of cash holdings and leverage.

[20% of marks]

Question 3.                                                                                                  [Total 100 marks]

3A. Deepwater Exploration Corp. (DeepX), an offshore oil exploration company, has two lines of  business:  the  deep-see  oil  exploration  division  and  the  drilling-equipment  leasing division. The two divisions generate roughly the same size of revenues. United Petroleum (UP), a diversified oil-refining firm, is considering taking over DeepX. Given the competitive advantages to be achieved, UP expects that the value of the combined entity will be larger than the sum of the values of two standalone firms. As of the end of 2021, UP is trading for $5 per share and its total market capitalization is $20 billion. DeepX is trading for $10 per share and its total market capitalization is $2 billion.

Required:

i)     You are the financial analyst in UP and are asked to collect data on risk-free rates and market returns. Your estimates are summarized as follows:

Determine the risk-free rate and the market risk premium that are appropriate to be used in the CAPM equation. Explain the rationale for your answers.

[20% of marks]

ii)     The CAPM-predicted returns on the exploration division and the leasing division of DeepX are 12.3% and 20. 1%, respectively. The cost of capital for UP is 12.5%. Explain what problem would arise if you used the UP’s cost of capital as the discount rate in valuing the divisions of DeepX.

[20% of marks]

iii)      Suppose that UP will use its shares to acquire DeepX. You have estimated the value of real gains to be $1 billion. Calculate the range of exchange ratios that can be offered in this transaction.

[20% of marks]

3B. Answer the following two separate questions.

i)      Consider a developing country where the tax system is designed to attract more foreign investors. In this country, foreign investors face lower tax rates on both equity income and bond interest income than do its citizens. Suppose that in the future, more foreign investors will invest in bonds in this country. The foreign investors’ demand for equity investment is expected to remain. No change is expected for the corporate tax rate .

Required: Based on the information provided, explain in which direction overall corporate leverage will change in this country.

[20% of marks]

ii)     There are different sources of financing available to start-up firms before they decide to go public.

Required: Discuss (1) the main characteristics of angel financing and venture capital, respectively, and explain (2) why venture capital financing is considered an important step. [20% of marks]

Question 4.                                                                                                  [Total 100 marks]

4A. David is the manager of a firm and will retire in three years from now. The firm has a perpetual  bond  with  an  annual  coupon  payment  $50  million  and  pays  no  tax.  The compensation package for David consists of fixed salary $0.5 million per year and 0. 1% of the firm’s EBIT as the bonus. David can choose to exert either high or low effort level. Exerting high effort costs him $0.2 million per year and this cost affects his personal utility (i.e., negative utility for him). Assume that David has no other income source, nor will he after his retirement. The table below summarizes the firm’s EBIT conditional on David’s effort level. Assume that neither the firm’s EBIT nor David’s income is correlated with the market portfolio. The risk-free rate equals 10%.

Required:

i)      For each effort level, (1) determine the value of David’s personal utility (i.e., present value of his utility in Years 1–3). For each effort level, (2) determine the value of the firm, including the present value of the terminal value (note: based on the information given, the terminal value as of the end of Year 3 is Zt=3  =  = $1, 100 mln). If David maximizes his personal utility, rather than the shareholder value, (3) what will the firm value be?

[20% of marks]

ii)      Determine the minimum bonus (as the percentage of EBIT) that is just enough to encourage David to exert high effort.

*Note: you must provide a numerical analysis to support your answer.

[20% of marks]

iii)      Suppose that the manager’s bonus cannot be changed. Explain how debt restructuring

might motivate David to exert high effort.

*Note: numerical analysis is not required.

[20% of marks]

4B. The rookie-training system in Korea’s music and entertainment business  is a unique feature that reportedly has enabled the global success of what is referred to as “K-pop” today. Simply put, the practice can be characterized as musician-incubating. Entertainment agency companies recruit young trainees and put them into a rigorous training period, typically three years, although ten years is not uncommon. In many cases, an agency company and trainees enter into a binding agreement, under which the company agrees to provide its trainees with various training needs (e.g., singing, dancing, foreign languages, etc.), paying all related expenses throughout the incubating stage. The trainees agree to work exclusively for the agency for a certain number of years after their official debut. Most of  these  young  trainees,  although  talented,  have  no  financial  resource  to  start  a professional musician career. As trainees get ready for their debut, the agency prepares for the music album production. The production involves composition, recording, and post- production marketing and distribution, thus requiring a large amount of investment by the agency company. The music and entertainment industry is volatile and the success of a new musician is highly uncertain. Many music album projects end up making losses. Once new musicians make a successful debut (e.g., BTS, Blackpink, etc.), their subsequent albums tend to make an above-average success.